![Sum-Product Decoding of Punctured Convolutional Code for Wireless LAN 7
ν nf c G
2(oct) G
1(oct)
6 29 117 155
7 24 321 267
8 52 563 731
9 17 1067 1405
10 36 3131 2417
11 11 4015 6243
12 28 13103 16111
13 13 21003 30611
14 22 45203 65011
15 17 100001 145207
16 25 221001 322207
Table 1. Examined higher degree parity check polynomials for code rate 1/2
Experimental result shows that higher degree parity check polynomial of degree ν = 13
provides the best performance. The higher degree parity check polynomial is given by
H
(P1, P2) =G
2(D)P1 + G
1(D)P2 (32)
G
1(D) =1 + D3
+ D7
+ D8
+ D12
+ D13
(33)
G
2(D) =1 + D + D9
+ D13
(34)
4.3 Simulation results for non-punctured code
Simulation condition is shown in Table 2. Hereafter, this condition was used, if simulation
condition is not specified. Figure 4 shows simulation results. The figure shows that
the performance for information bits of 2-Step Decoding with higher degree parity check
polynomial (denoted by conventional) is only 0.7[dB] inferior to that of BCJR at bit error rate
10−5.
Number of info bits per block 1024[bit]
Termination Zero-termination
Channel Additive white Gaussian noise
Maximum iterations 200
Table 2. Simulation condition
4.4 Simulation results for punctured codes
For non-punctured code, higher degree parity check polynomial with degree ν = 13 provides
the best performance. With that higher degree parity check polynomial, for punctured codes
with code rates 2/3 and 3/4, the sum-product decoding simulation were executed. The
simulation results are shown in Fig.5 and Fig.6.
From Fig.5 and Fig.6, it can be seen that the conventional method, that is sum-product
decoding with higher degree parity check polynomial with ν = 13, can not provide good
performance for punctured code with code rates 2/3 and 3/4.
7
Sum-Product Decoding of Punctured Convolutional Code for Wireless LAN](https://image.slidesharecdn.com/73970-250227165359-2b147e65/85/Advanced-Wireless-LAN-1st-Edition-Song-Guo-21-320.jpg)
![8 Will-be-set-by-IN-TECH
10-7
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
0 1 2 3 4 5 6
Sum-Product : Info bit
Sum-Product : Parity bit
BCJR
Eb/N0 [dB]
Bit
error
rate
Fig. 4. Bit error rate performance of conventional method for code rate 1/2
10-8
10-7
10
-6
10
-5
10-4
10
-3
10
-2
10
-1
100
0 1 2 3 4 5 6 7
Sum-Product : Info bit
Sum-Product : Parity bit
BCJR
Eb/N0 [dB]
Bit
error
rate
Fig. 5. Bit error rate performance of conventional method for code rate 2/3
8 Advanced Wireless LAN](https://image.slidesharecdn.com/73970-250227165359-2b147e65/85/Advanced-Wireless-LAN-1st-Edition-Song-Guo-22-320.jpg)
![Sum-Product Decoding of Punctured Convolutional Code for Wireless LAN 9
10-9
10-8
10
-7
10
-6
10
-5
10
-4
10
-3
10-2
10-1
10
0
0 2 4 6 8 10 12
Sum-Product : Info bit
Sum-Product : Parity bit
BCJR
Eb/N0 [dB]
Bit
error
rate
Fig. 6. Bit error rate performance of conventional method for code rate 3/4
5. Single punctured bit method (Proposed decoding method (1))
I inferred that the bad sum-product decoding performance for punctured codes is caused by
more than one punctured bits included in the parity check equation at time slot k. The reason
is as follows. Since received signals are not available for punctured bits, the channel values
for punctured bits are zero. This causes that every messages from punctured bit node to check
node are zero. In this case, like stopping set (Di et al., 2002), messages from the check node to
bit nodes are zero. Therefore, sum-product algorithm does not work.
In order to improve the sum-product decoding performance, this paper proposes to use
parity check equation that includes single punctured bit. The condition to include single
punctured bit in parity check equation is referred to as single punctured bit condition. If
single punctured bit is included in a parity check equation at time slot k, the message to the
corresponding bit node can be obtained from the corresponding check node Ck. In this case,
sum-product algorithm can work. Therefore, we expect that using higher degree parity check
polynomial such that parity check equation includes single punctured bit, brings performance
improvement of sum-product decoding of punctured codes.
5.1 Higher degree parity check polynomial satisfying single puncture bit condition
In this section, single punctured bit condition is derived for higher degree parity check
polynomial. A higher degree parity check equation is given by
H
(P1, P2) = G
2(D)P1 + G
1(D)P2 (35)
9
Sum-Product Decoding of Punctured Convolutional Code for Wireless LAN](https://image.slidesharecdn.com/73970-250227165359-2b147e65/85/Advanced-Wireless-LAN-1st-Edition-Song-Guo-23-320.jpg)
![12 Will-be-set-by-IN-TECH
(#{βi | (βi mod 3) = 2} = 0)
∧(#{αi | (αi mod 3) = 0} = 1) (58)
Similarly, if either Equation 59 or Equation 60 is satisfied, the higher degree parity check
polynomial satisfies single punctured bit condition at time slot k = 3l + 2, (l = 0, 1, 2, · · · ).
(#{βi | (βi mod 3) = 0} = 1)
∧(#{αi | (αi mod 3) = 1} = 0) (59)
(#{βi | (βi mod 3) = 0} = 0)
∧(#{αi | (αi mod 3) = 1} = 1) (60)
5.2 Search of higher degree parity check polynomial for decoding
In this paper, basically, the higher degree parity check polynomials for decoding are searched
as follows.
Step.1 Select higher degree parity check polynomials with degree ν ≤ 21 that satisfies single
punctured bit condition.
Step.2 Among those higher degree parity check polynomials, select the higher degree parity
check polynomial that provides the best sum-product decoding performance by using
computer simulation.
5.2.1 Code rate 2/3
In the Step.1, 208 higher degree parity check polynomials satisfy single punctured bit
condition. Since many higher degree parity check polynomials are selected, they are limited
by nf c. In this paper, among those higher degree parity check polynomials, 9 higher degree
parity check polynomials with lower nf c are selected. They are shown in Table 3.
No. ν nf c G
2(oct) G
1(oct)
1 8 29 755 403
2 9 17 1067 1405
3 11 38 6143 5251
4 14 26 62501 50107
5 16 26 364203 202011
6 16 33 203133 310001
7 16 43 310207 243025
8 17 16 624403 500211
9 17 42 445207 640025
Table 3. Examined higher degree parity check polynomials for code rate 2/3
The simulation results of Step.2 with higher degree parity check polynomials in Table 3 are
shown in Fig. 7. Simulation condition is shown in Table 2 and Eb/N0 = 5.0 [dB]. From Fig. 7,
it can be seen that higher degree parity check polynomial of No.5 with scaling factor fs = 0.9
provides the best performance.
12 Advanced Wireless LAN](https://image.slidesharecdn.com/73970-250227165359-2b147e65/85/Advanced-Wireless-LAN-1st-Edition-Song-Guo-26-320.jpg)
![Sum-Product Decoding of Punctured Convolutional Code for Wireless LAN 13
10-5
10-4
10
-3
10
-2
10-1
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
No.1
No.2
No.3
No.4
No.5
No.6
No.7
No.8
No.9
Scaling factor fs
Parity
bit
error
rate
Fig. 7. Simulation results of Step.2 for code rate 2/3 at Eb/N0 =5[dB]
5.2.2 Code rate 3/4
5.2.2.1 Step.1
For code rate 3/4, there are both puncture bits of parity P1 and parity P2. Decodable punctured
parity bit by sum-product algorithm with certain parity check equation is either parity P1 or
parity bit P2. From the viewpoint of decodable parity bit, single punctured bit condition can
be arranged as follows.
1. If either Equation 55 or Equation 57, or Equation 59 is satisfied, the higher degree parity
check polynomial includes single punctured bit of parity P1. Therefore, with the higher
degree parity check polynomial, punctured bits of parity P1 can be decoded. That higher
degree parity check polynomial is referred to as higher degree parity check polynomial for
P1.
2. If either Equation 56 or Equation 58 or Equation 60 is satisfied, the higher degree parity
check polynomial includes single punctured bit of parity P2. Therefore, with the higher
degree parity check polynomial, punctured bits of parity P2 can be decoded. That higher
degree parity check polynomial is referred to as higher degree parity check polynomial for
P2.
Therefore, for code rate 3/4, both higher degree parity check polynomials for P1 and P2 are
necessary to decode.
For code rate 3/4, there are 16 higher degree parity check polynomials for P1 and 16 higher
degree parity check polynomials for P2. The number of combination of higher degree parity
check polynomial for P1 and that for P2 is many. Therefore, they are limited by nf c. Higher
degree parity check polynomials that have lower nf c are selected as shown in Table 4 and
Table 5.
13
Sum-Product Decoding of Punctured Convolutional Code for Wireless LAN](https://image.slidesharecdn.com/73970-250227165359-2b147e65/85/Advanced-Wireless-LAN-1st-Edition-Song-Guo-27-320.jpg)
![14 Will-be-set-by-IN-TECH
No. ν nf c G
2(oct) G
1(oct)
1 12 30 14453 12121
2 21 64 17010055 10212103
Table 4. Examined higher degree parity check polynomials for P1
No. ν nf c G
2(oct) G
1(oct)
3 7 24 321 267
4 12 29 11055 15103
5 21 38 10540055 14222103
Table 5. Examined higher degree parity check polynomials for P2
5.2.2.2 Step.2
A block diagram of the decoder for code rate 3/4 is shown in Fig. 8. It is similar to a turbo
decoder. In Fig.8, DEC1 is sum-product algorithm decoder with higher degree parity check
polynomial for P1 and DEC2 is sum-product algorithm decoder with higher degree parity
check polynomial for P2. Channel value is denoted by λn. Extrinsic values of DEC1 and DEC2
are denoted by Le1(un) and Le2(un), respectively. A posteriori value of DEC2 is denoted by
Λ2,n.
In DEC1, Le2(un) is added to λn as follows.
λ
n =λn + Le2(un) (61)
The value λ
n is used as initial value of λn in Equation 17.
Similarly, in DEC2, Le1(un) is added to λn and that value is used as initial value of λn. In
computer simulation, the number of iteration of sum-product algorithm at each decoder was
set to 1. The maximum number of iteration between two decoders was set to 200. Other
simulation conditions are the same as shown in Table 2.
Le1(un) Le2(un)
Λ2,n
λn
DEC1 DEC2
Fig. 8. Block diagram of decoder of single punctured bit method for code rate 3/4
Figure 9 shows the simulation results of Step.2 for code rate 3/4 at Eb/N0 = 6[dB].
From Fig.9, it can be seen that the combination of higher degree parity check polynomials
No.2 and No.3 with scaling factor fs = 0.5 provides the best decoding performance.
14 Advanced Wireless LAN](https://image.slidesharecdn.com/73970-250227165359-2b147e65/85/Advanced-Wireless-LAN-1st-Edition-Song-Guo-28-320.jpg)
![Sum-Product Decoding of Punctured Convolutional Code for Wireless LAN 15
10
-4
10-3
10-2
10-1
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
No.1,No.3
No.1,No.4
No.1,No.5
No.2,No.3
No.2,No.4
No.2,No.5
Scaling factor fs
Parity
bit
error
rate
Fig. 9. Simulation results of Step.2 for code rate 3/4 at Eb/N0 = 6[dB]
5.3 Simulation results
5.3.1 Code rate 2/3
Figure 10 shows bit error rate performance of the single punctured bit method for code rate
2/3.
10-8
10-7
10-6
10-5
10-4
10
-3
10-2
10-1
100
0 1 2 3 4 5 6 7
Conventional : Info bit
Conventional : Parity bit
BCJR
Eb/N0 [dB]
Bit
error
rate
Single punctured bit : Info bit
Single punctured bit : Parity bit
Fig. 10. BER performance of single punctured bit method for code rate 2/3
15
Sum-Product Decoding of Punctured Convolutional Code for Wireless LAN](https://image.slidesharecdn.com/73970-250227165359-2b147e65/85/Advanced-Wireless-LAN-1st-Edition-Song-Guo-29-320.jpg)
![16 Will-be-set-by-IN-TECH
From Fig.10 it can be seen that the parity bit error rate performance of the single punctured bit
method is 1.12[dB] superior to that of the conventional method (higher degree parity check
polynomial of ν = 13) at bit error rate 10−5. The parity bit error rate performance of the single
punctured bit method is only 0.83[dB] inferior to that of BCJR.
From Fig.10, information bit error performance of the single punctured bit method is 1.28[dB]
superior to that of the conventional method at bit error rate 10−5. The information bit error
rate performance of the single punctured bit method is only 0.98 [dB] inferior to that of BCJR.
5.3.2 Code rate 3/4
10-6
10-5
10-4
10
-3
10
-2
10
-1
100
0 1 2 3 4 5 6 7 8 9 10 11
Conventional
Parity
bit
error
rate
Eb/N0[dB]
Single punctured bit
BCJR
Fig. 11. Parity bit error rate performance of single punctured bit method for code rate 3/4
Figure 11 shows parity bit error rate performance of the single punctured bit method for code
rate 3/4. From Fig.11 it can be seen that the parity bit error rate performance of the single
punctured bit method is 0.82[dB] superior to that of the conventional method (higher degree
parity check polynomial of ν = 13) at bit error rate 10−5. The parity bit error rate performance
of the single punctured bit method is 3.24[dB] inferior to that of BCJR.
Figure 12 shows information bit error rate performance of the single punctured bit method.
From Fig.12, it can be seen that the information bit error rate performance of the single
punctured bit method is 1.11[dB] superior to the conventional method at bit error rate 10−5.
The information bit error rate performance of the single punctured bit method is 4.11[dB]
inferior to that of BCJR at bit error rate 10−5.
6. Switching parity check method (proposed decoding method (2))
For code rate 3/4, the proposed method (1) can not provide good performance. Therefore,
this paper try to improve the sum-product decoding performance for code rate 3/4.
16 Advanced Wireless LAN](https://image.slidesharecdn.com/73970-250227165359-2b147e65/85/Advanced-Wireless-LAN-1st-Edition-Song-Guo-30-320.jpg)
![Sum-Product Decoding of Punctured Convolutional Code for Wireless LAN 17
10-6
10-5
10-4
10
-3
10
-2
10-1
100
0 1 2 3 4 5 6 7 8 9 10 11
Conventional
Information
bit
error
rate
Eb/N0[dB]
Single punctured bit
BCJR
Fig. 12. Information bit error rate performance of single punctured bit method for code rate
3/4
I inferred that the bad decoding performance is caused by the four-cycles of higher degree
parity check polynomial, since nf c of higher degree parity check polynomial satisfying single
punctured bit condition tends to be larger than nf c of higher degree parity check polynomial
that does not satisfy single punctured bit condition. Therefore, this paper proposes following
method. Only at first iteration, the higher degree parity check polynomial satisfying single
punctured bit condition is used to decode and after first iteration, another higher degree parity
check polynomial without single punctured bit condition is used to decode. By decoding,
only at first iteration, with higher degree parity check polynomial satisfying single punctured
bit condition, the a posteriori values of punctured bits are obtained. After obtaining the a
posteriori values of punctured bit, the higher degree parity check polynomial with lower nf c
may provide good bit error rate performance.
Figure 13 shows a block diagram of decoder of the switching parity check method. In Fig. 13,
DEC1 is a sum-product algorithm decoder with higher degree parity check polynomial for P1,
DEC2 is a sum-product algorithm decoder with higher degree parity check polynomial for P2
and DEC3 is a sum-product algorithm decoder with higher degree parity check polynomial
with lower nf c for iteration. Chanel values for DEC1, DEC2 and DEC3 are λ1,n, λ2,n and
λ3,n, respectively. A posteriori values of DEC1, DEC2 and DEC3 are Λ1,n, Λ2,n and Λ3,n,
respectively. Decoders DEC2 and DEC3 use the a posteriori value of previous decoder as the
channel value.
6.1 Search of higher degree parity check polynomial for decoding
This paper searches higher degree parity check polynomials for DEC1, DEC2 and DEC3 by
computer simulation.
17
Sum-Product Decoding of Punctured Convolutional Code for Wireless LAN](https://image.slidesharecdn.com/73970-250227165359-2b147e65/85/Advanced-Wireless-LAN-1st-Edition-Song-Guo-31-320.jpg)
![18 Will-be-set-by-IN-TECH
1st Iteration After 1st iteration
Λ1,n Λ2,n Λ3,n
λ1,n λ2,n λ3,n
DEC1 DEC2 DEC3
Fig. 13. Block diagram of decoder of switching parity check method for code rate 3/4
In this paper, the higher degree parity check polynomials for DEC1, DEC2 and DEC3
were selected from Table 4, Table 5 and Table 1, respectively. There are many number of
combination of the higher degree parity check polynomials. Therefore, this paper searches
the higher degree parity check polynomials as follows.
Step.1 At first, the higher degree parity check polynomial for DEC3 is determined by
decoding simulation with only DEC3.
Step.2 With the determined higher degree parity check polynomial for DEC3, the higher
degree parity check polynomials for DEC1 and DEC2 are determined by decoding
simulation with DEC1, DEC2 and DEC3.
Figure 14 shows the simulation results of Step.1 at Eb/N0 = 6[dB]. From Fig.14, it can be seen
that the higher degree parity check polynomial with ν = 15 provides the best performance.
Therefore, that higher degree parity check polynomial is used.
Figure 15 shows the simulation results of Step.2 at Eb/N0=7[dB]. From Fig.15, it can be seen
that the combination of higher degree parity check polynomials No.2 and No.5 with scaling
factor fs = 0.1 provides the best performance, where scaling factor fs = 0.1 is used for DEC1
and DEC2, and DEC3 uses fixed scaling factor fs = 1.
10-5
10-4
10-3
10-2
10-1
100
6 7 8 9 10 11 12 13 14 15 16
Parity
Bit
Error
Rate
Degree of Higher Degree Parity Check Polynomial ν
Fig. 14. Simulation results of step.1 in switching parity check method at Eb/N0 = 6[dB]
18 Advanced Wireless LAN](https://image.slidesharecdn.com/73970-250227165359-2b147e65/85/Advanced-Wireless-LAN-1st-Edition-Song-Guo-32-320.jpg)
![Sum-Product Decoding of Punctured Convolutional Code for Wireless LAN 19
10-7
10
-6
10-5
10
-4
10
-3
10
-2
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
No.1,No.3
No.1,No.4
No.1,No.5
No.2,No.3
No.2,No.4
No.2,No.5
Parity
Bit
Error
Rate
Scaling factor fs
Fig. 15. Simulation results of step.2 in switching parity check method at Eb/N0 = 7[dB]
6.2 Simulation results
Simulation results are shown in Fig.16 and 17. Figure 16 shows parity bit error rate
performance. From Fig.16, it can be seen that parity bit error rate performance of the switching
parity check method is 3.02[dB] superior to that of the conventional method and 2.2[dB]
superior to that of the single punctured bit method. Parity bit error rate performance of the
switching parity check method is only 1.04[dB] inferior to that of BCJR.
Figure 17 shows information bit error rate performance. From Fig.17, it can be seen that
information bit error rate performance of the switching parity check method is 4.16[dB]
superior to that of the conventional method and 3.05[dB] superior to that of the single
punctured bit method. Information bit error rate performance of the switching parity check
method is only 1.06 [dB] inferior to that of BCJR.
7. Decoding complexity
Table 6 and Table 7 show the numbers of operations per one bit decoding for sum-product
algorithm and BCJR, respectively. In both tables, Nadd denotes the number of additions, Nmult
denotes the number of multiplications and Ntotal denotes the total number of operations. For
sum-product algorithm, Nsp denotes the number of operations for tanh(·), tanh−1
(·). For
BCJR, Nsp denotes the number of operations for exp(·), log(·). In Table 6, for information bits,
Nadd shows the number of XOR’s. In Table 6, Nitr denotes the average number of iterations,
where the number was counted at Eb/N0=6[dB] by using computer simulation. For code rate
2/3, complexity of the single punctured bit method is shown. For code rate 3/4, complexity
of the switching parity check method is shown. It is necessary to notice that iteration of
sum-product algorithm is required for parity bits decoding only. For the switching parity
19
Sum-Product Decoding of Punctured Convolutional Code for Wireless LAN](https://image.slidesharecdn.com/73970-250227165359-2b147e65/85/Advanced-Wireless-LAN-1st-Edition-Song-Guo-33-320.jpg)
![20 Will-be-set-by-IN-TECH
10-6
10
-5
10
-4
10-3
10
-2
10
-1
10
0
0 1 2 3 4 5 6 7 8 9 10 11
Parity
Bit
Error
Rate
Eb/N0[dB]
Switching parity check
Conventional
Single punctured bit
BCJR
Fig. 16. Parity Bit Error Rate Performance of switching parity check method
10-6
10
-5
10
-4
10-3
10
-2
10
-1
100
0 1 2 3 4 5 6 7 8 9 10 11
Information
Bit
Error
Rate
Eb/N0[dB]
Switching parity check
Conventional
Single punctured bit
BCJR
Fig. 17. Information Bit Error Rate Performance of switching parity check method
20 Advanced Wireless LAN](https://image.slidesharecdn.com/73970-250227165359-2b147e65/85/Advanced-Wireless-LAN-1st-Edition-Song-Guo-34-320.jpg)
![Sum-Product Decoding of Punctured Convolutional Code for Wireless LAN 21
check method, it is necessary to notice that higher degree parity check polynomials No.2
and No.5 are used at only first iteration and after first iteration, higher degree parity check
polynomials with degree ν = 15 is used.
From those tables, for code rate 2/3, it can be seen that the number of operations of the single
punctured bit method is 0.1 times of that of BCJR. For code rate 3/4, the number of operations
of the switching parity check method is 0.2 times of that of BCJR.
For the both code rates, it can be seen that the number of operations of the proposed method
is much less than that of BCJR.
