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DESIGN OF BINARY LDPC CODES FOR SLEPIAN-WOLF CODING OF CORRELATED INFORMATION SOURCES by Saeed Anibaba Eleruja, Umar-Faruk Abdu-Aguye, Marcel Adrian Ambroze, Martin Tomlinson and Mohammed Zaki School of Computing, Electronics, and Mathematics Faculty of Science and Environment Plymouth University Plymouth, UK [email protected], [email protected], [email protected], [email protected], [email protected] presented at GlobalSIP 2017 5th IEEE Global Conference on Signal and Information Processing Technically co-sponsored by:

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Page 1: Saeed's Presentation at GlobalSIP'17 · 2019-03-01 · ^/'E K& /E Zz > W K ^ &KZ ^> W/ E rtK>& K /E' K& KZZ > d /E&KZD d/KE ^KhZ ^ Ç ^ v ] o µ i U h u r& µ l µ r P µ Ç UD o

DESIGN OF BINARY LDPC CODES FOR SLEPIAN-WOLF CODING OFCORRELATED INFORMATION SOURCES

by

Saeed Anibaba Eleruja, Umar-Faruk Abdu-Aguye, Marcel Adrian Ambroze, Martin Tomlinson and Mohammed ZakiSchool of Computing, Electronics, and Mathematics

Faculty of Science and EnvironmentPlymouth University

Plymouth, UK

[email protected], [email protected], [email protected], [email protected], [email protected]

presented at

GlobalSIP 2017

5th IEEE Global Conference on Signal and Information Processing

Technically co-sponsored by:

Page 2: Saeed's Presentation at GlobalSIP'17 · 2019-03-01 · ^/'E K& /E Zz > W K ^ &KZ ^> W/ E rtK>& K /E' K& KZZ > d /E&KZD d/KE ^KhZ ^ Ç ^ v ] o µ i U h u r& µ l µ r P µ Ç UD o

Introduction to Distributed Source CodingIntroduction to Distributed Source Coding

Distributed Source Coding refers to the compression ofmultiple statistically dependent sources that do notcommunicate with each other and therefore are encoded in adistributed manner

Slepian and Wolf, in 1973 laid the foundation of distributedsource coding when they proved the counter-intuitive resultthat separate encoding with joint decoding achieves the samecompression rate as joint encoding does

Low density parity check (LDPC) codes first introduced byGallager, in the early 1960s are favoured over other code typesbecause they have remarkably good performance whendecoded using low complexity iterative decoding schemes.

Page 3: Saeed's Presentation at GlobalSIP'17 · 2019-03-01 · ^/'E K& /E Zz > W K ^ &KZ ^> W/ E rtK>& K /E' K& KZZ > d /E&KZD d/KE ^KhZ ^ Ç ^ v ] o µ i U h u r& µ l µ r P µ Ç UD o

Forms of Distributed Source CodingForms of Distributed Source Coding Lossless Distributed Source Coding or Slepian-Wolf Coding(SWC)

Rate bound given by Slepian-Wolf Theorem The optimal rate region of two DMS is the set of rate pairs

that:•

•

•

Page 4: Saeed's Presentation at GlobalSIP'17 · 2019-03-01 · ^/'E K& /E Zz > W K ^ &KZ ^> W/ E rtK>& K /E' K& KZZ > d /E&KZD d/KE ^KhZ ^ Ç ^ v ] o µ i U h u r& µ l µ r P µ Ç UD o

Forms of Distributed Source CodingForms of Distributed Source Coding

Lossy Distributed Source Coding or Berger-Tung Coding(BTC) Tight Rate bound still remain unknown Wyner-Ziv Coding is a degraded form of BTC with decoder side information Distributed Video Coding is an application of Wyner-Ziv Coding

Page 5: Saeed's Presentation at GlobalSIP'17 · 2019-03-01 · ^/'E K& /E Zz > W K ^ &KZ ^> W/ E rtK>& K /E' K& KZZ > d /E&KZD d/KE ^KhZ ^ Ç ^ v ] o µ i U h u r& µ l µ r P µ Ç UD o

Sixteen Cases of Correlated Source CodingMost Interesting is (0011)

Sixteen Cases of Correlated Source CodingMost Interesting is (0011)

Page 6: Saeed's Presentation at GlobalSIP'17 · 2019-03-01 · ^/'E K& /E Zz > W K ^ &KZ ^> W/ E rtK>& K /E' K& KZZ > d /E&KZD d/KE ^KhZ ^ Ç ^ v ] o µ i U h u r& µ l µ r P µ Ç UD o

Asymmetric Slepian-Wolf CodingAsymmetric Slepian-Wolf Coding

noise is N

NXY

Page 7: Saeed's Presentation at GlobalSIP'17 · 2019-03-01 · ^/'E K& /E Zz > W K ^ &KZ ^> W/ E rtK>& K /E' K& KZZ > d /E&KZD d/KE ^KhZ ^ Ç ^ v ] o µ i U h u r& µ l µ r P µ Ç UD o

Modification of Gallager’s EquationsEven Parity-Check Code, ଵ ଶ

Modification of Gallager’s EquationsEven Parity-Check Code, ଵ ଶ

Considering the k = 2, n = 3 even parity-check codeReceived probability is given by

