IRJET- Review Paper on Study of Various Interleavers and their Significance

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 05 Issue: 10 | Oct 2018 www.irjet.net p-ISSN: 2395-0072
© 2018, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 430
Review paper on study of various Interleavers and their significance
Bobby Raje1, Karuna Markam2
1,2Department of Electronics, M.I.T.S, Gwalior, India
---------------------------------------------------------------------------------***------------------------------------------------------------------------------------
Abstract:- In digital communication, reliable
communication can be performed by reducing the
bandwidth in order to fulfill the Shannon’s channel
capacity rule but if the bandwidth is reduced than it limits
the data throughput. By introducing concept of interleaver
in encoders and decoders, this problem can be solved and
then it is not required to reduce bandwidth. The task is to
choose an optimum interleaver technique with change in
word length of information bits for best performance of
turbo codes. The different types of Interleavers has been
studied in this paper to understand pros and cons of
different interleaver. The placement of interleaver in turbo
encoder and decoder is also discussed. The difference
between convolution and block codes is studied to find the
advantages of convolution code against block codes.
Quality parameters like BER (bit error rate) and BER curve
are also studied to understand how to compare the quality
of communication on application of different Interleavers.
Keywords: Turbo Convolutional Codes (TCC), BS (Base
Station), MS (Mobile Stations), MAP (Maximum a
posteriori probability), QPP (Quadrature Permutation
Polynomials), RSC (Recursive Systematic Convolution),
BER (Bit error rate), Interleaver, Random interleaver, SNR
(Signal to noise ratio).
1. INTRODUCTION
In 1948, Shannon predicted that reliable communications
are achievable with the use of channel coding specially by
adding redundant information to the transmitted
messages. However, Shannon did not propose explicit
channel coding schemes for practical implementations.
Furthermore, although the amount of redundancy added
increases as the associated information delay increases, he
did not specify the maximum delay that may have to be
tolerated, to be able to communicate near the Shannon’s
limit. In recent years, researchers have been trying to
reduce the amount of latency inﬂicted by using turbo
codec’s interleaver that has to be tolerated for the sake of
attaining a given target performance.
Since the introduction of TCC in 1993, they have received
considerable attention as its performance is near the
Shannon capacity limit. TCC consists of an interleaver
which separates two-parallel concatenated convolutional
codes [1].
There are two classical kinds of interleaver, commonly
referred to as block and convolutional. In a block
interleaver, the input data is written along the rows of a
memory configured as a matrix, and then read out along
the columns. A variation of a block interleaver is a
pseudorandom block interleaver, in which data is written
in memory in sequential order and read in a
pseudorandom order. In a convolutional interleaver, the
data is multiplexed into and out of a fixed number of shift
registers [4].
Figure 1. Interleaving
Interleaving is a process of rearranging the ordering of a
data sequence in a one to one deterministic format
implemented at transmitter side and the inverse of this
process is called deinterleaving which restores the
received sequence to its original order which occurs at
receiver side as shown in Figure 1. Interleaving is a
practical technique to improve the error correcting
capability of coding.
2. INTERLEAVER
2.1. RANDOM INTERLEAVER
For the implementation of random interleaver, the BS
must accommodate a huge amount of memory for storing
the random patterns of interleaver, and this results in
serious concern of storage when it is required to entertain
a large quantity of users. Apart from it, during the initial
link of setting-up phase, there should be messages assign
between the BS and MS to inform each other about their
respective interleaver. Random interleaver scrambles the
data of different users with different pattern. Because of
the scrambling of data, considerable amount of bandwidth
will be consumed for transmission of all these interleaver
as well as computational complexity will be increase at
receiver ends. Spreading is the important characteristic of
random interleaver.

Figure 2. Random interleaver of data
The collision among interleaver is interpreted in the form
of the uncorrelation among the interleaver. If the
interleaver is not randomly generated, the system
performance degrades considerably and resulting in
higher values of Bit Error Ratio (BER). On the other hand, if
the interleaving patterns are generated more and more
random, then better values of BER are obtained for the
same parameters [2]. Figure 2 shows randomly selected
output sequences out of input sequences in case of random
interleaver.
Figure 3. Operation of the Random interleaver
Figure 3 shows the operation of the random interleaver
with N=8 [12]. The random interleaver is Pseudo random
interleaver in the true sense because a pseudo random
number generator or a look up table is used to map the
input sequence.
2.2. QPP INTERLEAVER
The benefits of polynomial Interleavers include special
performance, complete algebraic structure, and efficient
implementation (high speed and low memory
requirements) [2].
Parallel decoding can be enabled by using Interleaving/de-
interleaving and thus memory access contentions occurs
when MAP decoder simultaneously tries to read/write
from/to memory. The QPP interleaver is based on
algebraic constructions via permutation polynomials over
integer rings. It is known that permutation polynomials
generate contention-free Interleavers [10]. The QPP
Interleaver can be represented by a mathematical formula
given an information block length N the x-th interleaving
output position is specified by simple quadratic equation
(1):
( ) ( ) (1)
Where parameters f1 and f2 are integers and depend on
the block size N(0≤x, f1, f2<N) . For each block size, a
different set of parameters f1 and f2 are defined. In LTE, all
the block sizes are even numbers and are divisible by 4
and 8. The block size N is always divisible by16, 32 and 64
when is 512, 1024, and 2048, respectively. According to
definition, parameter f1 must be an odd number whereas
f2 must be an even number [11].
2.3. HELICAL INTERLEAVER
A helical interleaver writes data into row–wise but reads
data diagonal–wise. An example of helical interleaver is
shown below [5]:
Figure 4. Writing data row–wise in memory.
Figure 5. Reading data diagonal–wise from memory.
The Helical Interleaver block permutes the symbols in the
input signal by placing them in an array in a helical fashion
and then sending rows of the array to the output port.
2.4. ODD-EVEN INTERLEAVER
An odd-even interleaver is a block interleaver in which the
number of rows and columns must be odd numbers [5].
First, the bits are left un-interleaved and encoded, but only
the odd-positioned coded bits are stored. Then, the bits are
scrambled and encoded, but now only the even-positioned
coded bits are stored. Odd-even encoders can be used,
when the second encoder produces one output bit per one
input bit.
Figure 6. Operation of odd even interleaver