Code rate Classification Nadd Nmult Nsp Nitr Ntotal
2/3
Parity 10 23 24 3.04
175
Info 1 0 0 1
3/4
No.2 14 31 32 1
336
No.5 14 31 32 1
ν = 15 8 19 20 3.85
Info 1 0 0 1
Table 6. Complexity of sum-product algorithm
Code rate Nadd Nmult Nsp Ntotal
2/3, 3/4 640 1044 7 1691
Table 7. Complexity of BCJR
8. Conclusion
This paper proposes sum-product decoding methods for the punctured convolutional codes
of wireless LAN. The wireless LAN standard include the punctured convolutional codes with
code rate 2/3 and 3/4. This paper proposes to decode with the higher degree parity check
polynomial that satisfies single punctured bit condition as the single punctured bit method.
Single punctured bit condition is the condition to include single punctured bit in parity check
equation. For code rate 2/3, the performance of the single punctured bit method is 1.28[dB]
superior to that of the conventional method and only 0.98[dB] inferior to that of BCJR at
bit error rate 10−5. For code rate 3/4, the single punctured bit method can not provide
good performance. To improve the performance, this paper proposes following method as
the switching parity check method. Only at first iteration, the higher degree parity check
polynomial satisfying single punctured bit condition is used to decode and after first iteration,
another higher degree parity check polynomial with lower nf c without single punctured bit
condition is used to decode. For code rate 3/4, the performance of the switching parity check
method is 4.16[dB] superior to that of the conventional method, 3.05[dB] superior to that of
the single punctured bit method and only 1.06[dB] inferior to that of BCJR. Complexity of the
single punctured bit method is 0.1 times of that of BCJR for code rate 2/3. For code rate 3/4,
complexity of the switching parity check method is 0.2 times of that of BCJR. For the both code
rates, complexity of the proposed method is much less than that of BCJR.
9. Acknowledgment
This work was supported by Japan Society for the Promotion of Science (JSPS) Grant-in-Aid
for Scientific Research (C) 23560444.
21
Sum-Product Decoding of Punctured Convolutional Code for Wireless LAN](https://image.slidesharecdn.com/73970-250227165359-2b147e65/85/Advanced-Wireless-LAN-1st-Edition-Song-Guo-35-320.jpg)
![2
A MAC Throughput in the Wireless LAN
Ha Cheol Lee
Dept. of Information and Telecom. Eng., Yuhan University, Bucheon City,
Korea
1. Introduction
Over the past few years, mobile networks have emerged as a promising approach for future
mobile IP applications. With limited frequency resources, designing an effective MAC
(Medium Access Control) protocol is a hot challenge. IEEE 802.11b/g/a/n networks are
currently the most popular wireless LAN products on the market [1]. The conventional IEEE
802.11b and 802.11g/a specification provide up to 11 and 54 Mbps data rates, respectively.
However, the MAC protocol that they are based upon is the same and employs a
CSMA/CA (Carrier Sense Multiple Access/Collision Avoidance) protocol with binary
exponential back-off. IEEE 802.11 DCF (Distributed Coordination Function) is the de facto
MAC protocol for wireless LAN because of its simplicity and robustness [2,3]. Therefore,
considerable research efforts have been put on the investigation of the DCF performance
over wireless LAN [2]. With the successful deployment of IEEE 802.11a/b/g wireless LAN
and the increasing demand for real-time applications over wireless, the IEEE 802.11n
Working Group standardized a new MAC and PHY (Physical) layer specification to increase
the bit rate to be up to 600 Mbps [3]. The throughput performance at the MAC layer can be
improved by aggregating several frames before transmission [3]. Frame aggregation not
only reduces the transmission time for preamble and frame headers, but also reduces the
waiting time during CSMA/CA random backoff period for successive frame transmissions.
The frame aggregation can be performed within different sub-layers. In 802.11n, frame
aggregation can be performed either by A-MPDU (MAC Protocol Data Unit Aggregation) or
A-MSDU (MAC Service Data Unit Aggregation). Although frame aggregation can increase
the throughput at the MAC layer under ideal channel conditions, a larger aggregated frame
will cause each station to wait longer before its next chance for channel access. Under error-
prone channels, corrupting a large aggregated frame may waste a long period of channel
time and lead to a lower MAC efficiency [4]. On the other hand, wireless LAN mobile
stations that are defined as the stations that access the LAN while in motion are considered
in this chapter. The previous paper analyzed the IEEE 802.11b/g/n MAC performance for
wireless LAN with fixed stations, not for wireless LAN with mobile stations [5, 6, 7, 8, 9, 10].
On the contrary, Xi Yong [11] and Ha Cheol Lee [12] analyzed the MAC performance for
IEEE 802.11 wireless LAN with mobile stations, but considered only IEEE 802.11 and
802.11g/a wireless LAN specification. So, this chapter summarizes all the reference papers
and analyzes the IEEE 802.11b/g/a/n MAC performance for wireless LAN with fixed and
mobile stations. In other words, we will present the analytical evaluation of saturation](https://image.slidesharecdn.com/73970-250227165359-2b147e65/85/Advanced-Wireless-LAN-1st-Edition-Song-Guo-37-320.jpg)
![Advanced Wireless LAN
24
throughput with bit errors appearing in the transmitting channel. In Section 2, wireless LAN
history and standards are reviewed. In section 3, wireless LAN access network is reviewed.
IEEE 802.11b/g/a/n/ac/ad PHY and MAC layer are reviewed in Section 4. In Section 5,
frame error rate of wireless channel and the DCF saturation throughput are theoretically
derived. Finally, it is concluded with Section 6.
2. Wireless LAN history and standards
Standards in the IEEE project 802 target the PHY layer and MAC layer. When wireless LAN
was first conceived, it seemed that it would be just another PHY of one of the available
standards. The first candidate considered for this was IEEE’s most prominent standard 802.3
(Ethernet). However, it soon became obvious that the radio medium is very different from the
well-behaved wire. Due to tremendous attenuation even over short distances, collisions cannot
be detected. Hence, 802.3’s CSMA/CD (Carrier Sense Multiple Access/Collision Detection)
could not be applied. The next candidate standard to be considered was 802.4. Its coordinated
medium access, the token bus concept, was believed to be superior to 802.3’s contention-based
scheme. Hence, WLAN began as 802.4L. However, already in 1990 it was obvious that token
handling in radio networks was difficult. The standardization body realized that a wireless
communication standard would need its own very unique MAC. Finally, on March 21, 1991,
project 802.11 was approved. The first 802.11 standard was published in 1997. At the PHY layer
it provides three solutions: a FHSS (Frequency Hopping Spread Spectrum) and a DSSS (Direct
Sequence Spread Spectrum) PHY in the unlicensed 2.4 GHz band, and an infrared PHY at 316–
353 THz. Although all three provide a basic data rate of 1 Mb/s with an optional 2 Mb/s mode,
commercial infrared implementations do not exist. Similar to 802.3, basic 802.11 MAC operates
according to a listen-before-talk scheme, and is known as the DCF. It implements CSMA/CA
rather than collision detection as in 802.3. Indeed, as collision cannot be detected in the radio
environment, 802.11 waits for a backoff interval before each frame transmission rather than after
collisions. In addition to DCF, the original 802.11 standard specifies an optional scheme that
depends on a central coordination entity, the PCF (Point Coordination Function). This function
uses the so called PC (Point Coordinator) that operates during the so-called contention-free
period. The latter is a periodic interval during which only the PC initiates frame exchanges via
polling. However, the PCF’s poor robustness against hidden nodes resulted in negligible
adoption by manufacturers. Having published its first 802.11 standard in 1997, the WG
(Working Group) received feedback that many products did not provide the degree of
compatibility customers expected. As an example, often the default encryption scheme, called
WEP (Wired Equivalent Privacy), would not work between devices of different vendors. This
need for a certification program led to the foundation of the WECA (Wireless Ethernet
Compatibility Alliance) in 1999, renamed the WFA (Wi-Fi Alliance) in 2003. Wi-Fi certification
has become a well-known certification program that has significant market impact. The
tremendous success in the market and the perceived shortcomings of the base 802.11 standard
provided a basis and impetus for a prolific program of improvements and extensions. This has
led to revisions of the draft, driven by a complete alphabet of amendments. It is the purpose of
this article to review this process and explain both the contents of these amendments and their
interrelation. In the following we first describe the changes made to the PHY layer and then
turn to the improvements to the MAC layer. In both, we make a distinction between what has
already been accepted and what is currently in the process of being standardized [2].](https://image.slidesharecdn.com/73970-250227165359-2b147e65/85/Advanced-Wireless-LAN-1st-Edition-Song-Guo-38-320.jpg)
![A MAC Throughput in the Wireless LAN 25
Standard Spectrum
Maximum
physical
rate
Layer 2
data
rate
Tx
Compatible
with
Major disadvantage Major advantage
802.11n
2.4/5
GHz
600 Mbps
100
Mbps
MIMO
OFDM
802.11b/g/
a
Difficult to
implement
Highest bit rate
802.11b 2.4 GHz 11 Mbps
6-7
Mbps
DSSS 802.11
Bit rate too low for
many
emerging
applications
Widely deployed,
higher range
802.11g 2.4 GHz 54 Mbps
32
Mbps
OFDM
802.11/
802.11b
Limited number of
collocated WLANs
Higher bit rate in 2.4
GHz spectrum
802.11a 5.0 GHz 54 Mbps
32
Mbps
OFDM None
Smallest range of all
802.11
standards
Higher bit rate in less-
crowded spectrum
Table 1. Wireless LAN products on the market [1]
2.1 PHY related amendments
Although not interoperable, the DSSS and FHSS PHY initially seemed to have equal chances
in the market. The FHSS PHY even had a duplicate in the HomeRF group that aimed at
integrated voice and data services. This used plain 802.11 with FHSS for data transfer,
complemented with a protocol for voice that was very similar to the Digital Enhanced
Cordless Telecommunications standard. Neither HomeRF nor 802.11 saw FHSS extensions,
although plans for a second-generation HomeRF existed that targeted at 10 Mb/s. In
contrast, the high-rate project 802.11b was started in December 1997 and boosted the data
rates of the DSSS PHY to 11 Mb/s. This caused 802.11b to ultimately supersede FHSS,
including HomeRF, in the market. Figure 1 provides an overview of the 802.11 PHY
amendments and their dependencies [2].
Fig. 1. The 802.11 PHY layer amendments and their dependencies [2]](https://image.slidesharecdn.com/73970-250227165359-2b147e65/85/Advanced-Wireless-LAN-1st-Edition-Song-Guo-39-320.jpg)
![A MAC Throughput in the Wireless LAN 27
DSSS and OFDM is achieved through the provision of four different physical layers. These
layers, defined in the standard as ERPs (Extended Rate Physicals), coexist during a frame
exchange, so the sender and receiver have the option to select and use one of the four layers
as long as they both support it. The four different physical layers defined in the IEEE 82.11g
standard are the following :
ERP-DSSS/CCK: This is the old physical layer used by IEEE 802.11b. DSSS technology is
used with CCK modulation. The data rates provided are those of IEEE 802.11b.
ERP-OFDM: This is a new physical layer, introduced by IEEE 802.11g. OFDM is used to
provide IEEE 802.11a data rates at the 2.4 GHz band.
ERP-DSSS/PBCC: This physical layer was introduced in IEEE 802.11b and provides the
same data rates as the DSSS/CCK physical layer. It uses DSSS technology with the
PBCC coding algorithm. IEEE 802.11g extended the set of data rates by adding those of
22 and 33 Mb/s.
DSSS-OFDM: This is a new physical layer that uses a hybrid combination of DSSS and
OFDM. The packet physical header is transmitted using DSSS, while the packet payload
is transmitted using OFDM. The scope of this hybrid approach is to cover
interoperability aspects, as explained later. From the above four physical layers, the first
two are mandatory; every IEEE 802.11g device must support them. The other two are
optional. Column 2 of Table 3 summarizes the supported data rates for the different
physical layers of the IEEE 802.11g specification.
Table 3. Parameters of the different IEEE 802.11g physical layers [8]
2.1.2 802.11n
As the first project whose targeted data rate is measured on top of the MAC layer, 802.11n
provides user experiences comparable to the well known Fast Ethernet (802.3u). Far beyond
the minimum requirements that were derived from its wired paragon’s maximum data rate
of 100 Mb/s, 802.11n delivers up to 600 Mb/s. Its most prominent feature is MIMO
capability. A flexible MIMO (Multiple Input Multiple Output) concept allows for arrays of
up to four antennas that enable spatial multiplexing or beam forming. Its most debated
innovation is the usage of optional 40 MHz channels. Although this feature was already](https://image.slidesharecdn.com/73970-250227165359-2b147e65/85/Advanced-Wireless-LAN-1st-Edition-Song-Guo-41-320.jpg)
![Advanced Wireless LAN
28
being used as a proprietary extension to 802.11a and 802.11g chipsets, it caused an extensive
discussion on neighbor friendly behavior. Especially for the 2.4 GHz band, concerns were
raised that 40 MHz operation would severely affect the performance of existing 802.11,
Bluetooth (802.15.1), ZigBee (802.15.4), and other devices. The development of a
compromise, which disallows 40 MHz channelization for devices that cannot detect 20
MHz-only devices, prevented ratification of 802.11n until September 2009. As a consequence
of 20/40 MHz operation and various antenna configurations, 802.11n defines a total of 76
different MCSs. Since several of them provide similar data rates, WFA’s certification
program decides the MCSs finally used in the market. 802.11n’s PHY enhancements are
supported by medium access enhancements we introduce in the MAC section.
MCS
Index
Modulation
Coding
Rate
Spatial
Streams
802.11n Data Rate (Mbps)
20-MHz 40-MHz
L-GI S-GI L-GI S-GI
0 BPSK 1/2 1 6.5 7.2 13.5 15
1 QPSK 1/2 1 13 14.4 27 30
2 QPSK 3/4 1 19.5 21.7 40.5 45
3 16-QAM 1/2 1 26 28.9 54 60
4 16-QAM 3/4 1 39 43.3 81 90
5 64-QAM 2/3 1 52 57.8 108 120
6 64-QAM 3/4 1 58.5 65 122 135
7 64-QAM 5/6 1 65 72.2 135 150
8 BPSK 1/2 2 13 14.4 27 30
9 QPSK 1/2 2 26 28.9 54 60
10 QPSK 3/4 2 39 43.3 81 90
11 16-QAM 1/2 2 52 57.8 108 120
12 16-QAM 3/4 2 78 86.7 162 180
13 64-QAM 2/3 2 104 116 216 240
14 64-QAM 3/4 2 117 130 243 270
15 64-QAM 5/6 2 130 144 270 300
16 BPSK 1/2 3 19.5 21.7 40.5 45
17 QPSK 1/2 3 39 43.3 81 90
18 QPSK 3/4 3 58.5 65 121.5 135
19 16-QAM 1/2 3 78 86.7 162 180
20 16-QAM 3/4 3 117 130 243 270
21 64-QAM 2/3 3 156 173.3 324 360
22 64-QAM 3/4 3 175.5 195 364.5 405
23 64-QAM 5/6 3 195 216.7 405 450
24 BPSK 1/2 4 26 28.9 54 60
25 QPSK 1/2 4 52 57.8 108 120
26 QPSK 1/2 4 78 86.7 162 180
27 16-QAM 1/2 4 104 115.6 216 240
28 16-QAM 3/4 4 156 173.3 324 360
29 64-QAM 2/3 4 208 231.1 432 480
30 64-QAM 3/4 4 234 260 486 540
31 64-QAM 5/6 4 260 288.9 540 600
Table 4. Parameters of the IEEE 802.11n physical layer, MCS Rates 0-31 [13]](https://image.slidesharecdn.com/73970-250227165359-2b147e65/85/Advanced-Wireless-LAN-1st-Edition-Song-Guo-42-320.jpg)
![A MAC Throughput in the Wireless LAN 29
2.1.3 802.11ac/ad
802.11ac and 802.11ad develop amendments that fulfill the ITU’s (International
Telecommunication Union’s) requirements on proposals for the IMT Advanced standard.
Both target greater than 1 Gb/s throughput, but while 802.11ac considers the traditional
Wireless LAN frequencies below 6 GHz, 802.11ad competes with the Wireless Personal Area
Network TG (Task Group) 802.15.3c, standard ECMA 387, and the Wireless Gigabit Alliance
on the 60 GHz frequency spectrum. Due to their premature stage, both TGs are still in the
process of collecting input and specific proposals from their members. At the moment of
writing this article, 802.11ad has already started defining some additional requirements
regarding range (at least 10 m at 1 Gb/s), seamless session transfer of an active session from
the 60 GHz band to the 2.4/5 GHz band and vice versa, coexistence with other systems in
the band such as 802.15.3c, and support for uncompressed video requirements such as data
rate, packet loss ratio, and delay.
2.2 MAC related amendments
A key element to the 802.11 success is its simple MAC operation based on the DCF protocol.
This scheme has proven to be robust and adaptive to varying conditions, able to cover most
needs sufficiently well. Following the trends visible from the wired Ethernet, 802.11’s
success is mainly based on overprovisioning of its capacity. The available data rate was
sufficient to cover the original best effort applications, so complex resource scheduling and
management algorithms were unnecessary.However, this may change in the future. Because
of the growing popularity of 802.11, WLANs are expected to reach their capacity limits.
Moreover, applications like voice and video streaming pose different demands for quality of
service. Therefore, traffic differentiation and network management might become inevitable.
In the following we explain 802.11 MAC related extensions of the amendments introduced
in the previous section and those shown in Fig. 2 [2].
2.2.1 802.11e
The original project goal of 802.11e, approved at the end of March 2000, foresaw general
enhancements of the WLAN standard. Efficiency improvements, support for quality of service
(QoS), and security enhancements were its key elements. However, already in 2001, the 802.11
frame encryption algorithm WEP was broken by an attack. Thus, security enhancements were
displaced to a new TG called 802.11i. After intensive discussions, 802.11e was finally approved
in 2005 to support QoS. As a new medium access scheme, 802.11e provides the HCF (Hybrid
Coordination Function), where hybrid relates to HCF’s two MAC protocol versions with
centralized and distributed control, respectively. The first is implemented by HCF HCCA (HCF
Controlled Channel Access), an improved variant of the PCF requiring a central coordination
instance that schedules medium access. Until today no device implementing HCCA is known to
exist in the market. EDCA is HCF’s second MAC protocol. While DCF does not differentiate
between traffic with different QoS needs, EDCA (Enhanced Distributed Channel Access)
provides support for four traffic categories: voice, video, best effort, and background with
different rules to access the wireless medium. Accordingly, EDCA enables service
differentiation. Both centralized and distributed MAC protocols change the medium sharing
rules. Without 802.11e, a WLAN provides per packet fairness: regardless of the actual frame
transmission duration, devices back off after every single frame. In contrast, duration of all](https://image.slidesharecdn.com/73970-250227165359-2b147e65/85/Advanced-Wireless-LAN-1st-Edition-Song-Guo-43-320.jpg)
![Advanced Wireless LAN
30
HCCA and EDCA frame exchanges is bound by the TXOP (Transmission Opportunity) limit.
Thus, devices share time slices of the wireless medium. Those that use faster MCSs may
exchange multiple frames after a single successful contention and consequently achieve higher
throughput. Derived from EDCA, WFA has successfully branded and introduced to the market
an EDCA variant called WMM (Wi-Fi MultiMedia). WMM incorporates a subset of functions
from 802.11e draft 6 (November 2003). As the final 802.11e and WMM specifications differ,
some members of the 802.11 initiated a QoS Enhancement SG (Study Group) in May 2007. Its
intended goal was an adaptation of the 802.11e amendment to the WMM specification.
However, a project could never be approved, and the SG was dissolved in November 2007.
Fig. 2. The 802.11 MAC layer amendments [2]
3. Wireless LAN access network
This section shows infrastructure-based and ad hoc-based operation of wireless access
architecture in the 802.11b/a/g/n-based mobile LAN. The protocols of the various layers
are called the protocol stack. The TCP/IP protocol stack consists of five layers: the physical,
data link, network, transport and application layers. This section is focused on physical
layer and data link layer which consists of MAC and LLC (Logical Link Control) sub-layers.
An ad hoc network might be formed when people with laptops get together and want to
exchange data in the absence of a centralized AP (Access Point). Wireless LAN topology is
ad hoc-based or infrastructure-based as shown in Fig. 3. The ad hoc-based topology shows](https://image.slidesharecdn.com/73970-250227165359-2b147e65/85/Advanced-Wireless-LAN-1st-Edition-Song-Guo-44-320.jpg)
![A MAC Throughput in the Wireless LAN 31
that each user in the wireless network communicates directly with all others without a
backbone network. Infrastructure-based topology shows that all wireless users transmit to
an AP to communicate with users on the wired or wireless LAN. IEEE 802.11 operates in the
2.4 GHz band and supports data rates 1 Mbps to 2 Mbps. IEEE 802.11b uses DSSS (Direct
Sequence Spread Spectrum) but supports data rates of up to 11 Mbps. The modulation
scheme employed is called CCK (Complementary Code Keying). The operating frequency
range is 2.4 GHz and hence can interfere with some home appliances. IEEE 802.11g achieves
very high data rates compared to IEEE 802.11b and uses the 2.4 GHz frequency band. An
IEEE 802.11b client can operate with an 802.11g AP. IEEE 802.11a equipment is more
expensive and consumes more power, as it uses OFDM (Orthogonal Frequency Division
Multiplexing). OFDM uses 12 orthogonal channels in the 5 GHz range. The frequency
channels are nonoverlapping. The achievable data rates are 6, 9, 12, 18, 24, 36, 48 and 54
Mbps. IEEE 802.11a and 802.11b can operate next to each other without any interference.
Fig. 4 shows the IEEE 802.11b/a/g/n-based physical and MAC layer protocol stack.
