saeed's presentation at globalsip'17 · 2019-03-01 · ^/'e k& /e zz > w k ^...
Post on 08-Jul-2020
1 Views
Preview:
TRANSCRIPT
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
Saeed.Eleruja@Plymouth.ac.uk, Umar-Faruk.Abdu-Aguye@plymouth.ac.uk, M.Ambroze@plymouth.ac.uk, M.Tomlinson@plymouth.ac.uk, M.Ahmed@plymouth.ac.uk
presented at
GlobalSIP 2017
5th IEEE Global Conference on Signal and Information Processing
Technically co-sponsored by:
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.
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:•
•
•
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
Sixteen Cases of Correlated Source CodingMost Interesting is (0011)
Sixteen Cases of Correlated Source CodingMost Interesting is (0011)
Asymmetric Slepian-Wolf CodingAsymmetric Slepian-Wolf Coding
noise is N
NXY
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
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
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
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
The Conventional Decoder The Conventional Decoder
The Proposed Decoder The Proposed Decoder
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
ResultsResults
ResultsResults
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
top related