2.5. MATRIX INTRELEAVER
In the matrix interleaving, bits are fed in a matrix row by
row and read out column by column. At the transmitter,
the interleaver is used to feed the OFDM symbols with
different permutations of the information sequence so that
the generated parity sequences can be assumed
independent. At the receiver, the de-interleaver is used to
randomize the symbols after every decoding step, thus
making the iterative decoding more efficient. The column
size n is called the depth and the row size m is the span
and an interleaver is called as (n, m) matrix interleaver. At
the de-interleaver, information is written column-wise and
read out row-wise [4].
Figure 7. Matrix interleaver
If the Number of rows and Number of columns parameters
are 6 and 4, respectively, then the interleaver uses a 6-by-4
matrix for its internal computations. If the Array step size
parameter is 1, then the diagonals are as shown in the
figure below. Positions with the same colour form part of
the same diagonal, and diagonals with darker colours
precede those with lighter colours in the output signal as
shown in Figure 7.
Given an input signal of [1:24]', the block produces an
output of
[1; 6; 11; 16; 5; 10; 15; 20; 9; 14; 19; 24; 13; 18; 23;...
4; 17; 22; 3; 8; 21; 2; 7; 12]
3. TURBO ENCODER
A turbo encoder is the parallel concatenation of RSC codes
separated by an interleaver as shown in Figure 7. As per
process, the data flow dk first goes into the very first
elementary RSC encoder and then it passes through
interleaver. At last, it feeds a second elementary RSC
encoder. The input stream is also systematically
transmitted as Xk, and the redundancies produced by
encoders 1 and 2 are transmitted as Y1k and Y2k. The
main reason of using RSC encoders for turbo codes in place
of the traditional non-recursive non-systematic
convolutional codes, is to use their recursive nature and
not the fact that they are systematic [9].
Figure 8. Turbo encoder
A General Turbo encoder is shown in Figure 8. It employs
two identical RSC encoders connected in parallel with an
interleaver preceding the second RSC encoder. The two
RSC encoders are called as the constituent encoders of the
Turbo encoder. The information bits are encoded by both
RSC encoders. The data frame, length of size N, inserts
directly into the first encoder and after interleaving of
length N, it feeds the second encoder. Therefore, N
systematic bits can generate 2N parity bits and its gives a
code rate of 1/3 [5].
3.1CONVOLUTION CODES
In a block code, the block of n code digits generated by the
encoder in any time unit depends only on the block of k
input data digits within that time unit but in a
convolutional code, the block of n codes digits generated
by the encoder in a time unit depends not only on the
block of k message digits within that time but also on the
block data digits with a previous span of (N-1) time units
(N>1). In this way convolution codes are different from
block codes. For convolutional codes, k and n are usually
small. Convolutional codes can be devised for correcting
random errors, burst errors, or both. Convolution Encoder
can be easily implemented by using shift registers. It is
generated by combining the outputs of a K number of shift
registers through the employment of v number of
EXCLUSIVE-OR logic summers. For K=4 and v = 3,
convolution encoder looks like as shown in Figure 9. Here
M1 through M4 are 1-bit storage (memory) devices such as
flipflops [4].