Applications
TCP
IP
802.11 MAC
802.11 PHY
Applications
TCP
IP
802.3 MAC
802.3 PHY
802.11 MAC
802.11 PHY
802.3 MAC
802.3 PHY
Server
Fixed terminal
Mobile terminal
Backbone network
Access point
Applications
TCP
IP
802.11 MAC
802.11 PHY
Applications
TCP
IP
802.3 MAC
802.3 PHY
802.11 MAC
802.11 PHY
802.3 MAC
802.3 PHY
Server
Fixed terminal
Mobile terminal
Backbone network
Access point
(a) Infrastructure-based wireless LAN
(b) Ad-hoc mode operation in the wireless LAN
Fig. 3. Protocol stack in the IEEE 802.11 wireless LAN [12]](https://image.slidesharecdn.com/73970-250227165359-2b147e65/85/Advanced-Wireless-LAN-1st-Edition-Song-Guo-45-320.jpg)
![Advanced Wireless LAN
32
FCS
BO
P-HDR
IFS
BitStream (PMD-SDU)
IFS
PLCP-PDU
PLCP-SDU
Preamble
MAC-PDU
MAC-SDU
M-HDR FCS
BO
P-HDR
IFS
BitStream (PMD-SDU)
IFS
PLCP-PDU
PLCP-SDU
Preamble
MAC-PDU
MAC-SDU
M-HDR
Fig. 4. Protocol stack of physical and MAC layer [12]
IEEE 802.11 protocol stack consists of MAC layer and PHY layer. When a network layer
pushes a user packet down to the MAC layer as a MAC-SDU (MAC-Service Data Unit),
overheads are added to the MAC layer and MAC-PDU (MAC-Protocol Data Unit) is created.
The PHY layer is divided into a PLCP (Physical Layer Convergence Protocol) sublayer and a
PMD (Physical Medium Dependent) sublayer. In this PHY layer, the same procedure as
MAC layer is also executed. IEEE 802.11 MAC layer uses an 802.11 PHY layer, such as
802.11a/b/g, to perform the tasks such as carrier sensing, transmission, and reception of
802.11 frames. With regards to the MAC layer, the functional specifications are essentially
the same for all of them with minor differences.
4. Wireless LAN PHY/MAC layer
4.1 IEEE 802.11b/a/g PHY/MAC layer
When a higher layer pushes a user packet down to the MAC layer as a MAC-SDU, the MAC
layer header (M-HDR) and trailer (FCS) are added before and after the MSDU, respectively
and form a MAC-PDU. The PHY layer is again divided into a PLCP sub-layer and a PMD
sub-layer. Similarly the PLCP preamble and PLCP header (P-HDR) are attached to the
MPDU at the PLCP sub-layer. Different IFS (Inter Frame Space)s are added depending on
the type of MPDU. IEEE 802.11a operates in the 5 GHz band and uses OFDM. The
achievable data rates are 6, 9, 12, 18, 24, 36, 48, and 54 Mbps. 802.11g uses DSSS, OFDM, or
both at the 2.4 GHz ISM band to provide high data rates of up to 54 Mbps. 802.11g device
can operate with an 802.11b device. Combined use of both DSSS and OFDM is achieved
through the provision of four different physical layers. The four different physical layers
defined in the 802.11g standards are ERP-DSSS/CCK, ERP-OFDM, ERP-DSSS/PBCC and
DSSS-OFDM. The standards that support the highest data rate of 54 Mbps are ERP-OFDM
and DSSS-OFDM. ERP-OFDM is a new physical layer in IEEE 802.11g and OFDM is used to
provide IEEE 802.11a data rates at the 2.4 GHz band. DSSS-OFDM is a new physical layer
that uses a hybrid combination of DSSS and OFDM. The packet physical header is
transmitted using DSSS, while the packet payload is transmitted using OFDM. Basic access
scheme is CSMA/CA mechanism. The SIFS (Short Inter-Frame Space) and the slot time are
determined by the physical layer. DIFS (Distributed Inter-Frame Space) is defined based on
the above two intervals.](https://image.slidesharecdn.com/73970-250227165359-2b147e65/85/Advanced-Wireless-LAN-1st-Edition-Song-Guo-46-320.jpg)
![A MAC Throughput in the Wireless LAN 33
(a) 802.11b ERP-OFDM frame
(b) 802.11a and 802.11g ERP-OFDM frame
(c) 802.11g DSSS-OFDM frame
Fig. 5. Frame structure of IEEE 802.11b/a/g-based wireless LAN [12]
IEEE 802.11 MAC protocol supports the DCF and the PCF . The DCF uses the CSMA/CA
mechanism for contention-based access, while the PCF provides contention-free access.
The two modes are used alternately in time. IEEE 802.11 MAC protocol defines five
timing intervals. Two of them are the SIFS and the slot time that are determined by the
physical layer. The other three intervals are the PIFS (Priority InterFrame Space), DIFS
and EIFS (Extended InterFrame Space) that are defined based on the above two intervals.
But the PCF is restricted to infrastructure network configurations. Therefore, the DCF is
widely assumed under the consideration of ad hoc-based wireless LAN. Fig. 6 shows two
access schemes. IEEE 802.11 DCF stations access the channel via a basic access method or
the four-way handshaking access method with an additional RTS/CTS message
exchange. In the basic access method, the CSMA mechanism is applied. Stations wait for
the channel to be idle for a DIFS period of time and then execute backoff for data
transmission. Stations choose a random number between 0 and CW (Contention
Window)-1 with equal probability as a backoff timer. When the backoff timer reaches
zero, the data frame is transmitted. The receiver replies an ACK message upon
successfully receiving a data packet. In the four-way handshaking access method, when
the backoff timer of station reaches zero, the station first transmits a RTS frame. Upon
receiving the RTS frame, the receiver replies with a CTS frame after a SIFS period. Once
the RTS/CTS is exchanged successfully, the sender then transmits its data frame. The
RTS and CTS frames carry a duration field, information of time interval to transmit the](https://image.slidesharecdn.com/73970-250227165359-2b147e65/85/Advanced-Wireless-LAN-1st-Edition-Song-Guo-47-320.jpg)
![Advanced Wireless LAN
34
packet. Any station receiving RTS or CTS frames can read the duration field information.
That information is then used to update a NAV (Network Allocation Vector) value that
indicates to each station the amount of time that remains before the channel will become
idle. Therefore, a station detecting the RTS and CTS frames suitably delays further
transmission, and thus avoids collision. The NAV is thus referred to as a virtual carrier
sensing mechanism. The main purpose of the RTS/CTS handshaking is to resolve the so-
called hidden node problem.
(a) Basic access method
(b) Four-way handshaking access method
Fig. 6. IEEE 802.11 DCF channel access mechanism [14]
Parameter 802.11b 802.11g 802.11a
Tslot 20μs 9μs/20μs 9μs
Τ 1μs 1μs 1μs
TP 144μs 16μs/144μs 16μs
CWmin 31 31/15 15
TPHY 48μs 4μs/48μs 4μs
TSYM N/A N/A, 4μs 4μs
TDIFS 50μs 50μs/34μs 34μs
TSIFS 10μs 16μs 16μs
Table 5. Parameters of IEEE 802.11b/g/a [6, 7, 8]](https://image.slidesharecdn.com/73970-250227165359-2b147e65/85/Advanced-Wireless-LAN-1st-Edition-Song-Guo-48-320.jpg)
![A MAC Throughput in the Wireless LAN 35
MAC
scheme
Transmission TDIFS TSIFS TBO TRTS TCTS TACK TDATA (MSDU : bytes)
CSMA/CA
DSSS-1 50 10 310 N/A N/A 304 192+8×(34+MSDU)/1
DSSS-2 50 10 310 N/A N/A 304 192+8×(34+MSDU)/2
HR-5.5 50 10 310 N/A N/A 304 192+8×(34+MSDU)/5.5
HR-11 50 10 310 N/A N/A 304 192+8×(34+MSDU)/11
OFDM-6 34 9 67.5 N/A N/A 44 20+4×[(16+6+8×(34+MSDU))/24]
OFDM-12 34 9 67.5 N/A N/A 32 20+4×[(16+6+8×(34+MSDU))/48]
OFDM-24 34 9 67.5 N/A N/A 28 20+4×[(16+6+8×(34+MSDU))/96]
OFDM-54 34 9 67.5 N/A N/A 24 20+4×[(16+6+8×(34+MSDU))/216]
RTS/CTS
DSSS-1 50 10×3 310 352 304 304 192+8×(34+MSDU)/1
DSSS-2 50 10×3 310 352 304 304 192+8×(34+MSDU)/2
HR-5.5 50 10×3 310 352 304 304 192+8×(34+MSDU)/5.5
HR-11 50 10×3 310 352 304 304 192+8×(34+MSDU)/11
OFDM-6 34 9×3 67.5 52 44 44 20+4×[(16+6+8×(34+MSDU))/24]
OFDM-12 34 9×3 67.5 36 32 32 20+4×[(16+6+8×(34+MSDU))/48]
OFDM-24 34 9×3 67.5 28 28 28 20+4×[(16+6+8×(34+MSDU))/96]
OFDM-54 34 9×3 67.5 24 24 24 20+4×[(16+6+8×(34+MSDU))/216]
Table 6. Delay compents for different MAC schemes (unit : μs) [7]
4.2 IEEE 802.11n PHY/MAC layer
The key requirement that drove most of the development in 802.11n is the capability of at
least 100 Mb/s MAC throughput. Considering that the typical throughput of 802.11a/g is
25 Mb/s (with a 54 Mb/s PHY data rate), this requirement dictated at least a fourfold
increase in throughput. Defining the requirement as MAC throughput rather than PHY
data rate forced developers to consider the difficult problem of improving MAC
efficiency. The inability to achieve a throughput of 100 Mb/s necessitated substantial
improvements in MAC efficiency when designing the 802.11n MAC. Two basic concepts
are employed in 802.11n to increase the PHY data rates: MIMO and 40 MHz bandwidth
channels. Increasing from a single spatial stream and one transmit antenna to four spatial
streams and four antennas increases the data rate by a factor of four. The term spatial
stream is defined in the 802.11n standard as one of several bitstreams that are transmitted
over multiple spatial dimensions created by the use of multiple antennas at both ends of a
communications link. However, due to the inherent increased cost associated with
increasing the number of antennas, modes that use three and four spatial streams are
optional. And to allow for handheld devices, the two spatial streams mode is only
mandatory in an AP. 40 MHz bandwidth channel operation is optional in the standard
due to concerns regarding interoperability between 20 and 40 MHz bandwidth devices,
the permissibility of the use of 40 MHz bandwidth channels in the various regulatory
domains, and spectral efficiency. However, the 40 MHz bandwidth channel mode has
become a core feature due to the low cost of doubling the data rate from doubling the
bandwidth. Almost all 802.11n products on the market feature a 40 MHz mode of
operation. Other minor modifications were also made to the 802.11a/g waveform to](https://image.slidesharecdn.com/73970-250227165359-2b147e65/85/Advanced-Wireless-LAN-1st-Edition-Song-Guo-49-320.jpg)
![Fußnoten
[1] Statistischen Beweis hierfür siehe Anhang 1, Seite 71.
[2] Dieser Arbeitsvertrag der Bienenstöcke kommt im nächsten Kapitel zur
Besprechung.
[3] Statistischen Beweis hierfür siehe Anhang 2, Seite 73.
[4] Andere, weniger wichtige Formen von Bienenstöcken siehe Anhang 3, S.
74.
[5] Schmoller.
[6] Siehe Anhang 4, Seite 75.
[7] Das Warenhaus als Privatunternehmen hat keinen gemeinnützigen Zweck;
es ist hier bloß erwähnt um zu beweisen, daß die Technik des Betriebes
großer Warenlager etwas durchaus bekanntes, keinerlei Schwierigkeiten
bietendes ist.
[8] Siehe Anhang 5, Seite 77.
[9] Beweis hierfür siehe Anhang 6, Seite 78.
[10] Siehe Anhang 5, Seite 77.
[11] Siehe Anhang 7, Seite 82.
[12] Der Gesamtschaden des großen amerikanischen Kohlenarbeiterstreiks
1902 betrug nach der offiziellen Feststellung durch das Schiedsgericht 396
Millionen Mark, der amerikanische Stahlarbeiterstreik 1901 kostete 100
Millionen Mark, der belgische Generalstreik im Jahre 1902: 3 Millionen Franks
täglich.
[13] Siehe Anhang 8, Seite 83.
[14] Siehe Anhang 9, zwischen Seite 84 und 85.
[15] Durchschnittlicher Jahreslohn 700-1000 Mark. Siehe Anhang 1, Seite 71.
[16] Siehe Anhang 8, S. 83.
[17] Siehe Anhang 6, Seite 78.
[18] Siehe Anhang 1, Seite 71.
[19] Siehe Anhang 1, Seite 71.](https://image.slidesharecdn.com/73970-250227165359-2b147e65/85/Advanced-Wireless-LAN-1st-Edition-Song-Guo-62-320.jpg)
![[20] Siehe Anhang 6, Seite 78.
[21] Vorbilder dazu sind schon vorhanden bei einigen englischen
Genossenschaften, welche ganze Stadtanleihen übernommen haben.
[22] Siehe Anhang 1, Seite 71, und Anhang 6, Seite 78.
[23] Diese Summe von 200 Mark als Gesamt-Jahresausgabe pro Kopf im
Mittel dürfte wohl wesentlich zu niedrig gegriffen sein.
[24] Nach der Zeitschrift des Kgl. Preußischen Statistischen Bureaus 1902.
[25] Der Rest von M. 1191990 wahrscheinlich für Tantiemen, Vorträge etc.
verwendet.
[26] Siehe Beilage Nr. 1 zum Volksvertrag.
[27] Beispiel: Bei 9 Volksräten müssen mindestens 7 anwesend sein, denn 3
/4
× 9 = 63
/4, aufgerundet auf 7. – Bei 10 Volksräten müssen 8 anwesend sein,
denn 3
/4 × 10 = 71
/2, aufgerundet auf 8. – Bei 11 Volksräten ebenfalls 8,
denn 3
/4 × 11 = 81
/4, abgerundet auf 8.
[28] Um die verschiedenen Kategorien von Beamten in ihrem Verhältnis zur
Volkskasse zu unterscheiden, genügt es, einfach Ordnungszahlen einzuführen
und z. B. einen Anfänger oder Lehrling als Primus, einen ungelernten Gehilfen
oder Handlanger als Sekundus, das gelernte laufende Personal für die
niederen Arbeiten als Tertius, einen Vorarbeiter oder mittleren
Verwaltungsbeamten als Quartus zu bezeichnen u. s. w. bis hinauf zu dem
höchsten leitenden Beamten oder Dezimus. Mehr als zehn Stufen sind nicht
erforderlich. Diese oder ähnliche Worte bezeichnen genau das Verhältnis zur
Gesamtverwaltung, ohne die Bedeutung eines Titels zu haben oder als solche
gebraucht werden zu können.
[29] Muster eines Brüderscheins siehe Beilage Nr. 2 zum Volksvertrag.
[30] Senioren sind diejenigen Bienen, welche durch die Zahl ihrer Dienstjahre
das Recht erworben haben, ihr volles Normaleinkommen weiter zu beziehen
ohne zu arbeiten. Es ist damit nicht notwendig der Begriff des Alters zu
verbinden. Die Senioren sind infolge ihrer Dienste eine Art Ehrenmitglieder
der Bienenstöcke.
[31] Um die verschiedenen Kategorien von Bienen in ihrem Verhältnis zum
Bienenstock zu unterscheiden, genügt es, einfache Ordnungszahlen
einzuführen, z. B. einen Anfänger oder Lehrling als Primus, einen ungelernten
Gehilfen oder Handlanger als Sekundus, einen gelernten Handwerker als
Tertius, einen Vorarbeiter als Quartus usw. zu bezeichnen, bis etwa hinauf zu
dem höchsten leitenden Beamten, welcher ein Dezimus wäre. Dieselben
Bezeichnungen wären in analoger Weise auf die Verwaltungsbeamten](https://image.slidesharecdn.com/73970-250227165359-2b147e65/85/Advanced-Wireless-LAN-1st-Edition-Song-Guo-63-320.jpg)
Advanced Wireless LAN 1st Edition Song Guo
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- 5. Advanced Wireless LAN 1st Edition Song Guo Digital Instant Download Author(s): Song Guo ISBN(s): 9789535106456, 9535106457 Edition: 1 File Details: PDF, 6.30 MB Year: 2012 Language: english
- 7. ADVANCED WIRELESS LAN Edited by Song Guo
- 8. Advanced Wireless LAN Edited by Song Guo Published by InTech Janeza Trdine 9, 51000 Rijeka, Croatia Copyright © 2012 InTech All chapters are Open Access distributed under the Creative Commons Attribution 3.0 license, which allows users to download, copy and build upon published articles even for commercial purposes, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications. After this work has been published by InTech, authors have the right to republish it, in whole or part, in any publication of which they are the author, and to make other personal use of the work. Any republication, referencing or personal use of the work must explicitly identify the original source. As for readers, this license allows users to download, copy and build upon published chapters even for commercial purposes, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications. Notice Statements and opinions expressed in the chapters are these of the individual contributors and not necessarily those of the editors or publisher. No responsibility is accepted for the accuracy of information contained in the published chapters. The publisher assumes no responsibility for any damage or injury to persons or property arising out of the use of any materials, instructions, methods or ideas contained in the book. Publishing Process Manager Romina Skomersic Technical Editor Milan Domonji Cover Designer InTech Design Team First published June, 2012 Printed in Croatia A free online edition of this book is available at www.intechopen.com Additional hard copies can be obtained from orders@intechopen.com Advanced Wireless LAN, Edited by Song Guo p. cm. ISBN 978-953-51-0645-6
- 10. Contents Preface VII Chapter 1 Sum-Product Decoding of Punctured Convolutional Code for Wireless LAN 1 Toshiyuki Shohon Chapter 2 A MAC Throughput in the Wireless LAN 23 Ha Cheol Lee Chapter 3 MAC-Layer QoS Evaluation Metrics for IEEE 802.11e-EDCF Protocol over Nodes' Mobility Constraints 63 Khaled Dridi, Boubaker Daachi and Karim Djouani Chapter 4 Techniques for Preserving QoS Performance in Contention-Based IEEE 802.11e Networks 81 Alessandro Andreadis and Riccardo Zambon Chapter 5 QoS Adaptation for Realizing Interaction Between Virtual and Real Worlds Through Wireless LAN 101 Shinya Yamamoto, Naoki Shibata, Keiichi Yasumoto and Minoru Ito Chapter 6 Custom CMOS Image Sensor with Multi-Channel High-Speed Readout Dedicated to WDM-SDM Indoor Optical Wireless LAN 121 Keiichiro Kagawa
- 12. Preface A wireless local area network (LAN) is a data transmission system designed to provide network access between computing devices by using radio waves rather than a cable infrastructure. Wireless LANs are designed to operate in a small area such as a building or office complex. The past two decades have witnessed starling advances in wireless LAN technologies that were stimulated by its increasing popularity in the home due to ease of installation, and in commercial complexes offering wireless access to their customers. This book presents some of the latest development status of wireless LAN and provides an opportunity for readers to explore the problems that arise in the rapidly developed technologies in wireless LAN. This book consists of a number of self-contained chapters. Chapter 1 proposes various sum-product decoding methods for the punctured convolutional codes for the IEEE802.11n wireless LAN. It aims at providing high speed decoder by exploiting the higher degree parity check polynomial. The proposed sum-product decoding schemes achieve better performance than the conventional method with much reduced complexity. Chapter 2 theoretically analyzes the medium access control (MAC) layer throughput with distributed coordination function (DCF) protocol in the IEEE 802.11b/a/g/n-based wireless LANs under a fading channel model. Chapter 3 studies the stability region of the enhanced DCF (EDCF) MAC protocol under various mobility levels. Chapter 4 provides a survey of the main techniques introduced to improve quality-of-service (QoS) performance in wireless LANs. It represents the state of the art about current studies on how to preserve QoS in contention-based EDCA IEEE 802.11e networks under heavy loads. Chapter 5 proposes a framework for interaction between real and virtual users in hybrid shared space, in which a QoS adaptation mechanism is implemented for networks with bandwidth limitation. Finally, Chapter 6 proposes an indoor optical wireless LAN system using space- division-multiplexing (SDM) and wavelength-division-multiplexing (WDM) techniques. It presents the fabrication details of a dedicated complimentary-metal- oxide-semiconductor (CMOS) image sensor to realize a compact, high-speed, and intelligent optical wireless LAN. In summary, the topics on physical layer, MAC layer, QoS and systems included in this book are expected to benefit both practitioners working in wireless LAN systems
- 13. VIII Preface and researchers as well as graduate students with interest in this area. The editor is grateful to all authors for their contributions to the quality of this book. The assistance of reviewers for all chapters is also greatly appreciated. The University of Aizu provided an ideal working environment for the preparation of this book. The editor also appreciates the support of publishing process managers of InTech. Song Guo Senior Associate Professor, School of Computer Science and Engineering, The University of Aizu, Japan
- 15. 0 Sum-Product Decoding of Punctured Convolutional Code for Wireless LAN Toshiyuki Shohon Kagawa National College of Technology Japan 1. Introduction The next generation wireless Local Area Network (LAN) standard (IEEE802.11n) aims for high rate data transmission such as 100Mbps to 600Mbps. In order to implement that rate, high speed decoder for the convolutional code for the wireless LAN standard is necessary. From the viewpoint of high speed decoder, sum-product algorithm is an attractive decoding method, since decoding rule of sum-product algorithm is simple and sum-product algorithm is suit for parallel implementation. Furthermore, sum-product decoding is a soft-in soft-out decoding. The combined use of sum-product algorithm and another soft-in soft-out processing may provide good performance such as turbo equalization (Douillard et al., 1995; Laot et al., 2001). However, sum-product decoding for the convolutional code of the wireless LAN can not provide good performance. To improve the performance, the sum-product decoding method for the non-punctured convolutional code of the wireless LAN has been proposed (Shohon et al., 2009b; 2010). In the wireless LAN, however, punctured convolutional codes are also used. Therefore, this paper proposes sum-product decoding methods for the punctured convolutional codes of the wireless LAN. A sum-product decoding method for convolutional codes has been introduced in (Kschischang et al., 2001). The sum-product algorithm uses a Wiberg-type graph that represents a code trellis with hidden variables as code states and visible variables as code bits. In this case, the Wiberg-type graph is equivalent to the code trellis and the sum-product algorithm becomes precisely identical to BCJR algorithm (Berrou, C. et al.;C; Kschischang et al., 2001). This method only gives interpretation of BCJR algorithm as sum-product algorithm. To avoid confusion, the method of (Kschischang et al., 2001) is referred to as BCJR. This paper deals with sum-product algorithm that uses a Tanner graph that represents a parity check matrix of the code. This sum-product algorithm is the same as that for Low-Density Parity-Check code (Gallager, 1963; MacKay, 1999). The sum-product decoding method for recursive systematic convolutional codes has been proposed in (Shohon et al., 2009a). In the wireless LAN, the non-systematic convolutional code is used. For the non-punctured convolutional code of the wireless LAN, the sum-product decoding method has been proposed in (Shohon et al., 2009b; 2010). In this paper, for punctured codes of the wireless LAN, sum-product decoding methods are proposed. This paper is constructed as follows. In section 2, the convolutional codes used in the wireless LAN are explained. In section 3, the sum-product algorithm for convolutional codes is explained. In section 4, the sum-product decoding method for non-punctured convolutional code of the wireless LAN is explained and decoding performance of that 1
