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Adaptive Slepian-Wolf Decoding using Particle Filtering based Belief Propagation

This study presents an innovative approach for adaptive decoding in asymmetric Slepian-Wolf coding by integrating particle filtering with belief propagation (BP). Traditional methods assume static correlation statistics, limiting flexibility. Our approach updates particle locations and weights dynamically, enhancing performance in encoding/decoding discrete correlated sources. We explore the effectiveness of the proposed method through simulation results, demonstrating significant improvements in correlation estimation and decoding accuracy. Our findings suggest viable extensions to non-asymmetric scenarios, highlighting future directions for research in adaptive LDPC decoding.

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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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