1. Adaptive Slepian-Wolf Decoding using Particle Filtering based Belief Propagation
Samuel Cheng, Shuang Wang
and Lijuan Cui
University of Oklahoma
Tulsa, OK

2. Slepian-Wolf (SW) ProblemX
Encoder RX
X and Y are discrete, correlated sources Y) , (X ˆ
Separate Encoding:
R=RY+RX=H(X,Y) < H(X)+H(Y) (if RX≥H(X|Y), RY≥H(Y|X))
Joint Decoder
RX and RY are compression rates Y RY
Encoder
Joint Encoding:
R=RY+RX=H(X,Y) < H(X)+H(Y)
H(X)+H(Y) – separate enc and dec
Separate encoding is as efficient as joint encoding!

3. SW Problem: The Rate RegionY
separate encoding and decoding
H(X,Y)
H(Y)
Focus of this work
H(Y|X)
H(X|Y)
H(X)
H(X,Y) R X
Achievable rate region

4. Source Coding with Decoder Side Information (Asymmetric SW)^ X X
Source X
Lossless Encoder
Decoder Y R X
H(Y|X)
H(X)
H(Y)
H(X|Y) Y
H(X,Y) A B
Y – decoder side information (SI)

5. Prior Work of “Asymmetric” SW Coding
Trellis code based
Pradhan et al. ‘99
Turbo code based
Garcia-Frias et al. ’01
Bajcsy & Mitran ’01
Aaron & Girod ’02
Li et al. ’04
LDPC code based
Schonberg et al. ’02
Liveris et al. ’02, ’03
Garcia-Frias et al. ’03
None of the prior work is adaptive. The correlation statistics is assumed to be static and known a priori

6. H= Systematic (7,4) Hamming code C (can correct one bit error) ^ X X
Syndrome former
sT=HxT s
Conventional channel decoder
Source X
Correlation Channel Y
Systematic (7,4) Hamming code C (can correct one bit error) H= Ry
(3,7)
Suppose that realizations are:
xT = [ ]
sT = [ 010 ]
yT = [ ] Rx

7. LDPC based SW Coding Correlation model Encoding Decoding 1 1 ? 1 ?1 1 ? 1 ?
BSC p X Y ? 1 ? ?
X and Y are binary ? ?
p is static and known a priori X S Y X S

8. Belief Propagation Review
Variable node update i a
Factor node update
Belief update i

9. Adaptive LDPC based SW Coding
Correlation model
Encoding
Decoding 1 ? 1 ? 1 ?
BSC p X Y ? 1 ? ? ? ? X S P Y X S
Pj are continuous

10. BP cannot apply directly since p are continuous
Approximate distribution of p using Np particles (at {p1, p2, …, pNp} and with weights {w1, w2, …, wNp})
The message passing steps do not change
But locations and weights of particles of p should be updated appropriately  particle filtering

11. Particle Filter Particle Filter Steps:
Particle locations obtained from previous iteration
2. Particle weights obtained from
belief resulted generated by
last BP iteration
3. Resampling
4. Random walk

12. Random Walk
After the resampling step, particles congregate round the values with large weights. RW ensures the diversity of the particles.
RW is implemented by adding a Gaussian random variable with zero mean and variance on the current value of each new particle generated in resample step.

13. Adaptive LDPC based SW Coding
Correlation model
Encoding
Decoding 1 ? 1 ? 1 ?
BSC p X Y ? 1 ? ? ? ? X S P Y X S
Connection ratio = 1:1

14. Adaptive LDPC based SW Coding
Correlation model
Encoding
Decoding 1 1 ? ? 1 ?
BSC p X Y ? ? 1 ? ? ? ? ? ? X S P Y X S
Connection ratio  1:2

15. Results 16 particles were assigned to each pj
For the Random Walk, we assumed
and λ=0.01
The following results were obtained by taking average of 30 different codewords.
Code length = 20K
Regular codes were used

16. Correlation Estimation

17. Decoding Performance
Linearly changing correlations (1:16)

18. Correlation Estimation

19. Decoding Performance
Sinusoidally changing correlations

20. Conclusions
Adaptive decoding for asymmetric SW coding using BP + particle filtering is proposed.
Can accurately estimate dynamic change of correlation (connection ratio should not be too small)
The work has been extended to non-asymmetric case using code partitioning technique (submitted to ICASSP 2010); adaptive LDPC decoding was presented in CISS 2009.
Note that the theoretical limit (SW limit) shown is really an outer bound. Because the original SW limit is derived assuming the model statistics are known.
Future work: non parametric BP

21. Resampling Calculate Compare
The cumulative sum of the particle weights
and updated uniform number
where
is drawn from the uniform distribution . .
Compare
and to determine the number of replications for particle k
in the range
Systematic resampling process for an example with Np particles. Weight of particles is listed in the table.