- 16. 2 Will-be-set-by-IN-TECH method for punctured codes are shown. In section 5 and section 6, the sum-product decoding methods for punctured codes of the wireless LAN are proposed. In section 7, the decoding complexity is discussed. 2. Convolutional code for wireless LAN 2.1 Non-punctured code The convolutional code for the wireless LAN is a non-systematic code with rate 1/2 (IEEE Std 802.11, 2007). Let a sequence of information bits be denoted by x0, x1, · · · , xN−1, a sequence of parity bits 1 be denoted by p1,0, p1,1, · · · , p1,N−1, and a sequence of parity bits 2 be denoted by p2,0, p2,1, · · · , p2,N−1. Polynomial representation for each sequence is as follows. X(D) =x0 + x1D + x2D2 + · · · + xN−1DN−1 (1) P1(D) =p1,0 + p1,1D + p1,2D2 + · · · + p1,N−1DN−1 (2) P2(D) =p2,0 + p2,1D + p2,2D2 + · · · + p2,N−1DN−1 (3) Parity bit polynomials are given by P1(D) =G1(D)X(D), (4) P2(D) =G2(D)X(D). (5) For the wireless LAN standard, G1(D) and G2(D) are given by G1(D) =1 + D2 + D3 + D5 + D6 , (6) G2(D) =1 + D + D2 + D3 + D6 . (7) Polynomials X(D), P1(D), P2(D) are also represented by X, P1, P2 in this paper. 2.2 Punctured code In this section, puncturing method for wireless LAN will be explained. Puncturing is a procedure for omitting some of the encoded bits in the transmitter. The effect from puncturing will reducing the number of transmitted bits and increasing the coding rate. Figure 1(a) to Fig.1(b) shows the puncturing pattern for coding rate, r = 2/3, 3/4. info bit X0 A1 B0 X1 A0 B1 A0 B0 A1 punctured bit Parity 1 Parity 2 encoded data (a) Puncturing pattern for code rate 2/3 punctured bit info bit X0 A1 B0 X1 A0 B1 A0 B0 A1 Parity 1 Parity 2 encoded data B2 X2 A2 B2 (b) Puncturing pattern for code rate 3/4 Fig. 1. Puncturing pattern 2 Advanced Wireless LAN
- 17. Sum-Product Decoding of Punctured Convolutional Code for Wireless LAN 3 3. Sum-product algorithm for convolutional codes Sum-product algorithm is a message exchanging algorithm along with edge of the Tanner graph of the code. Tanner graph is a bipartite graph that represents the parity check matrix of the code. For convolutional code, it is easy to obtain tanner graph from parity check polynomial. This section explains parity check polynomial for convolutional codes, tanner graph and sum-product algorithm. 3.1 Parity check polynomial of convolutional code for wireless LAN From Equation 4 ∼ Equation 5, we can obtain following equations. G1(D)X + P1 = 0 (8) G2(D)X + P2 = 0 (9) Let left parts of Equation 8 and Equation 9 be defined as parity check polynomial. Horg,1(X, P1) = G1(D)X + P1 (10) Horg,2(X, P2) = G2(D)X + P2 (11) A tuple of polynomials (X, P1, P2) is a code word if following equations are satisfied. Horg,1(X, P1) = 0 (12) Horg,2(X, P2) = 0 (13) The degree of a parity check polynomial is denoted by ν, that is the maximum degree of coefficients of the polynomial. For example, since coefficients of Horg,1(X, P1) are {G1(D), 1}, the maximum degree is ν = 6 that is the maximum degree of G1(D). 3.2 Tanner graph of convolutional code From Equation 12, parity check equations at k and k + 1 time slots are given by Ck : xk−6 + xk−5 + xk−3 + xk−2 + xk + p1,k = 0, (14) Ck+1 : xk−5 + xk−4 + xk−2 + xk−1 + xk+1 + p1,k+1 = 0. (15) Those equations are corresponding to check nodes Ck and Ck+1, of the tanner graph. The part of tanner graph corresponding to those parity check equations is as shown in Fig.2. 3.3 Algorithm For convenience, bit node is denoted by un such that ⎧ ⎨ ⎩ u3n = xn u3n+1 = p1,n u3n+2 = p2,n (16) where information bit is xn and parity bits are p1,n, p2,n. Message from bit node, un, to check node Cm, is denoted by Vm,n. Message from check node, Cm, to bit node un, is denoted by Um,n. Sum-Product algorithm is described as follows. 3 Sum-Product Decoding of Punctured Convolutional Code for Wireless LAN
- 18. 4 Will-be-set-by-IN-TECH Ck Ck+1 xk−6 xk−5 xk−4 xk−3 xk−2 xk−1 xk p1,k xk+1 p1,k+1 Fig. 2. Part of Tanner graph Step1. Initialization Each message Vm,n is set to the initial value as follows. Vm,n = λn = 2rn σ2 (17) where, rn denotes received signal, σ2 denotes variance of additive white Gaussian noise and λn is channel value. Step2. Message from check node to bit node Each check node Cm updates the message on bit node un by gathering all incoming messages from other bit nodes that connected to check node Cm. Message Um,n is calculated by following equation (Gallager, 1963; Hagenauer, 1996; Richardson et al., 2001). Um,n = 2fs tanh −1 ⎧ ⎨ ⎩ ∏ n∈N (m)n tanh Vm,n 2 ⎫ ⎬ ⎭ (18) where, N (m) denotes the set of bit node numbers that connect to the check node Cm and fs is a scaling factor. This factor is used in the proposed method described later. When fs is not specified, fs = 1. Step3. Message from bit node to check node Each bit node n propagates its message to all check nodes that connect to it. Vm,n = λn + ∑ m∈M(n)m Um,n (19) where M(n) denotes the set of check node numbers that connect to the bit node, un. Step4. Tentative estimated code word computation By summing up all the messages from all check nodes connected to a bit node, the a posteriori value Λn can be obtained by Λn = λn + ∑ m∈M(n) Um,n. (20) 4 Advanced Wireless LAN
- 19. Sum-Product Decoding of Punctured Convolutional Code for Wireless LAN 5 The extrinsic value, Le(un), of bit node un can be obtained by Le(un) = ∑ m∈M(n) Um,n. (21) The tentative estimated bit u n can be obtained by u n = 0 i f sign(Λn) = +1 1 i f sign(Λn) = −1 (22) Step5. Stop criterion Tentative estimated code word u obtained in Step 4 is checked against the parity check matrix H. If H multiplied by Tentative estimated code word uT equal to zero vector, the decoder stop and outputs u, if not, it repeats Steps 2-5. HuT = 0 (23) If maximum iteration number of decoding is set, the tentative estimated code word u outputs after decoding procedure repeat the process until the maximum iteration is reached. 4. Sum-product decoding for wireless LAN (conventional method) This section will give summary of (Shohon et al., 2009b; 2010). Sum-product decoding can be performed by using Equation 10 and Equation 11 as parity check polynomials. However, the decoding provides bad performance. Since the code under consideration is a non-systematic code, there are no received signals corresponding to information bits and channel values for information bits are zero. It can be seen from Equation 10, Equation 11 that each check node has more than one information bit connections. Therefore reliability increment at check node cannot be obtained. Consequently, conventional sum-product algorithm cannot realize good performance. To improve the sum-product decoding performance, I have proposed the 2-step decoding method (Shohon et al., 2009b; 2010). 4.1 2-Step decoding The 2-step decoding method is as follows. (1) Only parity bits are decoded by sum-product algorithm. (2) With decoded parity bits, information bits are regenerated. 4.1.1 Decoding parity bits The parity check equation is derived from Equation 4 ∼ Equation 5 as follows. G2(D)P1(D) + G1(D)P2(D) = 0 (24) The left part of the equation is defined as parity check polynomial H(P1, P2). H(P1, P2) = G2(D)P1 + G1(D)P2 (25) Parity bits P1 and P2 can be decoded by sum-product algorithm based on parity check polynomial given by Equation 25. By using the decoded parity bits, information bits can be regenerated. 5 Sum-Product Decoding of Punctured Convolutional Code for Wireless LAN
- 20. 6 Will-be-set-by-IN-TECH 4.1.2 Decoding information bits Decoded information bit X̂ can be obtained by Equation 26 with decoded parity bits P̂1, P̂2. X̂ = Gx,1(D)P̂1 + Gx,2(D)P̂2 (26) where, Gx,1(D) =D4 + D2 (27) Gx,2(D) =D4 + D3 + D2 + D + 1 (28) From Equation 26, Equation 27, and Equation 28, it can be seen that information bit can be regenerated by using a non-recursive convolutional encoder with input P̂1, P̂2 and output X̂ as shown in Fig.3. D D D D D D D D P1 P2 X̂ Fig. 3. Information bits regenerator 4.2 Higher degree parity check polynomial I have proposed to use higher degree parity check polynomial to obtain further performance improvement (Shohon et al., 2009b; 2010). The method is a sum-product decoding with higher degree parity check polynomial than that of the original parity check polynomial. In this section, the method is applied to improve the sum-product decoding performance for parity bits. The higher degree parity check polynomial is denoted by H(P1, P2), that is given by H (P1, P2) =M(D)H(P1, P2) (29) =M(D)G2(D)P1 + M(D)G1(D)P2 (30) =G 2(D)P1 + G 1(D)P2 (31) where M(D) is a non-zero polynomial. Among possible higher degree parity check polynomials, we aim to select the optimum higher degree parity check polynomial by experiments and to use it for sum-product decoding. However, the number of prospective objects becomes too much when we include all possible higher degree parity check polynomials in the experimental objects. Therefore, we limit the range of degree of higher degree parity check polynomials (ν ≤ 16). For those higher degree parity check polynomials, we further limit the prospective objects by using nf c, that is the number of four-cycles per one check node (Shohon et al., 2009a). For every degree of higher degree parity check polynomial, we select the higher degree parity check polynomial that has the minimum nf c among higher degree parity check polynomials of object degree and include it in the experimental objects. By this means, Table 1 was obtained. 6 Advanced Wireless LAN
- 21. Sum-Product Decoding of Punctured Convolutional Code for Wireless LAN 7 ν nf c G 2(oct) G 1(oct) 6 29 117 155 7 24 321 267 8 52 563 731 9 17 1067 1405 10 36 3131 2417 11 11 4015 6243 12 28 13103 16111 13 13 21003 30611 14 22 45203 65011 15 17 100001 145207 16 25 221001 322207 Table 1. Examined higher degree parity check polynomials for code rate 1/2 Experimental result shows that higher degree parity check polynomial of degree ν = 13 provides the best performance. The higher degree parity check polynomial is given by H (P1, P2) =G 2(D)P1 + G 1(D)P2 (32) G 1(D) =1 + D3 + D7 + D8 + D12 + D13 (33) G 2(D) =1 + D + D9 + D13 (34) 4.3 Simulation results for non-punctured code Simulation condition is shown in Table 2. Hereafter, this condition was used, if simulation condition is not specified. Figure 4 shows simulation results. The figure shows that the performance for information bits of 2-Step Decoding with higher degree parity check polynomial (denoted by conventional) is only 0.7[dB] inferior to that of BCJR at bit error rate 10−5. Number of info bits per block 1024[bit] Termination Zero-termination Channel Additive white Gaussian noise Maximum iterations 200 Table 2. Simulation condition 4.4 Simulation results for punctured codes For non-punctured code, higher degree parity check polynomial with degree ν = 13 provides the best performance. With that higher degree parity check polynomial, for punctured codes with code rates 2/3 and 3/4, the sum-product decoding simulation were executed. The simulation results are shown in Fig.5 and Fig.6. From Fig.5 and Fig.6, it can be seen that the conventional method, that is sum-product decoding with higher degree parity check polynomial with ν = 13, can not provide good performance for punctured code with code rates 2/3 and 3/4. 7 Sum-Product Decoding of Punctured Convolutional Code for Wireless LAN
- 22. 8 Will-be-set-by-IN-TECH 10-7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 0 1 2 3 4 5 6 Sum-Product : Info bit Sum-Product : Parity bit BCJR Eb/N0 [dB] Bit error rate Fig. 4. Bit error rate performance of conventional method for code rate 1/2 10-8 10-7 10 -6 10 -5 10-4 10 -3 10 -2 10 -1 100 0 1 2 3 4 5 6 7 Sum-Product : Info bit Sum-Product : Parity bit BCJR Eb/N0 [dB] Bit error rate Fig. 5. Bit error rate performance of conventional method for code rate 2/3 8 Advanced Wireless LAN
- 23. Sum-Product Decoding of Punctured Convolutional Code for Wireless LAN 9 10-9 10-8 10 -7 10 -6 10 -5 10 -4 10 -3 10-2 10-1 10 0 0 2 4 6 8 10 12 Sum-Product : Info bit Sum-Product : Parity bit BCJR Eb/N0 [dB] Bit error rate Fig. 6. Bit error rate performance of conventional method for code rate 3/4 5. Single punctured bit method (Proposed decoding method (1)) I inferred that the bad sum-product decoding performance for punctured codes is caused by more than one punctured bits included in the parity check equation at time slot k. The reason is as follows. Since received signals are not available for punctured bits, the channel values for punctured bits are zero. This causes that every messages from punctured bit node to check node are zero. In this case, like stopping set (Di et al., 2002), messages from the check node to bit nodes are zero. Therefore, sum-product algorithm does not work. In order to improve the sum-product decoding performance, this paper proposes to use parity check equation that includes single punctured bit. The condition to include single punctured bit in parity check equation is referred to as single punctured bit condition. If single punctured bit is included in a parity check equation at time slot k, the message to the corresponding bit node can be obtained from the corresponding check node Ck. In this case, sum-product algorithm can work. Therefore, we expect that using higher degree parity check polynomial such that parity check equation includes single punctured bit, brings performance improvement of sum-product decoding of punctured codes. 5.1 Higher degree parity check polynomial satisfying single puncture bit condition In this section, single punctured bit condition is derived for higher degree parity check polynomial. A higher degree parity check equation is given by H (P1, P2) = G 2(D)P1 + G 1(D)P2 (35) 9 Sum-Product Decoding of Punctured Convolutional Code for Wireless LAN
- 24. 10 Will-be-set-by-IN-TECH Generally, polynomials G 1(D) and G 2(D) are given by G 1(D) = d1 ∑ i=1 Dαi (36) G 2(D) = d2 ∑ i=1 Dβi (37) If (P1, P2) is code word, it satisfies G 2(D)P1 + G 1(D)P2 = 0 (38) From Equation 36, Equation 37 and Equation 38, parity check equation at time slot k is represented by d1 ∑ i=1 p1,k−βi + d2 ∑ i=1 p2,k−αi = 0 (39) 5.1.1 Code rate 2/3 For code rate 2/3, punctured bits are p2,2n+1 | n = 0, 1, 2, · · · (40) From Equation 39 and Equation 40, it can be seen that punctured bits included in parity check equation at time slot k satisfies p2,k−αi = p2,2n+1 (41) Therefore, we obtain k − αi = 2n + 1 (42) αi = k − (2n + 1). (43) For time slot k = 2l, l = 0, 1, 2, · · · , αi = 2l − (2n + 1) (44) = 2(l − n) − 1 (45) Therefore, the set {αi | (αi mod 2) = 1} in higher degree parity check polynomial corresponds to punctured bits in the parity check equation at time slot k = 2l, l = 0, 1, 2, · · · . If Equation 46 is satisfied, the higher degree parity check polynomial satisfies single punctured bit condition at time slot k = 2l, l = 0, 1, 2, · · · . #{αi | (αi mod 2) = 1} = 1 (46) where #{x} denotes the number of elements in the set {x}. Similarly, if Equation 47 is satisfied, the higher degree parity check polynomial satisfies single punctured bit condition at time slot k = 2l + 1, l = 0, 1, 2, · · · . #{αi | (αi mod 2) = 0} = 1 (47) 10 Advanced Wireless LAN
- 25. Sum-Product Decoding of Punctured Convolutional Code for Wireless LAN 11 Therefore, if either Equation 46 or Equation 47 is satisfied, the higher degree parity check polynomial satisfies single punctured bit condition. 5.1.2 Code rate 3/4 For code rate 3/4, punctured bits are p1,3n+2 n = 0, 1, 2, · · · p2,3n+1 n = 0, 1, 2, · · · . (48) From Equation 39 and Equation 48, it can be seen that punctured bits included in parity check equation at time slot k satisfies p1,k−βi = p1,3n+2 n = 0, 1, 2, · · · p2,k−αi = p2,3n+1 n = 0, 1, 2, · · · . (49) Therefore, we obtain k − βi = 3n + 2 k − αi = 3n + 1 . (50) For time slot k = 3l, l = 0, 1, 2, · · · , 3l − βi = 3n + 2 (51) βi = 3(l − n) − 2 (52) 3l − αi = 3n + 1 (53) αi = 3(l − n) − 1 (54) From Equation 52, it can be seen that the set {βi | (βi mod 3) = 1} in higher degree parity check polynomial corresponds to punctured bits of parity bit P1 in the parity check equation at time slot k = 3l, l = 0, 1, 2, · · · . From Equation 54, it can be seen that the set {αi | (αi mod 3) = 2} in higher degree parity check polynomial correspond to punctured bits of the parity bit P2 in the parity check equation at time slot k = 3l, l = 0, 1, 2, · · · . Therefore, if either Equation 55 or Equation 56 is satisfied, the higher degree parity check polynomial satisfies single punctured bit condition at time slot k = 3l, l = 0, 1, 2, · · · . (#{βi | (βi mod 3) = 1} = 1) ∧(#{αi | (αi mod 3) = 2} = 0) (55) (#{βi | (βi mod 3) = 1} = 0) ∧(#{αi | (αi mod 3) = 2} = 1) (56) Similarly, if either Equation 57 or Equation 58 is satisfied, the higher degree parity check polynomial satisfies single punctured bit condition at time slot k = 3l + 1, (l = 0, 1, 2, · · · ). (#{βi | (βi mod 3) = 2} = 1) ∧(#{αi | (αi mod 3) = 0} = 0) (57) 11 Sum-Product Decoding of Punctured Convolutional Code for Wireless LAN
- 26. 12 Will-be-set-by-IN-TECH (#{βi | (βi mod 3) = 2} = 0) ∧(#{αi | (αi mod 3) = 0} = 1) (58) Similarly, if either Equation 59 or Equation 60 is satisfied, the higher degree parity check polynomial satisfies single punctured bit condition at time slot k = 3l + 2, (l = 0, 1, 2, · · · ). (#{βi | (βi mod 3) = 0} = 1) ∧(#{αi | (αi mod 3) = 1} = 0) (59) (#{βi | (βi mod 3) = 0} = 0) ∧(#{αi | (αi mod 3) = 1} = 1) (60) 5.2 Search of higher degree parity check polynomial for decoding In this paper, basically, the higher degree parity check polynomials for decoding are searched as follows. Step.1 Select higher degree parity check polynomials with degree ν ≤ 21 that satisfies single punctured bit condition. Step.2 Among those higher degree parity check polynomials, select the higher degree parity check polynomial that provides the best sum-product decoding performance by using computer simulation. 5.2.1 Code rate 2/3 In the Step.1, 208 higher degree parity check polynomials satisfy single punctured bit condition. Since many higher degree parity check polynomials are selected, they are limited by nf c. In this paper, among those higher degree parity check polynomials, 9 higher degree parity check polynomials with lower nf c are selected. They are shown in Table 3. No. ν nf c G 2(oct) G 1(oct) 1 8 29 755 403 2 9 17 1067 1405 3 11 38 6143 5251 4 14 26 62501 50107 5 16 26 364203 202011 6 16 33 203133 310001 7 16 43 310207 243025 8 17 16 624403 500211 9 17 42 445207 640025 Table 3. Examined higher degree parity check polynomials for code rate 2/3 The simulation results of Step.2 with higher degree parity check polynomials in Table 3 are shown in Fig. 7. Simulation condition is shown in Table 2 and Eb/N0 = 5.0 [dB]. From Fig. 7, it can be seen that higher degree parity check polynomial of No.5 with scaling factor fs = 0.9 provides the best performance. 12 Advanced Wireless LAN
- 27. Sum-Product Decoding of Punctured Convolutional Code for Wireless LAN 13 10-5 10-4 10 -3 10 -2 10-1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 No.1 No.2 No.3 No.4 No.5 No.6 No.7 No.8 No.9 Scaling factor fs Parity bit error rate Fig. 7. Simulation results of Step.2 for code rate 2/3 at Eb/N0 =5[dB] 5.2.2 Code rate 3/4 5.2.2.1 Step.1 For code rate 3/4, there are both puncture bits of parity P1 and parity P2. Decodable punctured parity bit by sum-product algorithm with certain parity check equation is either parity P1 or parity bit P2. From the viewpoint of decodable parity bit, single punctured bit condition can be arranged as follows. 1. If either Equation 55 or Equation 57, or Equation 59 is satisfied, the higher degree parity check polynomial includes single punctured bit of parity P1. Therefore, with the higher degree parity check polynomial, punctured bits of parity P1 can be decoded. That higher degree parity check polynomial is referred to as higher degree parity check polynomial for P1. 2. If either Equation 56 or Equation 58 or Equation 60 is satisfied, the higher degree parity check polynomial includes single punctured bit of parity P2. Therefore, with the higher degree parity check polynomial, punctured bits of parity P2 can be decoded. That higher degree parity check polynomial is referred to as higher degree parity check polynomial for P2. Therefore, for code rate 3/4, both higher degree parity check polynomials for P1 and P2 are necessary to decode. For code rate 3/4, there are 16 higher degree parity check polynomials for P1 and 16 higher degree parity check polynomials for P2. The number of combination of higher degree parity check polynomial for P1 and that for P2 is many. Therefore, they are limited by nf c. Higher degree parity check polynomials that have lower nf c are selected as shown in Table 4 and Table 5. 13 Sum-Product Decoding of Punctured Convolutional Code for Wireless LAN
- 28. 14 Will-be-set-by-IN-TECH No. ν nf c G 2(oct) G 1(oct) 1 12 30 14453 12121 2 21 64 17010055 10212103 Table 4. Examined higher degree parity check polynomials for P1 No. ν nf c G 2(oct) G 1(oct) 3 7 24 321 267 4 12 29 11055 15103 5 21 38 10540055 14222103 Table 5. Examined higher degree parity check polynomials for P2 5.2.2.2 Step.2 A block diagram of the decoder for code rate 3/4 is shown in Fig. 8. It is similar to a turbo decoder. In Fig.8, DEC1 is sum-product algorithm decoder with higher degree parity check polynomial for P1 and DEC2 is sum-product algorithm decoder with higher degree parity check polynomial for P2. Channel value is denoted by λn. Extrinsic values of DEC1 and DEC2 are denoted by Le1(un) and Le2(un), respectively. A posteriori value of DEC2 is denoted by Λ2,n. In DEC1, Le2(un) is added to λn as follows. λ n =λn + Le2(un) (61) The value λ n is used as initial value of λn in Equation 17. Similarly, in DEC2, Le1(un) is added to λn and that value is used as initial value of λn. In computer simulation, the number of iteration of sum-product algorithm at each decoder was set to 1. The maximum number of iteration between two decoders was set to 200. Other simulation conditions are the same as shown in Table 2. Le1(un) Le2(un) Λ2,n λn DEC1 DEC2 Fig. 8. Block diagram of decoder of single punctured bit method for code rate 3/4 Figure 9 shows the simulation results of Step.2 for code rate 3/4 at Eb/N0 = 6[dB]. From Fig.9, it can be seen that the combination of higher degree parity check polynomials No.2 and No.3 with scaling factor fs = 0.5 provides the best decoding performance. 14 Advanced Wireless LAN
