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.

What is FEC?Forward Error Correction (FEC).

It is a control errors technique used to enhance communication reliability over unreliable communication channel.

How dose it works?

m

(k symbols)

x

(n symbols)Channel

Error free

Error detected

Error correction

Encoder

x + noise

(n symbols)

DecoderEstimated m

(k symbols)

Types? Block Codes:

BlockEncoder

m = 10011…11

(k symbols)x= 10011…11110…1

(n symbols)

Bit Rate= k/n

ConvolutionalEncoder

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.

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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.

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Utilise the multipath propagation phenomenonThe 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.

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Direct pathτD1

Reflected path

Transmitter Receiver τR2

τR1

Reflected path

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Useful copies

Uti

lise

mul

tipa

th p

ropa

gati

on t

o …

(3)

Source

BCH/RS Encoder

Modulation

Distention

BCH/RS Decoder

Demodulation

Combiner

NLoS

NLoS

LoS

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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 =ۏ����������ێ�����ێ�����ێ�����0ۍ����������������� 11 1 0 11 1 0 1 1 0 0 00 1 1 0 0 00 010 10

0 010 100 1 1 0 0 010 10 10 10 1 10 ۑ��������������ے������������������0

ۑ��������������ۑ��������������ې�����

Note: L should be odd number Y= [0 1 0 1 0 1 1 0 0 0]

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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

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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.

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Simulation and Results Multipath and Hamming weight combiner

Hamming weight combiner with different threshold values.

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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.

Simulation and ResultsBCH 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.

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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.

Simulation and Results

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.

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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.

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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

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Thank You