(1) )|(2

2

2

)(

ci vr

iici aerccPp

Page 8: Saeed's Presentation at GlobalSIP'17 · 2019-03-01 · ^/'E K& /E Zz > W K ^ &KZ ^> W/ E rtK>& K /E' K& KZZ > d /E&KZD d/KE ^KhZ ^ Ç ^ v ] o µ i U h u r& µ l µ r P µ Ç UD o

Modification of Gallager’s EquationsEven Parity-Check Code, ଵ ଶ

The output probability of c1 being 1 is:

The extrinsic information for bit to be 1, is the sum of allproducts of the other bit probabilities for which the sum of the bitsis odd

The extrinsic information for bit to be 0, is the sum of allproducts of the other bit probabilities for which the sum of the bitsis even

(2) )( 02

10

12

00

11

02

11

10

12

11

00

11 pppppppppppp o

eip0

eip1

Page 9: Saeed's Presentation at GlobalSIP'17 · 2019-03-01 · ^/'E K& /E Zz > W K ^ &KZ ^> W/ E rtK>& K /E' K& KZZ > d /E&KZD d/KE ^KhZ ^ Ç ^ v ] o µ i U h u r& µ l µ r P µ Ç UD o

Solving for bit position

Adding (4) to (3) gives twice the sum of all even terms whilesubtracting gives the sum of all odd terms

(3) 1))(( 12

10

02

10

12

00

02

00

12

02

10

00 pppppppppppp

(4) )21)(21())(( 12

10

02

10

12

00

02

00

12

10

12

02

10

00 pppppppppppppp

ep 012

ep112

(5) 2

)21)(21(1 12

10

02

00

12

100

1 pppppp

p e

(6) 2

)21)(21(1 02

10

02

10

12

101

1 pppppp

p e

Modification of Gallager’s EquationsEven Parity-Check Code, ଵ ଶ

Page 10: Saeed's Presentation at GlobalSIP'17 · 2019-03-01 · ^/'E K& /E Zz > W K ^ &KZ ^> W/ E rtK>& K /E' K& KZZ > d /E&KZD d/KE ^KhZ ^ Ç ^ v ] o µ i U h u r& µ l µ r P µ Ç UD o

Modification of Gallager’s EquationsEven Parity-Check Code, ଵ ଶ

Modification of Gallager’s EquationsEven Parity-Check Code, ଵ ଶ

Solving for bit position

In General,

(7) 2

)21)(21(1 11

101

2

ppp e

(8) 2

)21(1 1

0

ij jei

pp

(9) 2

)21(1 1

1

ij jei

pp

Page 11: Saeed's Presentation at GlobalSIP'17 · 2019-03-01 · ^/'E K& /E Zz > W K ^ &KZ ^> W/ E rtK>& K /E' K& KZZ > d /E&KZD d/KE ^KhZ ^ Ç ^ v ] o µ i U h u r& µ l µ r P µ Ç UD o

The Conventional Decoder The Conventional Decoder

Page 12: Saeed's Presentation at GlobalSIP'17 · 2019-03-01 · ^/'E K& /E Zz > W K ^ &KZ ^> W/ E rtK>& K /E' K& KZZ > d /E&KZD d/KE ^KhZ ^ Ç ^ v ] o µ i U h u r& µ l µ r P µ Ç UD o

The Proposed Decoder The Proposed Decoder

Page 13: Saeed's Presentation at GlobalSIP'17 · 2019-03-01 · ^/'E K& /E Zz > W K ^ &KZ ^> W/ E rtK>& K /E' K& KZZ > d /E&KZD d/KE ^KhZ ^ Ç ^ v ] o µ i U h u r& µ l µ r P µ Ç UD o

The Binary Symmetric ChannelThe Binary Symmetric Channel

The correlation between the sources is defined as follows:

(1) )|(2

2

2

)(

ci vr

iici aerccPp

)( SNRQp

Page 14: Saeed's Presentation at GlobalSIP'17 · 2019-03-01 · ^/'E K& /E Zz > W K ^ &KZ ^> W/ E rtK>& K /E' K& KZZ > d /E&KZD d/KE ^KhZ ^ Ç ^ v ] o µ i U h u r& µ l µ r P µ Ç UD o

ResultsResults

Page 15: Saeed's Presentation at GlobalSIP'17 · 2019-03-01 · ^/'E K& /E Zz > W K ^ &KZ ^> W/ E rtK>& K /E' K& KZZ > d /E&KZD d/KE ^KhZ ^ Ç ^ v ] o µ i U h u r& µ l µ r P µ Ç UD o

ResultsResults

Page 16: Saeed's Presentation at GlobalSIP'17 · 2019-03-01 · ^/'E K& /E Zz > W K ^ &KZ ^> W/ E rtK>& K /E' K& KZZ > d /E&KZD d/KE ^KhZ ^ Ç ^ v ] o µ i U h u r& µ l µ r P µ Ç UD o

ConclusionConclusion

A very good compression was achieved with no apparent loss in performance compared to the conventional decoder

Additional computational overhead due to the formation of syndromes offset by the absence of encoding operation all together in the proposed model

The proposed model outperforms those presented in the previous works


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