- 29. Sum-Product Decoding of Punctured Convolutional Code for Wireless LAN 15 10 -4 10-3 10-2 10-1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 No.1,No.3 No.1,No.4 No.1,No.5 No.2,No.3 No.2,No.4 No.2,No.5 Scaling factor fs Parity bit error rate Fig. 9. Simulation results of Step.2 for code rate 3/4 at Eb/N0 = 6[dB] 5.3 Simulation results 5.3.1 Code rate 2/3 Figure 10 shows bit error rate performance of the single punctured bit method for code rate 2/3. 10-8 10-7 10-6 10-5 10-4 10 -3 10-2 10-1 100 0 1 2 3 4 5 6 7 Conventional : Info bit Conventional : Parity bit BCJR Eb/N0 [dB] Bit error rate Single punctured bit : Info bit Single punctured bit : Parity bit Fig. 10. BER performance of single punctured bit method for code rate 2/3 15 Sum-Product Decoding of Punctured Convolutional Code for Wireless LAN
- 30. 16 Will-be-set-by-IN-TECH From Fig.10 it can be seen that the parity bit error rate performance of the single punctured bit method is 1.12[dB] superior to that of the conventional method (higher degree parity check polynomial of ν = 13) at bit error rate 10−5. The parity bit error rate performance of the single punctured bit method is only 0.83[dB] inferior to that of BCJR. From Fig.10, information bit error performance of the single punctured bit method is 1.28[dB] superior to that of the conventional method at bit error rate 10−5. The information bit error rate performance of the single punctured bit method is only 0.98 [dB] inferior to that of BCJR. 5.3.2 Code rate 3/4 10-6 10-5 10-4 10 -3 10 -2 10 -1 100 0 1 2 3 4 5 6 7 8 9 10 11 Conventional Parity bit error rate Eb/N0[dB] Single punctured bit BCJR Fig. 11. Parity bit error rate performance of single punctured bit method for code rate 3/4 Figure 11 shows parity bit error rate performance of the single punctured bit method for code rate 3/4. From Fig.11 it can be seen that the parity bit error rate performance of the single punctured bit method is 0.82[dB] superior to that of the conventional method (higher degree parity check polynomial of ν = 13) at bit error rate 10−5. The parity bit error rate performance of the single punctured bit method is 3.24[dB] inferior to that of BCJR. Figure 12 shows information bit error rate performance of the single punctured bit method. From Fig.12, it can be seen that the information bit error rate performance of the single punctured bit method is 1.11[dB] superior to the conventional method at bit error rate 10−5. The information bit error rate performance of the single punctured bit method is 4.11[dB] inferior to that of BCJR at bit error rate 10−5. 6. Switching parity check method (proposed decoding method (2)) For code rate 3/4, the proposed method (1) can not provide good performance. Therefore, this paper try to improve the sum-product decoding performance for code rate 3/4. 16 Advanced Wireless LAN
- 31. Sum-Product Decoding of Punctured Convolutional Code for Wireless LAN 17 10-6 10-5 10-4 10 -3 10 -2 10-1 100 0 1 2 3 4 5 6 7 8 9 10 11 Conventional Information bit error rate Eb/N0[dB] Single punctured bit BCJR Fig. 12. Information bit error rate performance of single punctured bit method for code rate 3/4 I inferred that the bad decoding performance is caused by the four-cycles of higher degree parity check polynomial, since nf c of higher degree parity check polynomial satisfying single punctured bit condition tends to be larger than nf c of higher degree parity check polynomial that does not satisfy single punctured bit condition. Therefore, this paper proposes following method. Only at first iteration, the higher degree parity check polynomial satisfying single punctured bit condition is used to decode and after first iteration, another higher degree parity check polynomial without single punctured bit condition is used to decode. By decoding, only at first iteration, with higher degree parity check polynomial satisfying single punctured bit condition, the a posteriori values of punctured bits are obtained. After obtaining the a posteriori values of punctured bit, the higher degree parity check polynomial with lower nf c may provide good bit error rate performance. Figure 13 shows a block diagram of decoder of the switching parity check method. In Fig. 13, DEC1 is a sum-product algorithm decoder with higher degree parity check polynomial for P1, DEC2 is a sum-product algorithm decoder with higher degree parity check polynomial for P2 and DEC3 is a sum-product algorithm decoder with higher degree parity check polynomial with lower nf c for iteration. Chanel values for DEC1, DEC2 and DEC3 are λ1,n, λ2,n and λ3,n, respectively. A posteriori values of DEC1, DEC2 and DEC3 are Λ1,n, Λ2,n and Λ3,n, respectively. Decoders DEC2 and DEC3 use the a posteriori value of previous decoder as the channel value. 6.1 Search of higher degree parity check polynomial for decoding This paper searches higher degree parity check polynomials for DEC1, DEC2 and DEC3 by computer simulation. 17 Sum-Product Decoding of Punctured Convolutional Code for Wireless LAN
- 32. 18 Will-be-set-by-IN-TECH 1st Iteration After 1st iteration Λ1,n Λ2,n Λ3,n λ1,n λ2,n λ3,n DEC1 DEC2 DEC3 Fig. 13. Block diagram of decoder of switching parity check method for code rate 3/4 In this paper, the higher degree parity check polynomials for DEC1, DEC2 and DEC3 were selected from Table 4, Table 5 and Table 1, respectively. There are many number of combination of the higher degree parity check polynomials. Therefore, this paper searches the higher degree parity check polynomials as follows. Step.1 At first, the higher degree parity check polynomial for DEC3 is determined by decoding simulation with only DEC3. Step.2 With the determined higher degree parity check polynomial for DEC3, the higher degree parity check polynomials for DEC1 and DEC2 are determined by decoding simulation with DEC1, DEC2 and DEC3. Figure 14 shows the simulation results of Step.1 at Eb/N0 = 6[dB]. From Fig.14, it can be seen that the higher degree parity check polynomial with ν = 15 provides the best performance. Therefore, that higher degree parity check polynomial is used. Figure 15 shows the simulation results of Step.2 at Eb/N0=7[dB]. From Fig.15, it can be seen that the combination of higher degree parity check polynomials No.2 and No.5 with scaling factor fs = 0.1 provides the best performance, where scaling factor fs = 0.1 is used for DEC1 and DEC2, and DEC3 uses fixed scaling factor fs = 1. 10-5 10-4 10-3 10-2 10-1 100 6 7 8 9 10 11 12 13 14 15 16 Parity Bit Error Rate Degree of Higher Degree Parity Check Polynomial ν Fig. 14. Simulation results of step.1 in switching parity check method at Eb/N0 = 6[dB] 18 Advanced Wireless LAN
- 33. Sum-Product Decoding of Punctured Convolutional Code for Wireless LAN 19 10-7 10 -6 10-5 10 -4 10 -3 10 -2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 No.1,No.3 No.1,No.4 No.1,No.5 No.2,No.3 No.2,No.4 No.2,No.5 Parity Bit Error Rate Scaling factor fs Fig. 15. Simulation results of step.2 in switching parity check method at Eb/N0 = 7[dB] 6.2 Simulation results Simulation results are shown in Fig.16 and 17. Figure 16 shows parity bit error rate performance. From Fig.16, it can be seen that parity bit error rate performance of the switching parity check method is 3.02[dB] superior to that of the conventional method and 2.2[dB] superior to that of the single punctured bit method. Parity bit error rate performance of the switching parity check method is only 1.04[dB] inferior to that of BCJR. Figure 17 shows information bit error rate performance. From Fig.17, it can be seen that information bit error rate performance of the switching parity check method is 4.16[dB] superior to that of the conventional method and 3.05[dB] superior to that of the single punctured bit method. Information bit error rate performance of the switching parity check method is only 1.06 [dB] inferior to that of BCJR. 7. Decoding complexity Table 6 and Table 7 show the numbers of operations per one bit decoding for sum-product algorithm and BCJR, respectively. In both tables, Nadd denotes the number of additions, Nmult denotes the number of multiplications and Ntotal denotes the total number of operations. For sum-product algorithm, Nsp denotes the number of operations for tanh(·), tanh−1 (·). For BCJR, Nsp denotes the number of operations for exp(·), log(·). In Table 6, for information bits, Nadd shows the number of XOR’s. In Table 6, Nitr denotes the average number of iterations, where the number was counted at Eb/N0=6[dB] by using computer simulation. For code rate 2/3, complexity of the single punctured bit method is shown. For code rate 3/4, complexity of the switching parity check method is shown. It is necessary to notice that iteration of sum-product algorithm is required for parity bits decoding only. For the switching parity 19 Sum-Product Decoding of Punctured Convolutional Code for Wireless LAN
- 34. 20 Will-be-set-by-IN-TECH 10-6 10 -5 10 -4 10-3 10 -2 10 -1 10 0 0 1 2 3 4 5 6 7 8 9 10 11 Parity Bit Error Rate Eb/N0[dB] Switching parity check Conventional Single punctured bit BCJR Fig. 16. Parity Bit Error Rate Performance of switching parity check method 10-6 10 -5 10 -4 10-3 10 -2 10 -1 100 0 1 2 3 4 5 6 7 8 9 10 11 Information Bit Error Rate Eb/N0[dB] Switching parity check Conventional Single punctured bit BCJR Fig. 17. Information Bit Error Rate Performance of switching parity check method 20 Advanced Wireless LAN
- 35. Sum-Product Decoding of Punctured Convolutional Code for Wireless LAN 21 check method, it is necessary to notice that higher degree parity check polynomials No.2 and No.5 are used at only first iteration and after first iteration, higher degree parity check polynomials with degree ν = 15 is used. From those tables, for code rate 2/3, it can be seen that the number of operations of the single punctured bit method is 0.1 times of that of BCJR. For code rate 3/4, the number of operations of the switching parity check method is 0.2 times of that of BCJR. For the both code rates, it can be seen that the number of operations of the proposed method is much less than that of BCJR. Code rate Classification Nadd Nmult Nsp Nitr Ntotal 2/3 Parity 10 23 24 3.04 175 Info 1 0 0 1 3/4 No.2 14 31 32 1 336 No.5 14 31 32 1 ν = 15 8 19 20 3.85 Info 1 0 0 1 Table 6. Complexity of sum-product algorithm Code rate Nadd Nmult Nsp Ntotal 2/3, 3/4 640 1044 7 1691 Table 7. Complexity of BCJR 8. Conclusion This paper proposes sum-product decoding methods for the punctured convolutional codes of wireless LAN. The wireless LAN standard include the punctured convolutional codes with code rate 2/3 and 3/4. This paper proposes to decode with the higher degree parity check polynomial that satisfies single punctured bit condition as the single punctured bit method. Single punctured bit condition is the condition to include single punctured bit in parity check equation. For code rate 2/3, the performance of the single punctured bit method is 1.28[dB] superior to that of the conventional method and only 0.98[dB] inferior to that of BCJR at bit error rate 10−5. For code rate 3/4, the single punctured bit method can not provide good performance. To improve the performance, this paper proposes following method as the switching parity check method. Only at first iteration, the higher degree parity check polynomial satisfying single punctured bit condition is used to decode and after first iteration, another higher degree parity check polynomial with lower nf c without single punctured bit condition is used to decode. For code rate 3/4, the performance of the switching parity check method is 4.16[dB] superior to that of the conventional method, 3.05[dB] superior to that of the single punctured bit method and only 1.06[dB] inferior to that of BCJR. Complexity of the single punctured bit method is 0.1 times of that of BCJR for code rate 2/3. For code rate 3/4, complexity of the switching parity check method is 0.2 times of that of BCJR. For the both code rates, complexity of the proposed method is much less than that of BCJR. 9. Acknowledgment This work was supported by Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Scientific Research (C) 23560444. 21 Sum-Product Decoding of Punctured Convolutional Code for Wireless LAN
- 36. 22 Will-be-set-by-IN-TECH 10. References Benedetto, S.; Divsalar, D.; Montorsi, G. Pollara, F. (1998). Serial concatenation of interleaved codes: performance analysis, design, and iterative decoding. IEEE Trans. Inf. Theory, Vol. 44, No.3, 909-926 Berrou, C.; Glavieux, A. Thitimajshima, P. (1993). Near shannon limit error-correcting coding and decoding : Turbo-codes (1). IEEE International Conference on Communications (ICC93), 1064-1070 Berrou, C. Glavieux, A. (1996). Near optimum error correcting coding and decoding: Turbo-codes. IEEE Trans. Commun., Vol. 44, No. 10, 1261-1271 Di, C.; Proietti, D.; Telatar, E.; Richardson, T.; Urbanke, R. (2002). Finite length analysis of low-density parity-check codes, IEEE Trans. Inf. Theory, Vol.48, No.6, 1570-1579 Douillard, Catherine; Jézéquel, Michel; Berrou, Claude; Picart, Annie; Didier, Pierre Glavieux, Alain (1995). Iterative correction of intersymbol interference: Turbo-Equalization. European Trans. Telecommun., Vol.6, No.5, 507–511 Gallager, R. G. (1963). Low Density Parity Check Codes, Cambridge, MA: MIT Press Hagenauer, J.; Offer, E. Papke, L. (1996). Iterative decoding of binary block and convolutional codes. IEEE Trans. Inf. Theory, Vol. 42, No. 2, 429-445 IEEE Computer Society (2007). Part11:Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications, IEEE Std 802.11-2007 Kschischang, Frank R.; Frey, Brendan J. Loeliger, Hans-Andrea. Factor Graphs and the Sum-Product Algorithm, IEEE Trans. Inf. Theory, 498-519 Laot, Christophe; Glavieux, Alain Labat, Joël (2001). Turbo equalization: adaptive equalization and channel decoding jointly optimized, IEEE J. Selected Areas in Commun., Vol.19, No.9, 1744-1752 MacKay, D. J. C. (1999). Good error-correcting codes based on very sparse matrices, IEEE Trans. Inf. Theory, Vol. 45, No. 3, 399-431 Richardson, T. J. Urbanke, R.L. (2001). The capacity of low-density parity-check codes under message-passing decoding, IEEE Trans. Inf. Theory, Vol. 47, No. 2, 599-618 Shohon, T.; Ogawa, Y. Ogiwara, H. (2009a). Sum-Product decoding of convolutional codes, The Fourth International Workshop on Signal Design and its Application in Communications (IWSDA’09), 64-67 Shohon, T.; Razi, F.; Ogawa, Y. Ogiwara, H. (2009b). Sum-Product decoding of convolutional code for wireless LAN standard, The Fourth International Workshop on Signal Design and its Application in Communications (IWSDA’09), 68-71 Shohon, T.; Razi, F. Ogiwara, H. (2010). Sum-Product decoding of non-systematic convolutional codes, Far East Journal of Electronics and Communications, Vol.5, No.1, 25-35 22 Advanced Wireless LAN
- 37. 2 A MAC Throughput in the Wireless LAN Ha Cheol Lee Dept. of Information and Telecom. Eng., Yuhan University, Bucheon City, Korea 1. Introduction Over the past few years, mobile networks have emerged as a promising approach for future mobile IP applications. With limited frequency resources, designing an effective MAC (Medium Access Control) protocol is a hot challenge. IEEE 802.11b/g/a/n networks are currently the most popular wireless LAN products on the market [1]. The conventional IEEE 802.11b and 802.11g/a specification provide up to 11 and 54 Mbps data rates, respectively. However, the MAC protocol that they are based upon is the same and employs a CSMA/CA (Carrier Sense Multiple Access/Collision Avoidance) protocol with binary exponential back-off. IEEE 802.11 DCF (Distributed Coordination Function) is the de facto MAC protocol for wireless LAN because of its simplicity and robustness [2,3]. Therefore, considerable research efforts have been put on the investigation of the DCF performance over wireless LAN [2]. With the successful deployment of IEEE 802.11a/b/g wireless LAN and the increasing demand for real-time applications over wireless, the IEEE 802.11n Working Group standardized a new MAC and PHY (Physical) layer specification to increase the bit rate to be up to 600 Mbps [3]. The throughput performance at the MAC layer can be improved by aggregating several frames before transmission [3]. Frame aggregation not only reduces the transmission time for preamble and frame headers, but also reduces the waiting time during CSMA/CA random backoff period for successive frame transmissions. The frame aggregation can be performed within different sub-layers. In 802.11n, frame aggregation can be performed either by A-MPDU (MAC Protocol Data Unit Aggregation) or A-MSDU (MAC Service Data Unit Aggregation). Although frame aggregation can increase the throughput at the MAC layer under ideal channel conditions, a larger aggregated frame will cause each station to wait longer before its next chance for channel access. Under error- prone channels, corrupting a large aggregated frame may waste a long period of channel time and lead to a lower MAC efficiency [4]. On the other hand, wireless LAN mobile stations that are defined as the stations that access the LAN while in motion are considered in this chapter. The previous paper analyzed the IEEE 802.11b/g/n MAC performance for wireless LAN with fixed stations, not for wireless LAN with mobile stations [5, 6, 7, 8, 9, 10]. On the contrary, Xi Yong [11] and Ha Cheol Lee [12] analyzed the MAC performance for IEEE 802.11 wireless LAN with mobile stations, but considered only IEEE 802.11 and 802.11g/a wireless LAN specification. So, this chapter summarizes all the reference papers and analyzes the IEEE 802.11b/g/a/n MAC performance for wireless LAN with fixed and mobile stations. In other words, we will present the analytical evaluation of saturation
- 38. Advanced Wireless LAN 24 throughput with bit errors appearing in the transmitting channel. In Section 2, wireless LAN history and standards are reviewed. In section 3, wireless LAN access network is reviewed. IEEE 802.11b/g/a/n/ac/ad PHY and MAC layer are reviewed in Section 4. In Section 5, frame error rate of wireless channel and the DCF saturation throughput are theoretically derived. Finally, it is concluded with Section 6. 2. Wireless LAN history and standards Standards in the IEEE project 802 target the PHY layer and MAC layer. When wireless LAN was first conceived, it seemed that it would be just another PHY of one of the available standards. The first candidate considered for this was IEEE’s most prominent standard 802.3 (Ethernet). However, it soon became obvious that the radio medium is very different from the well-behaved wire. Due to tremendous attenuation even over short distances, collisions cannot be detected. Hence, 802.3’s CSMA/CD (Carrier Sense Multiple Access/Collision Detection) could not be applied. The next candidate standard to be considered was 802.4. Its coordinated medium access, the token bus concept, was believed to be superior to 802.3’s contention-based scheme. Hence, WLAN began as 802.4L. However, already in 1990 it was obvious that token handling in radio networks was difficult. The standardization body realized that a wireless communication standard would need its own very unique MAC. Finally, on March 21, 1991, project 802.11 was approved. The first 802.11 standard was published in 1997. At the PHY layer it provides three solutions: a FHSS (Frequency Hopping Spread Spectrum) and a DSSS (Direct Sequence Spread Spectrum) PHY in the unlicensed 2.4 GHz band, and an infrared PHY at 316– 353 THz. Although all three provide a basic data rate of 1 Mb/s with an optional 2 Mb/s mode, commercial infrared implementations do not exist. Similar to 802.3, basic 802.11 MAC operates according to a listen-before-talk scheme, and is known as the DCF. It implements CSMA/CA rather than collision detection as in 802.3. Indeed, as collision cannot be detected in the radio environment, 802.11 waits for a backoff interval before each frame transmission rather than after collisions. In addition to DCF, the original 802.11 standard specifies an optional scheme that depends on a central coordination entity, the PCF (Point Coordination Function). This function uses the so called PC (Point Coordinator) that operates during the so-called contention-free period. The latter is a periodic interval during which only the PC initiates frame exchanges via polling. However, the PCF’s poor robustness against hidden nodes resulted in negligible adoption by manufacturers. Having published its first 802.11 standard in 1997, the WG (Working Group) received feedback that many products did not provide the degree of compatibility customers expected. As an example, often the default encryption scheme, called WEP (Wired Equivalent Privacy), would not work between devices of different vendors. This need for a certification program led to the foundation of the WECA (Wireless Ethernet Compatibility Alliance) in 1999, renamed the WFA (Wi-Fi Alliance) in 2003. Wi-Fi certification has become a well-known certification program that has significant market impact. The tremendous success in the market and the perceived shortcomings of the base 802.11 standard provided a basis and impetus for a prolific program of improvements and extensions. This has led to revisions of the draft, driven by a complete alphabet of amendments. It is the purpose of this article to review this process and explain both the contents of these amendments and their interrelation. In the following we first describe the changes made to the PHY layer and then turn to the improvements to the MAC layer. In both, we make a distinction between what has already been accepted and what is currently in the process of being standardized [2].
