Utilise Multipath Propagation to Improve the performance of BCH and RS Codes

Utilise Multipath Propagation to Improve the
performance of BCH and RS Codes
Presenter: Alyaa Al-Barrak,
Co-authors: Ali Al-Sherbaz,
Triantafyllos Kanakis,
Robin Crockett
The University of Northampton,
The School of Science and Technology,
Department of Computing and Immersive Technologies
8th Computer Science & Electronic Engineering Conference

Outlines
• Forward Error Correction (FEC);
• FEC Codes Types;
• FEC Codes Error Correction Capability;
• Multipath propagation phenomenon;
• The aim of paper
• Utilise the multipath propagation phenomenon;
• Hamming weight combiner;
• How signals are chosen; and,
• Simulation and Results.

Forward Error Correction (FEC).
It is a control errors technique used to enhance communication reliability
over unreliable communication channel.
m
(k symbols)
x
(n symbols)
Error free
Error detected
Error correction
x + noise
(n symbols)
Estimated m
(k symbols)
 Block Codes:
m = 10011…11
(k symbols)
x= 10011…11110…1
(n symbols)
Bit Rate= k/n
m = 10011…11
(k symbols)
x= 101011…111
(n symbols)
Bit Rate = k/n
 Convolutional Codes:
3

Error correction capability
10
 BCH Codes (invented in 1959)
 Reed-Solmono Codes (invented in 1960)
n k Error correction capability (t)
31 26 1
31 21 2
31 16 3
31 11 5
31 6 7
n k Error correction capability (t)
31 29 1
31 27 2
31 25 3
31 23 4
31 21 5 4

Multipath propagation
NLoS
Multipath is a propagation phenomenon in wireless communication. According to it,
the receiver antenna will receive two or more copies of the same signal from
different routes.
5

The aim of paper
Improve the the performance of forward error correction (FEC) codes without extra
redundancy, in order to improve data transmission reliability and increase the bit rate
over wireless communication channels.
RELATED WORK
Most research focuses on:
1. Increase redundancy to improve the error correction capability (Turbo code 1993).
2. Analysing the performance of various FEC techniques rather than how to improve
it without extra redundancy.
6

Utilise the multipath propagation phenomenon
The paper has been considered the received signals (Line-of-sight (LoS) and Non-
line-of-sight (NLoS)) as redundant copies of the transmitted signal. All signals differ in
their transmission length and propagation delay.
7

Direct path
τD1
Transmitter Receiver
τR2
τR1
8
Useful copies

Utilisemultipathpropagationto…(3)
LoS
9

Hamming weight combiner
LoS C1 = [0 1 0 1 0 1 1 0 0 0],
Useful NLoS C2 = [1 1 1 1 0 1 1 0 0 0],
Useful NLoS C3 = [0 0 0 0 0 1 1 0 0 0],
Useful NLoS C4 = [1 1 1 1 1 1 1 1 1 1],
Useful NLoS C5 = [0 0 0 0 0 0 0 0 0 0].
𝐿𝑐 =
0 1
1 1
0 1
1 1
0 1 1 0 0 0
0 1 1 0 0 0
0 0
1
0
1
0
0 0
1
0
1
0
0 1 1 0 0 0
1
0
1
0
1
0
1
0
1 1
0 0
Note: L should be odd number Y= [0 1 0 1 0 1 1 0 0 0]
10

How signals are chosen?
There are variations methods to select multipath signals to be combined
such as:
 First N signals: Only the first N signals received are combined;
 Best N signals: Only the N signals with highest SNR are combined;
and,
 Threshold: Combines only the signals that above a threshold
11

Simulation and Results
 BCH and RS codes with different error correction capability;
 Number of paths 3, 5, 7, and 9 paths;
 Additive white Gaussian noise channel; and
 The threshold value was set as 40%..75% from SNR of LoS signal to
choose NLoS signals.
12

 Multipath and Hamming weight combiner
Hamming weight combiner with different threshold values.
13
The combined packets (useful NLoS+LoS) improved the signals, where the
improvement is increased when the number of combined paths are
increased. Also, the performance improvement depends on the threshold
value.

BCH codes, Multipath, and Hamming weight combiner
 BCH (15, 11), BCH (127, 120) and BCH (255, 247) codes have error correction capability t1=1. BCH
(15, 7), BCH (127, 113) and BCH (255, 239) codes have error correction capability t1=2.
14
The combining of three paths improved the performance of BCH codes which
have error correction capability t1=1. Furthermore, their performance is better
than the performance of BCH codes which have error correction capability t2=2.

 RS (15, 13), RS (127, 125) and RS (255, 253) codes have error correction capability t1=1. RS (15, 11),
RS (127, 123) and RS (255, 251) codes have error correction capability t1=2.
15
The combining of three paths improved the performance of RS codes which have
error correction capability t1=1. Furthermore, their performance is better than the
performance of RS codes which have error correction capability t2=2.
RS codes, Multipath, and Hamming weight combiner

Conclusions
My proposed improved the performance of FEC with low
redundancy and low error correction capability to perform
better than the one with higher redundancy and higher error
correction capability. This is achieved through utilising an
existing phenomenon in the wireless communication called
multipath propagation and proposing a combiner known as
Hamming weight combiner with low complexity.
16

Future work
This research could be extended by analysing
and evaluating the performance of FEC
techniques with high modulation schemes,
multiple-input multiple-output (MIMO) systems
and over different wireless channel models
17

References
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[3] K. S. Zigangirov, Theory of code division multiple access communication, Canada: John Wiley & Sons, 2004.
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[11] K. D. Rao, Channel coding techniques for wireless communications, New Delhi: Springer, 2015.
[12] Y. Di, "The evaluation and application of forward error coding," Harbin, 2011.
[13] P. Shrivastava and U. P. Singh, "Error detection and correction using Reed Solomon Codes," International Journal of Advanced Research in
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[14] S. B. Wicker and V. K. Bhargava, Reed-Solomon Codes and their applications, New York: John Wiley & Sons, 1999 .
[15] J. Adamek, Foundations of Coding: theory and applications of errorcorrecting codes with an introduction to cryptography and information
theory, 1st ed., Wiley-Interscience, 1991.
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Utilise Multipath Propagation to Improve the performance of BCH and RS Codes

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