Figure 9. Block diagram of convolutional encoder
4. TURBO DECODER
In a turbo encoder with T constituent encoders, the
encoder output contains a single systematic output and T
parity outputs from the RSC encoders (assuming no
puncturing), T – 1 of which operate on an interleaved
version of original data block. Thus, the output of the turbo
encoder can be viewed as the output of T independent RSC
encoders, except the systematic information only need be
transmitted for one of the encoders. The decoder can
reconstruct the systematic bits for the other encoders
because it knows the interleaving patterns that were used.
Thus, the decoder can be decomposed into T convolutional
decoders with each one operating on the output of a single
constituent encoder. In order to get the best possible
estimate of the original message, these separate decoders
must be able to share the results of their calculations. To
accomplish this, turbo decoders use iterative feedback
decoding. Figure 9 shows a schematic of a turbo decoder
for the classical turbo code with T=2 [5].
Figure 10. Block diagram of turbo decoder
Since turbo codes have two constituents-code components,
an iterative algorithm is appropriate for their decoding.
Any decoding method that yields the likelihood of the bits
as its output can be used in the iterative decoding scheme
as shown in figure 10.
5. EXPERIMENTAL PARAMETERS
5.1. BIT ERROR RATE (BER)
Bit error rate, (BER) is a key quality parameter used to find
the quality of system that transmit digital data from one
location to another. It is a figure of merit of a receiver. It is
an important parameter in radio data links, fiber optic data
systems, Ethernet, or any system that transmits data over
a network of some form where noise, interference, and
phase jitter may cause quality degradation of the digital
signal [8].
In the region of high signal-to noise ratio, the performance
of any binary code is dominated by its minimum distance
dmin (the minimum Hamming distance between code
words) and its multiplicity values, Amin (number of code
words with weight dmin) and Wmin (sum of the Hamming
weights of Amin information frames generating the code
words with weight dmin).At very high signal-to-noise
ratios (SNR), that is very low error rates, the code
performance practically coincides with the union bound,
truncated to the contribution of the minimum distance.
The BER code performance can then be approximated by
equation (2)
(2)
Where k/n is the code rate and K is the information frame
length [6].
5.2. BER CURVE
When a curve is plotted between BER and SNR of Turbo
code, the resulting curve has waterfall shape that abruptly
flattens. This part is called error floor. The error floor
condition occurs due to small minimum distance in turbo
code as the performance curve flattens out as shown in
Figure 11. There is a large effect on free distance in turbo
codes due to interleaving. Appropriate interleaver are used
for lowering error floor in turbo codes.

Figure 11. A BER curve showing the waterfall region and
the error floor
The interference is due to the external factors and cannot
be removed by the system design. However, it is possible
to set the bandwidth of the system. By reducing the
bandwidth, the interference can be reduced but reducing
bandwidth also limits the data throughput [8].
6. CONCLUSION
Turbo encoders make use of interleaver at receiver side
and de-interleaver is used at receiver side in turbo
decoders. Interleaver is very important for improving the
performance of the turbo codes. Quality of an interleaver
can be determined by drawing BER curve corresponds to
it. Water fall region helps in determining which interleaver
is better in which set of conditions.
REFERENCES
[1] Poonguzhali, C. Arun, “Effect of Interleaver
Algorithm on the Performance of Modified Turbo
Codes”, Middle-East Journal of Scientific Research,
2016.
[2] Neelam Kumari, A.K.Singh, “IDMA Technology and
Comparison survey of Interleavers”, International
Journal of Scientific and Research Publications,
Volume 3, Issue 9, September 2013.
[3] Ching-Lung Chi, “Quadratic Permutation
Polynomial Interleavers for LTE Turbo Coding”,
International Journal of Future Computer and
Communication, Vol. 2, No. 4, August 2013.
[4] Vineet Chaturvedi, Vivek Kumar Gupta,
“Performance Analysis for Different Interleavers
in Various Modulation Schemes with OFDM over
an AWGN Channel”, IOSR Journal of Engineering
Apr. 2012, Vol. 2(4).
[5] Mojaiana Synthia, Md. Shipon Ali, “Performance
Study of Turbo Code with Interleaver Design”,
International Journal of Scientific & Engineering
Research Volume 2, Issue 7, July-2011.
[6] Alaa Eldin.Hassan, Mona Shokair, Atef Abou
Elazm, D.Truhachev, C.Schlegel, “Proposed
Deterministic Interleavers For Ccsds Turbo Code
Standard”, Journal of Theoretical and Applied
Information Technology, 2005-2010.
[7] Sina Vaﬁ, Tadeusz Wysocki, “On the Performance
of Turbo Codes with Convolutional Interleavers”,
Asia-Pacific Conference on Communications,
Perth, Western Australia, 3 - 5 October 2005.
[8] Irfan Ali, “Bit-Error-Rate (BER) Simulation Using
MATLAB”, International Journal of Engineering
Research and Applications, Vol. 3, Issue 1, January
-February 2013.
[9] Bhavana Shrivastava, Yudhishthir Raut, Ravi
Shankar Mishra, “Performance of Turbo Code for
UMTS in AWGN channel”, International Journal of
Advanced Computer Research, Volume-1, Issue-1,
September 2011.
[10] O.Y. Takeshita, “On maximum contention-free
interleavers and permutation polynomials over
integer rings”, IEEE Trans. Inform. Theory, Mar
2006.
[11] J. Sun, O.Y. Takeshita, “Interleavers for turbo codes
using permutation polynomials over integer
rings”, IEEE Trans. Inform. Theory, Jan 2005.
[12] C. Fragouli and R. D. Wesel, “Semi random
interleaver design criteria,” in Global
telecommunication Conference’ 99, (Rio de
Janeiro, Brazil), December 1999.

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