- 39. A MAC Throughput in the Wireless LAN 25 Standard Spectrum Maximum physical rate Layer 2 data rate Tx Compatible with Major disadvantage Major advantage 802.11n 2.4/5 GHz 600 Mbps 100 Mbps MIMO OFDM 802.11b/g/ a Difficult to implement Highest bit rate 802.11b 2.4 GHz 11 Mbps 6-7 Mbps DSSS 802.11 Bit rate too low for many emerging applications Widely deployed, higher range 802.11g 2.4 GHz 54 Mbps 32 Mbps OFDM 802.11/ 802.11b Limited number of collocated WLANs Higher bit rate in 2.4 GHz spectrum 802.11a 5.0 GHz 54 Mbps 32 Mbps OFDM None Smallest range of all 802.11 standards Higher bit rate in less- crowded spectrum Table 1. Wireless LAN products on the market [1] 2.1 PHY related amendments Although not interoperable, the DSSS and FHSS PHY initially seemed to have equal chances in the market. The FHSS PHY even had a duplicate in the HomeRF group that aimed at integrated voice and data services. This used plain 802.11 with FHSS for data transfer, complemented with a protocol for voice that was very similar to the Digital Enhanced Cordless Telecommunications standard. Neither HomeRF nor 802.11 saw FHSS extensions, although plans for a second-generation HomeRF existed that targeted at 10 Mb/s. In contrast, the high-rate project 802.11b was started in December 1997 and boosted the data rates of the DSSS PHY to 11 Mb/s. This caused 802.11b to ultimately supersede FHSS, including HomeRF, in the market. Figure 1 provides an overview of the 802.11 PHY amendments and their dependencies [2]. Fig. 1. The 802.11 PHY layer amendments and their dependencies [2]
- 40. Advanced Wireless LAN 26 2.1.1 802.11a/g The first extension project, 802.11a, started in September 1997. It added an OFDM (Orthogonal Frequency Division Multiplexing) PHY that supports up to 54 Mb/s data rate. Since 802.11a operates in the 5 GHz band, communication with plain 802.11 devices is impossible. This lack of interoperability led to the formation of 802.11g, which introduced the benefits of OFDM to the 2.4 GHz band. As 802.11g’s extended rate PHY provides DSSS-compatible signaling, an easy migration from 802.11 to 802.11g devices became possible. During the standardization process, a single manufacturer already sold pre-802.11g chipsets. With its proprietary PBCC (Packet Binary Convolutional Code), additional data rates of 22 Mb/s and 33 Mb/s were supported. Today rarely applied, PBCC set a de facto standard and became an optional MCS (Modulation and Coding Scheme) of 802.11g. To comply with the European regulatory requirements for the 5 GHz band, 802.11h was introduced at the end of 2003. While in the United States the FCC describes absolute radio output power limits, in Europe antenna gain must not be used for transmission. Furthermore, satellite uplink and radar stations must be secured from interference. Therefore, 802.11h defines MAC mechanisms for DFS (Dynamic Frequency Selection) and TPC (Transmit Power Control), which we explain in the MAC section. Ratified in 2004, 802.11j describes the necessary means to comply with Japanese regulatory requirements for the operation of 802.11 equipment in the 4.9 GHz and 5 GHz frequency bands. Besides requirements on medium access discussed in the next section, 802.11j is the first amendment that defines PHY operation with 10 MHz bandwidth in addition to the formerly preferred 20 MHz channelization. Data Rate (Mbits/sec) Modulation Coding Rate (R) Coding Bits Per Subcarrier (NBPSC) Coded Bits per OFDM symbol (NCBPS) Data Bits Per OFDM Symbol (NDBPS) 6 BPSK 1/2 1 48 24 9 BPSK 3/4 1 48 36 12 QPSK 1/2 2 96 48 18 QPSK 3/4 2 96 72 24 16-QAM 1/2 4 192 96 36 16-QAM 3/4 4 192 144 48 64-QAM 2/3 6 288 192 54 64-QAM 3/4 6 288 216 Table 2. Parameters of the IEEE 802.11a physical layer While IEEE 802.11b uses only DSSS technology, IEEE 802.11g uses DSSS, OFDM, or both at the 2.4 GHz ISM band to provide high data rates of up to 54 Mb/s. Combined use of both
- 41. A MAC Throughput in the Wireless LAN 27 DSSS and OFDM is achieved through the provision of four different physical layers. These layers, defined in the standard as ERPs (Extended Rate Physicals), coexist during a frame exchange, so the sender and receiver have the option to select and use one of the four layers as long as they both support it. The four different physical layers defined in the IEEE 82.11g standard are the following : ERP-DSSS/CCK: This is the old physical layer used by IEEE 802.11b. DSSS technology is used with CCK modulation. The data rates provided are those of IEEE 802.11b. ERP-OFDM: This is a new physical layer, introduced by IEEE 802.11g. OFDM is used to provide IEEE 802.11a data rates at the 2.4 GHz band. ERP-DSSS/PBCC: This physical layer was introduced in IEEE 802.11b and provides the same data rates as the DSSS/CCK physical layer. It uses DSSS technology with the PBCC coding algorithm. IEEE 802.11g extended the set of data rates by adding those of 22 and 33 Mb/s. DSSS-OFDM: This is a new physical layer that uses a hybrid combination of DSSS and OFDM. The packet physical header is transmitted using DSSS, while the packet payload is transmitted using OFDM. The scope of this hybrid approach is to cover interoperability aspects, as explained later. From the above four physical layers, the first two are mandatory; every IEEE 802.11g device must support them. The other two are optional. Column 2 of Table 3 summarizes the supported data rates for the different physical layers of the IEEE 802.11g specification. Table 3. Parameters of the different IEEE 802.11g physical layers [8] 2.1.2 802.11n As the first project whose targeted data rate is measured on top of the MAC layer, 802.11n provides user experiences comparable to the well known Fast Ethernet (802.3u). Far beyond the minimum requirements that were derived from its wired paragon’s maximum data rate of 100 Mb/s, 802.11n delivers up to 600 Mb/s. Its most prominent feature is MIMO capability. A flexible MIMO (Multiple Input Multiple Output) concept allows for arrays of up to four antennas that enable spatial multiplexing or beam forming. Its most debated innovation is the usage of optional 40 MHz channels. Although this feature was already
- 42. Advanced Wireless LAN 28 being used as a proprietary extension to 802.11a and 802.11g chipsets, it caused an extensive discussion on neighbor friendly behavior. Especially for the 2.4 GHz band, concerns were raised that 40 MHz operation would severely affect the performance of existing 802.11, Bluetooth (802.15.1), ZigBee (802.15.4), and other devices. The development of a compromise, which disallows 40 MHz channelization for devices that cannot detect 20 MHz-only devices, prevented ratification of 802.11n until September 2009. As a consequence of 20/40 MHz operation and various antenna configurations, 802.11n defines a total of 76 different MCSs. Since several of them provide similar data rates, WFA’s certification program decides the MCSs finally used in the market. 802.11n’s PHY enhancements are supported by medium access enhancements we introduce in the MAC section. MCS Index Modulation Coding Rate Spatial Streams 802.11n Data Rate (Mbps) 20-MHz 40-MHz L-GI S-GI L-GI S-GI 0 BPSK 1/2 1 6.5 7.2 13.5 15 1 QPSK 1/2 1 13 14.4 27 30 2 QPSK 3/4 1 19.5 21.7 40.5 45 3 16-QAM 1/2 1 26 28.9 54 60 4 16-QAM 3/4 1 39 43.3 81 90 5 64-QAM 2/3 1 52 57.8 108 120 6 64-QAM 3/4 1 58.5 65 122 135 7 64-QAM 5/6 1 65 72.2 135 150 8 BPSK 1/2 2 13 14.4 27 30 9 QPSK 1/2 2 26 28.9 54 60 10 QPSK 3/4 2 39 43.3 81 90 11 16-QAM 1/2 2 52 57.8 108 120 12 16-QAM 3/4 2 78 86.7 162 180 13 64-QAM 2/3 2 104 116 216 240 14 64-QAM 3/4 2 117 130 243 270 15 64-QAM 5/6 2 130 144 270 300 16 BPSK 1/2 3 19.5 21.7 40.5 45 17 QPSK 1/2 3 39 43.3 81 90 18 QPSK 3/4 3 58.5 65 121.5 135 19 16-QAM 1/2 3 78 86.7 162 180 20 16-QAM 3/4 3 117 130 243 270 21 64-QAM 2/3 3 156 173.3 324 360 22 64-QAM 3/4 3 175.5 195 364.5 405 23 64-QAM 5/6 3 195 216.7 405 450 24 BPSK 1/2 4 26 28.9 54 60 25 QPSK 1/2 4 52 57.8 108 120 26 QPSK 1/2 4 78 86.7 162 180 27 16-QAM 1/2 4 104 115.6 216 240 28 16-QAM 3/4 4 156 173.3 324 360 29 64-QAM 2/3 4 208 231.1 432 480 30 64-QAM 3/4 4 234 260 486 540 31 64-QAM 5/6 4 260 288.9 540 600 Table 4. Parameters of the IEEE 802.11n physical layer, MCS Rates 0-31 [13]
- 43. A MAC Throughput in the Wireless LAN 29 2.1.3 802.11ac/ad 802.11ac and 802.11ad develop amendments that fulfill the ITU’s (International Telecommunication Union’s) requirements on proposals for the IMT Advanced standard. Both target greater than 1 Gb/s throughput, but while 802.11ac considers the traditional Wireless LAN frequencies below 6 GHz, 802.11ad competes with the Wireless Personal Area Network TG (Task Group) 802.15.3c, standard ECMA 387, and the Wireless Gigabit Alliance on the 60 GHz frequency spectrum. Due to their premature stage, both TGs are still in the process of collecting input and specific proposals from their members. At the moment of writing this article, 802.11ad has already started defining some additional requirements regarding range (at least 10 m at 1 Gb/s), seamless session transfer of an active session from the 60 GHz band to the 2.4/5 GHz band and vice versa, coexistence with other systems in the band such as 802.15.3c, and support for uncompressed video requirements such as data rate, packet loss ratio, and delay. 2.2 MAC related amendments A key element to the 802.11 success is its simple MAC operation based on the DCF protocol. This scheme has proven to be robust and adaptive to varying conditions, able to cover most needs sufficiently well. Following the trends visible from the wired Ethernet, 802.11’s success is mainly based on overprovisioning of its capacity. The available data rate was sufficient to cover the original best effort applications, so complex resource scheduling and management algorithms were unnecessary.However, this may change in the future. Because of the growing popularity of 802.11, WLANs are expected to reach their capacity limits. Moreover, applications like voice and video streaming pose different demands for quality of service. Therefore, traffic differentiation and network management might become inevitable. In the following we explain 802.11 MAC related extensions of the amendments introduced in the previous section and those shown in Fig. 2 [2]. 2.2.1 802.11e The original project goal of 802.11e, approved at the end of March 2000, foresaw general enhancements of the WLAN standard. Efficiency improvements, support for quality of service (QoS), and security enhancements were its key elements. However, already in 2001, the 802.11 frame encryption algorithm WEP was broken by an attack. Thus, security enhancements were displaced to a new TG called 802.11i. After intensive discussions, 802.11e was finally approved in 2005 to support QoS. As a new medium access scheme, 802.11e provides the HCF (Hybrid Coordination Function), where hybrid relates to HCF’s two MAC protocol versions with centralized and distributed control, respectively. The first is implemented by HCF HCCA (HCF Controlled Channel Access), an improved variant of the PCF requiring a central coordination instance that schedules medium access. Until today no device implementing HCCA is known to exist in the market. EDCA is HCF’s second MAC protocol. While DCF does not differentiate between traffic with different QoS needs, EDCA (Enhanced Distributed Channel Access) provides support for four traffic categories: voice, video, best effort, and background with different rules to access the wireless medium. Accordingly, EDCA enables service differentiation. Both centralized and distributed MAC protocols change the medium sharing rules. Without 802.11e, a WLAN provides per packet fairness: regardless of the actual frame transmission duration, devices back off after every single frame. In contrast, duration of all
- 44. Advanced Wireless LAN 30 HCCA and EDCA frame exchanges is bound by the TXOP (Transmission Opportunity) limit. Thus, devices share time slices of the wireless medium. Those that use faster MCSs may exchange multiple frames after a single successful contention and consequently achieve higher throughput. Derived from EDCA, WFA has successfully branded and introduced to the market an EDCA variant called WMM (Wi-Fi MultiMedia). WMM incorporates a subset of functions from 802.11e draft 6 (November 2003). As the final 802.11e and WMM specifications differ, some members of the 802.11 initiated a QoS Enhancement SG (Study Group) in May 2007. Its intended goal was an adaptation of the 802.11e amendment to the WMM specification. However, a project could never be approved, and the SG was dissolved in November 2007. Fig. 2. The 802.11 MAC layer amendments [2] 3. Wireless LAN access network This section shows infrastructure-based and ad hoc-based operation of wireless access architecture in the 802.11b/a/g/n-based mobile LAN. The protocols of the various layers are called the protocol stack. The TCP/IP protocol stack consists of five layers: the physical, data link, network, transport and application layers. This section is focused on physical layer and data link layer which consists of MAC and LLC (Logical Link Control) sub-layers. An ad hoc network might be formed when people with laptops get together and want to exchange data in the absence of a centralized AP (Access Point). Wireless LAN topology is ad hoc-based or infrastructure-based as shown in Fig. 3. The ad hoc-based topology shows
- 45. A MAC Throughput in the Wireless LAN 31 that each user in the wireless network communicates directly with all others without a backbone network. Infrastructure-based topology shows that all wireless users transmit to an AP to communicate with users on the wired or wireless LAN. IEEE 802.11 operates in the 2.4 GHz band and supports data rates 1 Mbps to 2 Mbps. IEEE 802.11b uses DSSS (Direct Sequence Spread Spectrum) but supports data rates of up to 11 Mbps. The modulation scheme employed is called CCK (Complementary Code Keying). The operating frequency range is 2.4 GHz and hence can interfere with some home appliances. IEEE 802.11g achieves very high data rates compared to IEEE 802.11b and uses the 2.4 GHz frequency band. An IEEE 802.11b client can operate with an 802.11g AP. IEEE 802.11a equipment is more expensive and consumes more power, as it uses OFDM (Orthogonal Frequency Division Multiplexing). OFDM uses 12 orthogonal channels in the 5 GHz range. The frequency channels are nonoverlapping. The achievable data rates are 6, 9, 12, 18, 24, 36, 48 and 54 Mbps. IEEE 802.11a and 802.11b can operate next to each other without any interference. Fig. 4 shows the IEEE 802.11b/a/g/n-based physical and MAC layer protocol stack. Applications TCP IP 802.11 MAC 802.11 PHY Applications TCP IP 802.3 MAC 802.3 PHY 802.11 MAC 802.11 PHY 802.3 MAC 802.3 PHY Server Fixed terminal Mobile terminal Backbone network Access point Applications TCP IP 802.11 MAC 802.11 PHY Applications TCP IP 802.3 MAC 802.3 PHY 802.11 MAC 802.11 PHY 802.3 MAC 802.3 PHY Server Fixed terminal Mobile terminal Backbone network Access point (a) Infrastructure-based wireless LAN (b) Ad-hoc mode operation in the wireless LAN Fig. 3. Protocol stack in the IEEE 802.11 wireless LAN [12]
- 46. Advanced Wireless LAN 32 FCS BO P-HDR IFS BitStream (PMD-SDU) IFS PLCP-PDU PLCP-SDU Preamble MAC-PDU MAC-SDU M-HDR FCS BO P-HDR IFS BitStream (PMD-SDU) IFS PLCP-PDU PLCP-SDU Preamble MAC-PDU MAC-SDU M-HDR Fig. 4. Protocol stack of physical and MAC layer [12] IEEE 802.11 protocol stack consists of MAC layer and PHY layer. When a network layer pushes a user packet down to the MAC layer as a MAC-SDU (MAC-Service Data Unit), overheads are added to the MAC layer and MAC-PDU (MAC-Protocol Data Unit) is created. The PHY layer is divided into a PLCP (Physical Layer Convergence Protocol) sublayer and a PMD (Physical Medium Dependent) sublayer. In this PHY layer, the same procedure as MAC layer is also executed. IEEE 802.11 MAC layer uses an 802.11 PHY layer, such as 802.11a/b/g, to perform the tasks such as carrier sensing, transmission, and reception of 802.11 frames. With regards to the MAC layer, the functional specifications are essentially the same for all of them with minor differences. 4. Wireless LAN PHY/MAC layer 4.1 IEEE 802.11b/a/g PHY/MAC layer When a higher layer pushes a user packet down to the MAC layer as a MAC-SDU, the MAC layer header (M-HDR) and trailer (FCS) are added before and after the MSDU, respectively and form a MAC-PDU. The PHY layer is again divided into a PLCP sub-layer and a PMD sub-layer. Similarly the PLCP preamble and PLCP header (P-HDR) are attached to the MPDU at the PLCP sub-layer. Different IFS (Inter Frame Space)s are added depending on the type of MPDU. IEEE 802.11a operates in the 5 GHz band and uses OFDM. The achievable data rates are 6, 9, 12, 18, 24, 36, 48, and 54 Mbps. 802.11g uses DSSS, OFDM, or both at the 2.4 GHz ISM band to provide high data rates of up to 54 Mbps. 802.11g device can operate with an 802.11b device. Combined use of both DSSS and OFDM is achieved through the provision of four different physical layers. The four different physical layers defined in the 802.11g standards are ERP-DSSS/CCK, ERP-OFDM, ERP-DSSS/PBCC and DSSS-OFDM. The standards that support the highest data rate of 54 Mbps are ERP-OFDM and DSSS-OFDM. ERP-OFDM is a new physical layer in IEEE 802.11g and OFDM is used to provide IEEE 802.11a data rates at the 2.4 GHz band. DSSS-OFDM is a new physical layer that uses a hybrid combination of DSSS and OFDM. The packet physical header is transmitted using DSSS, while the packet payload is transmitted using OFDM. Basic access scheme is CSMA/CA mechanism. The SIFS (Short Inter-Frame Space) and the slot time are determined by the physical layer. DIFS (Distributed Inter-Frame Space) is defined based on the above two intervals.
