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Adaptive Slepian-Wolf Decoding using Particle Filtering based Belief Propagation

Adaptive Slepian-Wolf Decoding using Particle Filtering based Belief Propagation. Samuel Cheng, Shuang Wang and Lijuan Cui University of Oklahoma Tulsa, OK. ˆ. ˆ. ( X. ,. Y ). Separate Encoding: R=R Y +R X =H(X,Y) < H(X)+H(Y) (if R X ≥H(X|Y), R Y ≥H(Y|X)). Slepian-Wolf (SW) Problem.

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Adaptive Slepian-Wolf Decoding using Particle Filtering based Belief Propagation

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

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

  3. SW Problem: The Rate Region R Y 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. R Y H(X,Y) A Y H(Y) Y – decoder side information (SI) B H(Y|X) H(X|Y) H(X) H(X,Y) R X Source Coding with Decoder Side Information (Asymmetric SW) ^ X X Decoder Lossless Encoder Source X

  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. Correlation Channel ^ X X s Syndrome former sT=HxT Conventional channel decoder Source X Y Systematic (7,4) Hamming code C (can correct one bit error) 1 0 0 1 0 1 1 0 1 0 1 1 0 1 0 0 1 0 1 1 1 H= Ry (3,7) Suppose that realizations are: sT = [ 010 ] xT = [ 0100000 ] 7 6 5 4 3 yT = [ 1100000 ] Rx 3 4 5 6 7

  7. 0 1 0 0 1 0 0 0 0 0 LDPC based SW Coding Correlation model Encoding Decoding 1 ? 1 ? 0 BSC p X Y 0 ? 1 0 ? 0 ? X and Y are binary 0 0 ? 0 ? p is static and known a priori S X Y S X

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

  9. ? 0 ? 1 0 ? 0 1 ? 0 ? 0 0 ? 0 ? 0 Pj are continuous Adaptive LDPC based SW Coding Correlation model Encoding Decoding 1 ? 1 ? 0 BSC p X Y 0 ? 1 0 ? 0 ? 0 0 ? 0 ? S X Y S X P

  10. BP cannot apply directly since p are continuous • Approximate distribution of pusing 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. ? 0 ? 1 0 ? 0 1 ? 0 ? 0 0 ? 0 ? 0 Adaptive LDPC based SW Coding Correlation model Encoding Decoding 1 ? 1 ? 0 BSC p X Y 0 ? 1 0 ? 0 ? 0 0 ? 0 ? S X Y S X P Connection ratio = 1:1

  14. 0 1 0 0 1 0 0 0 0 0 Adaptive LDPC based SW Coding Correlation model Encoding Decoding 1 ? ? 1 ? 0 BSC p X Y 0 ? ? 1 0 ? 0 ? ? 0 0 ? ? 0 ? S X Y S X P 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

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