- 47. A MAC Throughput in the Wireless LAN 33 (a) 802.11b ERP-OFDM frame (b) 802.11a and 802.11g ERP-OFDM frame (c) 802.11g DSSS-OFDM frame Fig. 5. Frame structure of IEEE 802.11b/a/g-based wireless LAN [12] IEEE 802.11 MAC protocol supports the DCF and the PCF . The DCF uses the CSMA/CA mechanism for contention-based access, while the PCF provides contention-free access. The two modes are used alternately in time. IEEE 802.11 MAC protocol defines five timing intervals. Two of them are the SIFS and the slot time that are determined by the physical layer. The other three intervals are the PIFS (Priority InterFrame Space), DIFS and EIFS (Extended InterFrame Space) that are defined based on the above two intervals. But the PCF is restricted to infrastructure network configurations. Therefore, the DCF is widely assumed under the consideration of ad hoc-based wireless LAN. Fig. 6 shows two access schemes. IEEE 802.11 DCF stations access the channel via a basic access method or the four-way handshaking access method with an additional RTS/CTS message exchange. In the basic access method, the CSMA mechanism is applied. Stations wait for the channel to be idle for a DIFS period of time and then execute backoff for data transmission. Stations choose a random number between 0 and CW (Contention Window)-1 with equal probability as a backoff timer. When the backoff timer reaches zero, the data frame is transmitted. The receiver replies an ACK message upon successfully receiving a data packet. In the four-way handshaking access method, when the backoff timer of station reaches zero, the station first transmits a RTS frame. Upon receiving the RTS frame, the receiver replies with a CTS frame after a SIFS period. Once the RTS/CTS is exchanged successfully, the sender then transmits its data frame. The RTS and CTS frames carry a duration field, information of time interval to transmit the
- 48. Advanced Wireless LAN 34 packet. Any station receiving RTS or CTS frames can read the duration field information. That information is then used to update a NAV (Network Allocation Vector) value that indicates to each station the amount of time that remains before the channel will become idle. Therefore, a station detecting the RTS and CTS frames suitably delays further transmission, and thus avoids collision. The NAV is thus referred to as a virtual carrier sensing mechanism. The main purpose of the RTS/CTS handshaking is to resolve the so- called hidden node problem. (a) Basic access method (b) Four-way handshaking access method Fig. 6. IEEE 802.11 DCF channel access mechanism [14] Parameter 802.11b 802.11g 802.11a Tslot 20μs 9μs/20μs 9μs Τ 1μs 1μs 1μs TP 144μs 16μs/144μs 16μs CWmin 31 31/15 15 TPHY 48μs 4μs/48μs 4μs TSYM N/A N/A, 4μs 4μs TDIFS 50μs 50μs/34μs 34μs TSIFS 10μs 16μs 16μs Table 5. Parameters of IEEE 802.11b/g/a [6, 7, 8]
- 49. A MAC Throughput in the Wireless LAN 35 MAC scheme Transmission TDIFS TSIFS TBO TRTS TCTS TACK TDATA (MSDU : bytes) CSMA/CA DSSS-1 50 10 310 N/A N/A 304 192+8×(34+MSDU)/1 DSSS-2 50 10 310 N/A N/A 304 192+8×(34+MSDU)/2 HR-5.5 50 10 310 N/A N/A 304 192+8×(34+MSDU)/5.5 HR-11 50 10 310 N/A N/A 304 192+8×(34+MSDU)/11 OFDM-6 34 9 67.5 N/A N/A 44 20+4×[(16+6+8×(34+MSDU))/24] OFDM-12 34 9 67.5 N/A N/A 32 20+4×[(16+6+8×(34+MSDU))/48] OFDM-24 34 9 67.5 N/A N/A 28 20+4×[(16+6+8×(34+MSDU))/96] OFDM-54 34 9 67.5 N/A N/A 24 20+4×[(16+6+8×(34+MSDU))/216] RTS/CTS DSSS-1 50 10×3 310 352 304 304 192+8×(34+MSDU)/1 DSSS-2 50 10×3 310 352 304 304 192+8×(34+MSDU)/2 HR-5.5 50 10×3 310 352 304 304 192+8×(34+MSDU)/5.5 HR-11 50 10×3 310 352 304 304 192+8×(34+MSDU)/11 OFDM-6 34 9×3 67.5 52 44 44 20+4×[(16+6+8×(34+MSDU))/24] OFDM-12 34 9×3 67.5 36 32 32 20+4×[(16+6+8×(34+MSDU))/48] OFDM-24 34 9×3 67.5 28 28 28 20+4×[(16+6+8×(34+MSDU))/96] OFDM-54 34 9×3 67.5 24 24 24 20+4×[(16+6+8×(34+MSDU))/216] Table 6. Delay compents for different MAC schemes (unit : μs) [7] 4.2 IEEE 802.11n PHY/MAC layer The key requirement that drove most of the development in 802.11n is the capability of at least 100 Mb/s MAC throughput. Considering that the typical throughput of 802.11a/g is 25 Mb/s (with a 54 Mb/s PHY data rate), this requirement dictated at least a fourfold increase in throughput. Defining the requirement as MAC throughput rather than PHY data rate forced developers to consider the difficult problem of improving MAC efficiency. The inability to achieve a throughput of 100 Mb/s necessitated substantial improvements in MAC efficiency when designing the 802.11n MAC. Two basic concepts are employed in 802.11n to increase the PHY data rates: MIMO and 40 MHz bandwidth channels. Increasing from a single spatial stream and one transmit antenna to four spatial streams and four antennas increases the data rate by a factor of four. The term spatial stream is defined in the 802.11n standard as one of several bitstreams that are transmitted over multiple spatial dimensions created by the use of multiple antennas at both ends of a communications link. However, due to the inherent increased cost associated with increasing the number of antennas, modes that use three and four spatial streams are optional. And to allow for handheld devices, the two spatial streams mode is only mandatory in an AP. 40 MHz bandwidth channel operation is optional in the standard due to concerns regarding interoperability between 20 and 40 MHz bandwidth devices, the permissibility of the use of 40 MHz bandwidth channels in the various regulatory domains, and spectral efficiency. However, the 40 MHz bandwidth channel mode has become a core feature due to the low cost of doubling the data rate from doubling the bandwidth. Almost all 802.11n products on the market feature a 40 MHz mode of operation. Other minor modifications were also made to the 802.11a/g waveform to
- 50. Advanced Wireless LAN 36 increase the data rate. The highest encoder rate in 802.11a/g is 3/4. This was increased to 5/6 in 802.11n for an 11 percent increase in data rate. With the improvement in RF (Radio Frequency) technology, it was demonstrated that two extra frequency subcarriers could be squeezed into the guard band on each side of the spectral waveform and still meet the transmit spectral mask. This increased the data rate by 8 percent over 802.11a/g. Lastly, the waveform in 802.11a/g and mandatory operation in 802.11n contains an 800 ns guard interval between each OFDM symbol. An optional mode was defined with a 400 ns guard interval between each OFDM symbol to increase the data rates by another 11 percent. Another functional requirement of 802.11n was interoperability between 802.11a/g and 802.11n. The TG decided to meet this requirement in the physical layer by defining a waveform that was backward compatible with 802.11a and OFDM modes of 802.11g. The preamble of the 802.11n mixed format waveform begins with the preamble of the 802.11a/g waveform. This includes the 802.11a/g short training field, long training field, and signal field. This allows 802.11a/g devices to detect the 802.11n mixed format packet and decode the signal field. Even though the 802.11a/g devices will not be able to decode the remainder of the 802.11n packet, they will be able to properly defer their own transmission based on the length specified in the signal field. The remainder of the 802.11n Mixed format waveform includes a second short training field, additional long training fields, and additional signal fields followed by the data. These new fields are required for MIMO training and signaling of the many new modes of operation. To ensure backward compatibility between 20 MHz bandwidth channel devices (including 802.11n and 802.11a/g) and 40 MHz bandwidth channel devices, the preamble of the 40 MHz waveform is identical to the 20 MHz waveform and is repeated on the two adjacent 20 MHz bandwidth channels that form the 40 MHz bandwidth channel. This allows 20 MHz bandwidth devices on either adjacent channel to decode the signal field and properly defer transmission. The preamble in 802.11a has a length of 20 μs; with the additional training and signal fields, the 802.11n mixed format packet has a preamble with a length of 36 μs for one spatial stream up to 48 μs for four spatial streams. Unfortunately, MIMO training and backward compatibility increases the overhead, which reduces efficiency. In environments free from legacy devices (termed greenfield) backward compatibility is not required. By eliminating the components of the preamble that support backward compatibility, the greenfield format preamble is 12 μs shorter than the mixed format preamble. This difference in efficiency becomes more pronounced when the packet length is short, as in the case of VoIP traffic. Therefore, the use of the greenfield format is permitted even in the presence of legacy devices with proper MAC protection, although the overhead of the MAC protection may reduce the efficiency gained from the PHY. Range was considered as a performance metric in the PAR and comparison criteria. To increase the data rate at a given range requires enhanced robustness of the wireless link. 802.11n defines implicit and explicit TxBF (Transmit BeamForming) methods and STBC (Space-Time Block Coding), which improves link performance over MIMO with basic SDM (Spatial-Division Multiplexing). The standard also defines a new optional LDPC (Low Density Parity Check) encoding scheme, which provides better coding performance over the basic convolutional code. To break the 100 Mb/s throughput barrier, frame aggregation was added to the 802.11n MAC as the key method of increasing efficiency. The issue is that as the data rate increases, the time on air of the data portion of the packet decreases. However, the PHY and MAC overhead remain
- 51. Another Random Scribd Document with Unrelated Content
- 52. Den Vorsitz in der Jahresversammlung führt der Delegierte der Volkskasse oder ein in dessen Verhinderung durch die Volkskasse ernannter Stellvertreter. Der Vorsitzende bestimmt die Reihenfolge der Gegenstände der Tagesordnung. Die Beschlüsse und Wahlen der Jahresversammlung erfolgen mit einfacher Stimmenmehrheit und können, wenn sich kein Widerspruch erhebt, durch Zuruf erfolgen. Bei Stimmengleichheit gilt der Antrag als abgelehnt. Über alle Beschlüsse und Wahlen der Jahresversammlung ist ein Protokoll aufzunehmen, das vom Vorsitzenden und von sämtlichen anwesenden Mitgliedern des Vorstandsausschusses zu unterzeichnen ist. § 15. Kompetenzen der Jahresversammlung. Zur Zuständigkeit der Jahresversammlung gehört: a. Die Entgegennahme des Jahresberichts, der Jahresabrechnung sowie der Abrechnung mit der Volkskasse; Entgegennahme des Berichts über die Höhe der Ergänzungseinkommen. Jede Biene hat das Recht, hierüber Fragen zu stellen und Aufschlüsse zu verlangen. Eine Beschlußfassung darüber findet nicht statt. b. Die Beschlußfassung über Anträge des Vorstandsausschusses betreffend die Verwendung eines Teiles der Ergänzungseinkommen für die allgemeinen Zwecke und sozialen Einrichtungen des Bienenstocks. c. Die Wahl der Mitglieder des Vorstandsausschusses für das kommende Jahr, und zwar für jedes Mitglied einzeln. d. Die freie Diskussion aller aus den Kreisen der Bienen kommenden Anträge über Angelegenheiten der Volkskasse und der Bienenstöcke. Auf Wunsch kann über solche Anträge eine Probeabstimmung stattfinden um festzustellen, ob die Mehrheit für oder gegen einen solchen Antrag ist. Ein Beschluß kann jedoch nicht gefaßt werden. Die auf diese Weise zutage getretenen Wünsche dienen dem Vorstandsausschuß sowie der Volkskasse als Anregungen zur Förderung des Gesamtinteresses. Diskussionen über Fragen der Politik und Religion sind verboten. 4. Teil. Pflichten und Rechte der Bienen. § 16. Pflichten der Bienen. Solche Brüder, welche in Bienenstöcken angestellt werden, heißen Bienen. Sie werden solange als Bienen ihres Bienenstocks betrachtet, als sie von demselben Einkommen oder Anteile beziehen, gleichgültig ob aktiv oder inaktiv. Die Pflichten der Bienen sind grundsätzlich dieselben wie die der Brüder, sie sind jedoch infolge ihres besonderen Verhältnisses zum Bienenstock wesentlich erweitert. Die allgemeinsten und vornehmsten Pflichten der Bienen sind das Wirken des einzelnen für die Gesamtheit im Sinne des Solidarismus sowie unantastbare Ehrenhaftigkeit und Wahrhaftigkeit. Im besonderen haben die Bienen folgende Pflichten: 1. Zahlung eines Bienenbeitrags an die Volkskasse in Höhe von 1% sämtlicher ihnen von den Bienenstöcken als Gegenwert ihrer Arbeit ausbezahlten Beträge. 2. Beziehen ihrer Lebensbedürfnisse und sonstigen Leistungen aus Bienenstöcken, soweit dieselben hierzu ausreichen.
- 53. 3. Anerkennung des Volksvertrags, des Arbeitsvertrags der Bienenstöcke und der Arbeitsordnung des Bienenstocks, in welchem sie tätig sind, sowie Befolgung der im Interesse des Gesamtwohls vom Vorstandsausschuß ihres Bienenstocks getroffenen Anordnungen und Disziplinarvorschriften. 4. Streitigkeiten in Sachen des Volksvertrags und der Bienenstöcke den Organen der Volkskasse oder der Bienenstöcke unter Ausschluß der Gerichte vorzulegen und sich deren Schiedsspruch zu unterwerfen. 5. Alle Handlungen zu unterlassen, welche der Volkskasse, den Bienenstöcken, den Brüdern oder Bienen Nachteile bringen, und beizutragen mit voller Kraft und ganzem Können zur Förderung der Interessen und Zwecke der Volkskasse sowie zur Erreichung der größten Leistung des Bienenstocks bei geringstem Aufwande, und zur geordneten sachgemäßen Abwicklung seiner Geschäfte. 6. Auf Wunsch der Volkskasse oder des Vorstandsausschusses ihres Bienenstocks kostenlose Übernahme kleiner Ämter, welche zur Pflege des Solidarismus oder im Interesse der Organisation der Volkskasse, der Bienenstöcke oder gemeinnütziger Zwecke notwendig erscheinen, sofern sie dadurch ihren Berufspflichten nicht entzogen werden. 7. Keinerlei Provisionen, Geschenke oder Sondervorteile für ihre Mitwirkung in den Angelegenheiten der Volkskasse und Bienenstöcke anzunehmen oder zu geben. § 17. Die Bienenbeiträge. Bienen können an einem bestimmten Zeitpunkt solche volljährige Brüder sein, welche ihren Brüderbeitrag (§ 27 des Volksvertrags) wenigstens 60 Monate lang ohne Einziehung des Brüderscheins geleistet haben, und welche nach einer halbjährigen Probezeit in einem Bienenstock von dem Vorstandsausschuß desselben zu Bienen erklärt wurden. Männer können vor Erledigung ihrer Hauptmilitärpflicht nicht zu Bienen ernannt werden. Die Einzahlung der Bienenbeiträge an die Volkskasse geschieht durch den Vorstand des Bienenstocks, der zu diesem Zweck 1% aller an die Bienen als Gegenwert ihrer Arbeit zur Auszahlung gelangenden Beträge zurückbehält. Geleistete Bienenbeiträge werden niemals zurückvergütet. § 18. Bienenschein. Bienenakten. Der Bienenstock stellt jeder seiner Bienen eine Karte, Bienenschein genannt, aus, welcher bei jeder Ausübung eines Bienenrechts als Legitimation vorzulegen ist. Der Bienenschein ist persönlich und darf unter keinen Umständen abgetreten werden. Der Bienenstock legt für jede seiner Bienen einen Bienenakt an, welchem die Personalien, alle geleisteten Beiträge und erworbenen Rechte, sowie die Unterbrechungen der Beitragsleistungen und etwaige Einziehungen der Bienenscheine und deren Gründe eingetragen werden. Bemerkungen über das politische oder religiöse Bekenntnis der Bienen dürfen diese Akten nicht enthalten. Beim Austritt aus dem Bienenstock erhält die Biene gegen Auslieferung ihres Bienenscheins einen neuen Brüderschein, welcher einen vollständigen Auszug aus dem betreffenden Akt mit Ausnahme der Gründe für etwaige Einziehungen enthält, und welcher ihr als Legitimation gegenüber der Volkskasse und andern Bienenstöcken dient. Die alten Brüder- und Bienenscheine werden zu den Akten gelegt. Auf Grund dieser Akten tauscht der Bienenstock verlorne, eingezogene oder schadhaft gewordene Scheine gegen neue um. Wechselt eine Biene ihren Bienenstock, so wird deren Bienenakt dem neuen Bienenstock übergeben. § 19. Rechte der Bienen.
- 54. Die Rechte der Bienen sind grundsätzlich dieselben wie die der Brüder, sind jedoch infolge ihres besonderen Verhältnisses zum Bienenstock wesentlich erweitert. Das allgemeinste und vornehmste Recht der Bienen ist das Eintreten der Gesamtheit für jeden einzelnen im Sinne des Solidarismus. Im besonderen haben die Bienen folgende Rechte: 1. Volksräte auf Grund des Volksvertrags zu wählen und selbst zu Volksräten gewählt zu werden, und während ihrer Tätigkeit als Volksräte im vollen Bezuge ihrer Einkommen und Rechte aus ihrem Bienenstock zu bleiben. 2. Neue Bienenstöcke auf Grund des Volksvertrags und des Arbeitsvertrags der Bienenstöcke zu errichten, soweit der Stammfonds der Volkskasse jeweils für die entsprechenden Haftungen ausreicht. 3. In vorhandenen Bienenstöcken, soweit es die Verhältnisse jeweils gestatten, als Bienen angestellt zu werden. Angestellte Bienen können nur infolge Einziehung ihres Bienenscheins (§ 20) entlassen werden. Krankheit, Invalidität oder allgemeine Verhältnisse, wie Schwankungen der Konjunktur, Überproduktion u. dgl. können niemals Entlassungen von Bienen begründen, letztere werden vielmehr durch allgemeine Änderung der Arbeitszeit für alle Bienen eines Bienenstocks oder gleichartiger Bienenstöcke eines Bezirks oder des ganzen Landes nach den Beschlüssen des Volksrats unter Aufrechterhaltung der Normaleinkommen ausgeglichen. Dagegen können Bienen, wenn es die geschäftlichen Verhältnisse erfordern, in andere Bienenstöcke versetzt werden. Bienen, deren Bienenstöcke durch Feuersbrünste, Überschwemmungen oder Naturereignisse ganz oder teilweise außer Betrieb kommen, werden bis zur Wiederaufnahme des Betriebs von der Volkskasse andern Bienenstöcken zugeteilt. 4. Von den Bienenstöcken Waren und Leistungen für ihren eigenen Bedarf und denjenigen ihrer unter 17 Jahre alten Angehörigen zu Bienenpreisen gegen Barzahlung zu erhalten, soweit die vorhandenen Bienenstöcke solche zu liefern imstande sind, und zwar in der Reihenfolge der Anmeldung. Bienenpreis einer Ware ist derjenige Preis, welcher entsteht aus der Verteilung der gesamten Betriebskosten des Bienenstocks auf die Arbeitsprodukte desselben, also der wirkliche Selbstkostenpreis. 5. Lieferungen und Leistungen für Bienenstöcke auszuführen, soweit solche zu vergeben sind. 6. Die Volkskasse zur Verwaltung ihrer Gelder und als Sparkasse für ihre Ersparnisse zu benutzen gegen Auszahlung des vollen sich hieraus ergebenden Zinsertrages. 7. In den Genuß aller Vorteile zu treten, welche durch das Bestehen des Volksvertrags und des Arbeitsvertrags der Bienenstöcke für Brüder und Bienen vorhanden sind oder sein werden. 8. Bei Streitigkeiten in Sachen des Volksvertrags und der Bienenstöcke kostenlosen Schiedsspruch durch die Organe der Volkskasse und der Bienenstöcke zu erlangen. 9. Eine bestimmte Anzahl von Beamten, Meistern und Arbeitern ihres Bienenstocks in den Vorstandsausschuß desselben zu wählen bzw. in diesen Vorstandsausschuß gewählt zu werden. 10. Auf richtige und rechtzeitige Auszahlung der mit ihren Bienenstöcken vereinbarten Normaleinkommen unter allen Umständen, ausgenommen bei Arbeitseinstellungen infolge von Kriegen, Revolutionen und Streiken. In diesen Ausnahmefällen beschließt der Volksrat darüber, ob eine gänzliche oder zeitweise Aufhebung, oder eine allgemeine, gleichmäßig verteilte Reduktion der Normaleinkommen stattfinden muß. Die Normaleinkommen der Bienen werden zwischen diesen und dem Vorstand des Bienenstocks frei vereinbart und der Genehmigung des Vorstandsausschusses unterbreitet. Dabei sind die Fähigkeiten, das Verhalten und die Leistungen der Bienen, d. h. der Nutzen, den sie der Gesamtheit zu leisten imstande sind, ausschlaggebend. Akkordarbeit ist dabei nicht ausgeschlossen, sie gibt der Biene im Gegenteil Gelegenheit zur Betätigung ihrer Talente und zur Erhöhung ihres Normaleinkommens und damit aller andern Bezüge, welche demselben proportional sind. Mit der zunehmenden Gesamtzahl der Dienstjahre in Bienenstöcken soll (wenn nicht
- 55. ausnahmsweise ganz besondere Gründe vorliegen) keine Abnahme der Normaleinkommen eintreten, da die Gesamtzahl der Dienstjahre als Biene als ein der Gesamtheit geleisteter Dienst anerkannt wird. 11. Auf einen jährlichen, bei der Anstellung der Biene zu vereinbarenden Erholungsurlaub bei Fortbezug der Normaleinkommen, zu einem von dem Vorstand zu bestimmenden Zeitpunkte. 12. Auf richtige und rechtzeitige Auszahlung nach der jeweiligen Jahresversammlung ihres Bienenstocks der Ergänzungseinkommen, soweit solche vorhanden, nach Maßgabe dieses Arbeitsvertrags. 13. Während militärischer Übungen in Friedenszeiten, Krankheiten, Wochenbetten und Folgen von Unfällen auf einen Zuschuß in der Höhe der Hälfte ihrer Normaleinkommen, sowie freie ärztliche Behandlung zu Hause oder in den Krankenhäusern des Bienenstocks; ferner kostenlose Arzneien und Krankengeräte. Dieser Zuschuß beginnt mit dem Tage des Aufhörens des Normaleinkommens und endet mit der Erklärung des Chefarztes ihres Bienenstocks, daß die Krankheit zu Ende oder Invalidität eingetreten ist. Die Krankheits- und Unfallszuschüsse, zu welchen auch die Anteile für Invalidität infolge von Unfällen im Dienste gehören, kommen ebenfalls unter allen Umständen, ausgenommen bei Arbeitseinstellungen infolge von Kriegen, Revolutionen und Streiken zur Auszahlung. 14. Im Falle der Invalidität und bei Erreichung des Seniorenalters auf einen jährlichen Invaliditäts- bzw. Seniorenanteil, dessen Höhe abhängt von der Anzahl der aktiven Dienstjahre als Biene in Bienenstöcken, und dessen Maximalhöhe, wie folgt, festgesetzt ist: 1. bis 5. Dienstjahr 0,4 des letzten Normaleinkommens 6. 10. 0,5 11. 15. 0,6 16. 20. 0,7 21. 30. 0,8 31. 44. 0,9 über 44 1,0 Bei Berechnung der Dienstjahre kommen Unterbrechungen durch Urlaub, Krankheit und militärische Übungen im Frieden nicht in Abzug. Diese Maximalsätze werden nur dann ausbezahlt, wenn der Anteilfonds der Volkskasse dazu ausreicht. Andernfalls werden die Sätze für alle Bienenstöcke gleichmäßig prozentual herabgesetzt. (§ 5 des Volksvertrags.) Der Invaliditätsanteil beginnt mit dem Tage der Feststellung der Invalidität durch den Chefarzt des Bienenstocks und endet mit dem Aufhören der Invalidität ebenfalls nach der Erklärung desselben. Der Seniorenanteil beginnt mit dem vollendeten 65. Lebensjahr (Seniorenalter) und endet mit dem Tode. Weist der Anteilfonds der Volkskasse dauernde und beträchtliche Überschüsse auf, so können dieselben verwendet werden zur langsamen, gleichmäßigen Herabsetzung des Seniorenalters. 15. Witwen von männlichen Bienen haben das Recht, bis zu ihrem Tode oder ihrer Wiederverehelichung auf einen Witwenanteil in der Höhe von 0,4 der Normaleinkommen ihrer Männer im Augenblicke ihres Todes, wenn sie aktiv waren, bzw. des Invaliditäts- oder Seniorenanteils, wenn sie im Genuß solcher waren. Jedes von einer männlichen Biene hinterlassene Kind hat das Recht, bis zur Großjährigkeit bzw. bei Töchtern bis zu ihrer Verheiratung auf 1 /4 des Witwenanteils. Der Anteil für Witwen und Waisen zusammen darf 0,8 des Normalbezugs des verstorbenen Manns nicht überschreiten. Diese Anteile beginnen mit dem Tage, welcher auf den Tod des Mannes folgt. Sie werden nur an solche Witwen ausbezahlt, welche an diesem Tage Schwestern sind, und nur an solche Waisenkinder, welche an diesem Tage entweder noch nicht das 17. Lebensjahr erreicht haben, oder, falls sie es überschritten haben, Brüder sind. 16. Doppelwaisen von Bienen haben das Recht, auf Kosten des Bienenstocks bis zur ausreichenden Erwerbsfähigkeit, spätestens Großjährigkeit erzogen zu werden, wobei dieselben Bedingungen maßgebend sind wie für einfache Waisen.
- 56. 17. Im Falle ihres Todes auf Kosten des Bienenstocks bestattet zu werden, und zwar für alle Bienen in gleichen Formen. 18. Sämtliche Auszahlungen an aktive und inaktive Bienen bzw. deren Witwen und Waisen erfolgen durch denjenigen Bienenstock, deren Mitglieder sie sind bzw. zuletzt waren. § 20. Unterbrechung der Bienenrechte. Einziehung des Bienenscheins. Der Arbeitsvertrag der Bienenstöcke ist ein freier und seitens der Bienen freiwillig eingegangen. Die Nichterfüllung der in § 16 aufgezählten Bienenpflichten bedeutet demnach freiwilligen Austritt aus dem Arbeitsvertrag und Verzicht auf die Bienenrechte. In diesem Fall hat derjenige Beamte der Volkskasse oder des Bienenstocks, bei welchem in Ausübung seines Amts und bei Ausübung eines Bienenrechts die Nichterfüllung der Bienenpflicht stattfindet, den Bienenschein der betreffenden Bienen einzuziehen. Letztere können dagegen Einspruch bei dem Delegierten ihres Bienenstocks erheben. Dieser legt den Fall demjenigen unbeteiligten Bienenstock seines Bezirks vor, welcher darüber am besten zu urteilen in der Lage ist, und dessen Vorstandsausschuß in kürzester Frist in erster und letzter Instanz in einer Plenarsitzung darüber entscheidet, wobei die betroffenen Bienen auf ihren Wunsch gehört werden müssen. Zweifelhafte Fälle und solche, welche offensichtlich aus Unkenntnis, Irrtum und ohne Absicht stattfanden, sind stets zugunsten der betroffenen Bienen auszulegen. Bei Bestätigung der Einziehung wird der Grund derselben in die Bienenakten eingetragen, der Bienenschein eingezogen und durch Aufstemplung des Buchstaben E entwertet. Die bis zum Tage der Einziehung des Bienenscheins erworbenen Rechte können unter keinen Umständen entzogen werden. Dagegen können die Bienen freiwillig darauf verzichten. Nach Einziehung des Bienenscheins kann die Eigenschaft als Biene laut § 17 durch 60 Monate langes Einzahlen eines Brüderbeitrags an die Volkskasse ohne neuerliche Einziehung wieder erworben werden. Der entscheidende Vorstandsausschuß hat jedoch das Recht, je nach dem Sachverhalt sofort beim Schiedsspruch oder später die Bienenrechte schon nach 20 oder 40, statt 60 Monaten wieder zuzulassen. 5. Teil. Pflichten der Bienenstöcke zur Volkskasse und unter sich. § 21. Pflichten zur Volkskasse. Jeder Bienenstock übernimmt bei seiner Errichtung die Pflichten einer Filiale der Volkskasse und hat die in seinem Wirkungskreis liegenden Geschäfte der Volkskasse auf seine Kosten aber unter Leitung des Delegierten der Volkskasse zu besorgen. Zu diesem Zwecke hat er dem Delegierten die erforderlichen Räume, Beamten und sonstigen Hilfsmittel unentgeltlich zu liefern. Wenn mehrere Bienenstöcke einen gemeinsamen Delegierten haben, so teilen sie die Kosten der Geschäftsführung der Delegierten pro rata ihrer Bienenzahl. § 22. Gegenseitige und gemeinsame Bezüge von Waren und Leistungen. Ein Bienenstock darf Waren und Arbeiten grundsätzlich nur an Bienenstöcke, Bienen und Brüder liefern oder nur von solchen beziehen und zwar nur zu Bienenpreisen. Nur wenn die Zahl und Leistungsfähigkeit der Bienenstöcke, Bienen und Brüder hierzu nicht ausreicht, darf der Bienenstock mit andern Firmen und Personen abschließen, wobei die Bienenpreise nicht maßgebend sind. Die Bienenstöcke dürfen für Arbeiten ihres laufenden Betriebes nur Bienen beschäftigen; die Zuziehung der Heimarbeit ist verboten.
- 57. Für die Beschaffung derjenigen Materialien, Rohstoffe und Leistungen, welche für mehrere Bienenstöcke dieselben sind, haben dieselben eine gemeinsame Geschäftsstelle zu halten oder einen der Bienenstöcke mit dem gemeinsamen Bezug zu beauftragen. Die Kosten werden pro rata der bezogenen Mengen auf die beteiligten Bienenstöcke verteilt. § 23. Gegenseitige Tauschlager. Jeder Bienenstock hat ein Lager seiner eigenen Produkte und der laufenden Lebensmittel und Gebrauchsgegenstände aus andern Bienenstöcken (mit der Beschränkung des § 21 auch aus andern Quellen) zu halten und den Bienen und Brüdern zu Bienenpreisen abzugeben. Durch diese Lager tauschen die Bienenstöcke ihre Arbeitsprodukte gegenseitig gegen Verrechnung zu Bienenpreisen aus, sie heißen daher Tauschlager. Mehrere örtlich nicht zu weit voneinander entfernte Bienenstöcke können ein Tauschlager gemeinsam halten bzw. getrennte Warengattungen führen, die sich gegenseitig ergänzen. Die Volkskasse entscheidet im Einzelfall, ob dies zulässig ist. Solche Waren, welche nicht auf Lager gehalten werden können, hat jeder Bienenstock auf Verlangen der Bienen oder Brüder zu Bienenpreisen zu besorgen. Für solche Waren, deren Verkauf nicht durch unmittelbare Lieferung erfolgt, soll statt des Tauschlagers ein bloßes Musterlager gehalten werden, nach dessen Mustern die bestellten Waren in kürzester Lieferfrist geliefert werden. Jeder Bienenstock hat somit den andern Bienenstöcken als kostenlose Absatzstelle ihrer Waren zu dienen. § 24. Allgemeine Gegenseitigkeitsverpflichtungen. Die Gegenseitigkeit der Leistungen und Unterstützungen ist im weitesten Sinne aufzufassen, findet also auch statt für Vertretungen, Auskünfte, für die Auszahlung der Zinsen, Rückzahlung der Schuldscheine und sonstige Geldoperationen und geschäftliche Erledigungen aller Art, jeweils gegen Verrechnung der erwachsenden Selbstkosten. Im Zweifelsfalle entscheidet über den Umfang dieser Gegenseitigkeitspflichten die Volkskasse. Die Bildung von Ringen, Syndikaten, Trusts zwischen mehreren Bienenstöcken oder Gruppen von Bienenstöcken ist untersagt. 6. Teil. Die sozialen Einrichtungen der Bienenstöcke. § 25. Allgemeine Grundsätze. Die Aufgabe des Bienenstocks gegen seine Bienen ist nicht erschöpft mit der Erhöhung des Einkommens durch Auszahlung des vollen Betriebserträgnisses, mit der Verminderung der Ausgaben durch die Verteilungslager zu Bienenpreisen und mit dem Schutze der Bienen gegen natürliche Ungleichheiten und soziale Schädlichkeiten durch seine vorsorglichen Bestimmungen. Der Bienenstock hat außerdem die Pflicht, alle diejenigen Einrichtungen zu treffen, welche das Familienleben heben, die Mühe und Sorge des Haushaltes sowie des Unterrichts und der Erziehung der Kinder erleichtern und im weitesten Sinne für das körperliche, geistige und sittliche Wohl der Bienen zu sorgen. Die in diesem Arbeitsvertrag vorgeschriebenen, für alle Bienenstöcke obligatorischen Einrichtungen sind nur die wichtigsten zur Erreichung dieser Ziele; dieselben sollen mit den Fortschritten der Zeit vermehrt, verbessert und vervollständigt werden im Sinne des Solidarismus. Diese Einrichtungen können je nach der Sachlage jeweils einem einzigen Bienenstock oder mehreren, örtlich nicht weit getrennten Bienenstöcken gemeinsam gehören, letzteres jedoch nur ausnahmsweise,
- 58. bei kleinen Betrieben und mit Zustimmung des Direktoriums der Volkskasse. Sämtliche hierher gehörende Einrichtungen der Bienenstöcke stehen den Bienen der betreffenden Bienenstöcke und ihren Familienmitgliedern zur Verfügung: letztere, falls über 17 Jahre alt, müssen sich jedoch durch ihren Brüderschein legitimieren. Die Brüder haben gegen Vorzeigung ihres Brüderscheins ebenfalls das Recht der Benutzung, soweit die Verhältnisse es jeweils gestatten. § 26. Einrichtungen für das körperliche Wohl. a. Ernährung. Jeder Bienenstock hat eine geräumige, helle, gut ventilierte und geheizte Speiseanstalt zu errichten, in welcher den Benutzern nahrhafte, wohlschmeckende, gut zubereitete Speisen zu Bienenpreisen verabfolgt werden, und in welchen Speisewärmer kostenlos für diejenigen vorhanden sind, welche ihre Speisen selbst mitbringen. Die Abgabe von Tee und Kaffee als Getränk hat darin unentgeltlich stattzufinden. Auch muß dort gesundes Trinkwasser beliebig zur Verfügung stehen. b. Wohnung. Der Bienenstock hat für gesunde, helle, luftige und geräumige Wohnungen für seine Bienen, sei es in eigenen oder fremden Bauten zu sorgen und dieselben zu Bienenpreisen zu vermieten, aber niemals zu verkaufen; auf Versorgung mit gutem Wasser und guter Beleuchtung ist dabei hauptsächlich zu achten. Auch zur Beschaffung behaglicher und praktischer Wohnungseinrichtungen zu Bienenpreisen hat der Bienenstock mitzuwirken. Für ledige Bienen, sowohl Männer als Frauen, sind Logierhäuser oder Heime anzulegen, welche ebenfalls zu Bienenpreisen benutzbar sind. c. Gesundheitspflege. Jeder Bienenstock hat ein vorzüglich eingerichtetes Krankenhaus zu errichten mit Instrumentarium, Apotheke, Krankenwagen oder Bahre, Medizinalbädern, Desinfektionsapparat etc. Dasselbe soll eine getrennte Abteilung für Wöchnerinnen in Verbindung mit einem Säuglingsheim haben, in welchen die Aufnahmen ohne Unterscheidung der Ehelichkeit oder Unehelichkeit stattfinden. Da, wo dieses Krankenhaus nicht auf dem Grundstück des Bienenstockes steht oder sich nicht nahe genug befindet, ist im Bienenstock ein Verbandslokal anzulegen (Samariterstube), welches nur diesem Zwecke dient, mit den nötigen Betten, Instrumenten und Geräten. Diese Anstalten stehen unter der Leitung eines oder mehrerer Ärzte, welche vom Bienenstock fest angestellt sind und zu demselben im Verhältnis der Bienen stehen müssen. Ein Arzt kann auch mehreren Bienenstöcken angehören. Diese Ärzte haben zu festgesetzten Zeiten, während der Arbeitszeit der Bienen, Sprechstunde am Sitz des Bienenstocks zu halten und die sich meldenden Kranken im Krankenhaus des Bienenstocks oder zu Hause zu pflegen. Keine Kategorie von Krankheiten ist hiervon ausgeschlossen. Sie haben ferner die Hygiene der Wohnung und der Ernährung der Bienen und die Gesundheit der Kinder derselben laufend zu überwachen, denselben mit Rat und Tat beizustehen und ihr Hauptaugenmerk auf das Verhüten der Krankheiten, insbesondere der Betriebskrankheiten, sowie auf die Unfallverhütung zu lenken. Sie haben als Hausfreunde aufklärend und erzieherisch zu wirken und das höchste Gut der Bienen, ihre Gesundheit, zu hüten. Sie haben ferner die Hygiene sämtlicher Betriebe des Bienenstocks sowie seiner Schulen und Erziehungsanstalten laufend zu überwachen und eine Statistik der Hygiene ihres Bienenstocks zu führen. Die Ärzte werden hierbei unterstützt durch fest angestellte Pflegeschwestern und Heilgehilfen sowie im Nebenamt durch eine Anzahl Bienen des Bienenstocks, welche im Samariterdienst ausgebildet sind. Zu den obligatorischen Hygienemaßnahmen der Bienenstöcke gehören noch die vollkommensten Einrichtungen zur Verhütung von Unfällen und zur Verhütung der Betriebskrankheiten, gesonderte Umkleide- und Waschräume für die Bienen, sowie Dusche-, Wannen- und Schwimmbäder; endlich Spiel- und Turnplätze, möglichst in Verbindung mit den Schulen. Der Bienenstock hat alljährlich eine möglichst große Anzahl von Kindern in Ferienkolonien zu schicken. Ferner sollen die Bienenstöcke möglichst Genesungsheime für Rekonvaleszenten errichten. Die Benutzung sämtlicher Hygieneeinrichtungen sub c. ist kostenlos, nur für die Ferienkolonien können die beteiligten Eltern, eventuell auch der Stipendienfonds, zu Beiträgen herangezogen werden.
- 59. § 27. Einrichtungen für das geistige und sittliche Wohl. a. Erziehung, Unterricht und Fortbildung. Die Bienenstöcke haben zur kostenlosen Benutzung zu halten: 1. Kinderhorte und Kleinkinderschulen; 2. Elementarschulen, da wo die vorhandenen Volksschulen nicht ausreichen oder zu weit entfernt sind; 3. gesonderte Lehrlingswerkstätten mit bezahlten Lehrlingen in obligatorischer Verbindung mit Fortbildungsschulen, deren Kurse nur in den Tagesstunden stattfinden; 4. Haushaltungsschulen für nicht mehr schulpflichtige Mädchen in Verbindung mit den Heimen für ledige weibliche Bienen; 5. Schulen für weibliche Erwerbsarbeiten für nicht mehr schulpflichtige Mädchen, zugleich Näh- und Strickschule für schulpflichtige Mädchen, deren Kurse nur in den Tagesstunden stattfinden dürfen; 6. an den Abenden und eventuell Sonntags Vortragszyklen (möglichst mit Projektionen) oder sonstigen anschaulichen Vorführungen für Erwachsene über nützliche und bildende Themen, z. B. Samariterwesen und Krankenpflege, Literatur, Volkswirtschaft, Geschichte, Kunst und Kunstpflege etc., in erster Linie aber über das Wesen und den Nutzen des Solidarismus; 7. eine Bibliothek guter Bücher. Sämtliche Schulen und Vorträge werden gehalten teils von hierzu speziell angestellten Bienen, teils von dem Personal der Bienenstöcke im Nebenamt. b. Geselligkeit und Erholung. Jeder Bienenstock hat zur Pflege des Gefühls der Zusammengehörigkeit und der Einigkeit einen Gesellschaftssaal oder ein Gesellschaftshaus zu errichten mit Restaurant und möglichst mit Garten zur kostenlosen Benutzung entweder für einzelne oder für zwanglose Zusammenkünste geselliger Vereinigungen und zur Veranstaltung von bildenden Unterhaltungen, Theatervorstellungen, Musik- und Gesangsvorträgen, sowie von Spielen, Turn- und Sportübungen und Ausflügen. Es soll hiermit verbunden sein ein Lesezimmer mit guten Zeitschriften und Büchern. Im Restaurant des Gesellschaftshauses werden Speisen und Getränke zu den Bedingungen des § 26 a verabreicht. § 28. Stipendienfonds. Der Stipendienfonds des Bienenstocks dient für solche Zwecke, welche im Arbeitsvertrag nicht speziell vorgesehen sind, insbesondere für folgende: Ermöglichung höherer Studien für besonders hervorragende Leute, Studienreisen und Ausstellungsreisen für Ausbildung in speziellen Fragen oder Branchen, Unterstützungen bei ungewöhnlich schweren Umständen, zur Erhöhung von Senioren-, Invaliditäts-, Witwen- und Waisenanteilen in den Übergangszeiten, solange die Dienstzeiten noch nicht lange genug sind, um zu genügend hohen Anteilen zu berechtigen, Unterstützung solcher Kranker oder Erholungsbedürftiger, welche besonders lange, kostspielige oder auswärtige Kuren gebrauchen, Beteiligung an Ferienkolonien, eventuell Beteiligung an gemeinnützigen Bestrebungen, welche nicht direkt mit der Volkskasse und den Bienenstöcken zusammenhängen. Über die Verwendung des Stipendienfonds beschließt der Vorstandsausschuß des Bienenstocks. Entsprechend den rein wirtschaftlichen Zwecken des Bienenstocks dürfen hierbei niemals gesonderte konfessionelle oder politische Interessen unterstützt werden. 7. Teil. Übergangsbestimmungen.
- 60. § 29. Da der gegenwärtige Text des Arbeitsvertrages voraussetzt, daß sowohl die Volkskasse als eine größere Anzahl von Bienenstöcken mit ihrer gesamten Organisation schon bestehen, so sind für den Anfang, solange das noch nicht der Fall ist, besondere Übergangsbestimmungen erforderlich, welche sich auf die ersten Maßnahmen zur Herbeiführung dieser Organisationen selbst bis zu ihrem völligen Funktionieren beziehen. Diese Bestimmungen können hier nicht im einzelnen gegeben werden, da sie von den jeweiligen Verhältnissen abhängen. Sie werden sich u. a. beziehen auf den Anstellungsmodus der ersten Bienen, bevor die Beiträge während der vorgeschriebenen Anzahl Monate geleistet werden konnten u. dgl.
- 62. Fußnoten [1] Statistischen Beweis hierfür siehe Anhang 1, Seite 71. [2] Dieser Arbeitsvertrag der Bienenstöcke kommt im nächsten Kapitel zur Besprechung. [3] Statistischen Beweis hierfür siehe Anhang 2, Seite 73. [4] Andere, weniger wichtige Formen von Bienenstöcken siehe Anhang 3, S. 74. [5] Schmoller. [6] Siehe Anhang 4, Seite 75. [7] Das Warenhaus als Privatunternehmen hat keinen gemeinnützigen Zweck; es ist hier bloß erwähnt um zu beweisen, daß die Technik des Betriebes großer Warenlager etwas durchaus bekanntes, keinerlei Schwierigkeiten bietendes ist. [8] Siehe Anhang 5, Seite 77. [9] Beweis hierfür siehe Anhang 6, Seite 78. [10] Siehe Anhang 5, Seite 77. [11] Siehe Anhang 7, Seite 82. [12] Der Gesamtschaden des großen amerikanischen Kohlenarbeiterstreiks 1902 betrug nach der offiziellen Feststellung durch das Schiedsgericht 396 Millionen Mark, der amerikanische Stahlarbeiterstreik 1901 kostete 100 Millionen Mark, der belgische Generalstreik im Jahre 1902: 3 Millionen Franks täglich. [13] Siehe Anhang 8, Seite 83. [14] Siehe Anhang 9, zwischen Seite 84 und 85. [15] Durchschnittlicher Jahreslohn 700-1000 Mark. Siehe Anhang 1, Seite 71. [16] Siehe Anhang 8, S. 83. [17] Siehe Anhang 6, Seite 78. [18] Siehe Anhang 1, Seite 71. [19] Siehe Anhang 1, Seite 71.
- 63. [20] Siehe Anhang 6, Seite 78. [21] Vorbilder dazu sind schon vorhanden bei einigen englischen Genossenschaften, welche ganze Stadtanleihen übernommen haben. [22] Siehe Anhang 1, Seite 71, und Anhang 6, Seite 78. [23] Diese Summe von 200 Mark als Gesamt-Jahresausgabe pro Kopf im Mittel dürfte wohl wesentlich zu niedrig gegriffen sein. [24] Nach der Zeitschrift des Kgl. Preußischen Statistischen Bureaus 1902. [25] Der Rest von M. 1191990 wahrscheinlich für Tantiemen, Vorträge etc. verwendet. [26] Siehe Beilage Nr. 1 zum Volksvertrag. [27] Beispiel: Bei 9 Volksräten müssen mindestens 7 anwesend sein, denn 3 /4 × 9 = 63 /4, aufgerundet auf 7. – Bei 10 Volksräten müssen 8 anwesend sein, denn 3 /4 × 10 = 71 /2, aufgerundet auf 8. – Bei 11 Volksräten ebenfalls 8, denn 3 /4 × 11 = 81 /4, abgerundet auf 8. [28] Um die verschiedenen Kategorien von Beamten in ihrem Verhältnis zur Volkskasse zu unterscheiden, genügt es, einfach Ordnungszahlen einzuführen und z. B. einen Anfänger oder Lehrling als Primus, einen ungelernten Gehilfen oder Handlanger als Sekundus, das gelernte laufende Personal für die niederen Arbeiten als Tertius, einen Vorarbeiter oder mittleren Verwaltungsbeamten als Quartus zu bezeichnen u. s. w. bis hinauf zu dem höchsten leitenden Beamten oder Dezimus. Mehr als zehn Stufen sind nicht erforderlich. Diese oder ähnliche Worte bezeichnen genau das Verhältnis zur Gesamtverwaltung, ohne die Bedeutung eines Titels zu haben oder als solche gebraucht werden zu können. [29] Muster eines Brüderscheins siehe Beilage Nr. 2 zum Volksvertrag. [30] Senioren sind diejenigen Bienen, welche durch die Zahl ihrer Dienstjahre das Recht erworben haben, ihr volles Normaleinkommen weiter zu beziehen ohne zu arbeiten. Es ist damit nicht notwendig der Begriff des Alters zu verbinden. Die Senioren sind infolge ihrer Dienste eine Art Ehrenmitglieder der Bienenstöcke. [31] Um die verschiedenen Kategorien von Bienen in ihrem Verhältnis zum Bienenstock zu unterscheiden, genügt es, einfache Ordnungszahlen einzuführen, z. B. einen Anfänger oder Lehrling als Primus, einen ungelernten Gehilfen oder Handlanger als Sekundus, einen gelernten Handwerker als Tertius, einen Vorarbeiter als Quartus usw. zu bezeichnen, bis etwa hinauf zu dem höchsten leitenden Beamten, welcher ein Dezimus wäre. Dieselben Bezeichnungen wären in analoger Weise auf die Verwaltungsbeamten
- 64. anzuwenden. Mehr als zehn Stufen sind nicht erforderlich. Diese oder ähnliche Worte bezeichnen genau das Verhältnis zur Gesamtverwaltung, ohne die Bedeutung eines Titels zu haben oder als solcher gebraucht werden zu können. Anmerkungen zur Transkription: In Dieser Vertrag heißt »Arbeitsvertrag der Bienenstöcke«. stand nach Arbeitsvertrag ein zusätzliches schließendes Anführungszeichen. Dieses wurde entfernt, da der ganze Terminus gesperrt gedruckt und von Anführungszeichen umschlossen ist. In Diese Wohnungen dürfen niemals an die Bienen verkauft werden, um ein Abhängigkeitsverhältnis derselben vom Bienenstock zu vermeiden. stand Anhängigkeitsverhältnis und wurde zu Abhängigkeitsverhältnis geändert.
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