Document Type : Research Articles

Author

Bist o Noh Bahman Bulvar, University of Tabriz, Tabriz, Iran Bist o Noh Bahman Bulvar

Abstract

In this paper, we present a practical encoding and decoding scheme for the binary Wyner-Ziv problem based on graph-based codes. Our proposed scheme uses low-density generator-matrix (LDGM) codes in lossy source coding part and low-density parity-check (LDPC) codes in syndrome generation and decoding part. Actually, we apply Bias-Propagation algorithm for lossy source coding or binary quantization and Sum-Product algorithm for syndrome-based channel decoding. Using appropriate degree distributions for LDGM codes and optimized degree distributions for LDPC codes, we will be able to achieve close rate-distortion performance to the theoretical Wyner-Ziv bound. Also, we extend our proposed scheme for presenting a practical coding scheme for the binary Chief Executive Officer (CEO) problem. In our scheme, encodig is based on binary-quantization and Slepian-Wolf coding using source-splitting technique. It is shown that, source-splitting technique is an efficient strategy for achieving non-corner points in Slepian-Wolf rate region. We show that, this technique along with iterative message-passing algorithms can be efficient for having close rate-distortion performance to the Berger-Tung inner bound of binary CEO problem for non-corner points too.

Keywords

Main Subjects

[1] C. Berrou and A. Glavieux, “Near optimum error correcting coding and decoding: turbo-codes,” IEEE Transactions on Communications, vol. 44, no. 10, pp. 1261–1271, Oct 1996.

[2] T. J. Richardson, M. A. Shokrollahi, and R. L. Urbanke, “Design of capacity approaching irregular low-density parity-check codes,” IEEE Transactions on Information Theory, vol. 47, no. 2, pp. 619–637, Feb 2001.

[3] Z. Sun, M. Shao, J. Chen, K. M. Wong, and X. Wu, “Achieving the rate-distortion bound with low-density generator matrix codes,” IEEE Transactions on Communications, vol. 58, no. 6, pp. 1643–1653, June 2010.

[4] E. Martinian and J. Yedidia, “Iterative quantization using codes on graphs,” in Allerton Conference on Control, Computing, and Communication, October 2003.

[5] D. Slepian, and J. Wolf, "Noiseless coding of correlated information sources", IEEE Transactions on information Theory, vol. 19, no. 4, pp. 471-480, 1973.

[6] A. Wyner and J. Ziv, “The rate-distortion function for source coding with side information at the decoder,” IEEE Transactions on Information Theory, vol. 22, no. 1, pp. 1–10, Jan 1976.

[7] M. J. Wainwright and E. Martinian, “Low-density graph codes that are optimal for binning and coding with side information,” IEEE Transactions on Information Theory, vol. 55, no. 3, pp. 1061–1079, March 2009.

[8] X. Chen, Z. Lin, C. Chen, and X. Deng, "Low-Delay Digital and Hybrid Digital/Analog Schemes for Wyner-Ziv Problem over Gaussian Broadcast Channel", IEEE Transactions on Vehicular Technology, 2023.

[9] R. Zamir, Lattice coding for signals and networks. Cambridge: Cambridge University Press, 2014.

[10] S. Eghbalian-Arani and H. Behroozi, “Polar codes for a quadratic gaussian wyner-ziv problem,” in Wireless Communication Systems (ISWCS 2013), Proceedings of the Tenth International Symposium on, Aug 2013, pp. 1–5.

[11] S. Kumar, A. Vem, K. Narayanan, and H. D. Pfister, “Spatially-coupled codes for side-information problems,” in IEEE International Symposium on Information Theory, June 2014, pp. 516–520.

[12] N. Zhang, and M. Tao, "An adaptive distributed source coding design for distributed learning", In 13th International Conference on Wireless Communications and Signal Processing (WCSP), pp. 1-5, 2021, October.

[13] S. Watanabe and S. Kuzuoka, “Universal wyner-ziv coding for distortion constrained general side information,”IEEE Transactions on Information Theory, vol. 60, no. 12, pp. 7568–7583, Dec 2014.

[14] E. Dupraz, A. Roumy, and M. Kieffer, “Universal wyner-ziv coding for gaussian sources,” in 2013 IEEE International Conference on Acoustics, Speech and Signal Processing, May 2013, pp. 5132–5135.

[15] A. El Gamal and Y.-H. Kim, Network information theory. Cambridge university press, 2011.

[16] M. Pathegama, and A. Barg, "Smoothing of binary codes, uniform distributions, and applications", Entropy, vol. 25, no. 11, 2023.

[17] J. Chen and T. Berger, “Successive wyner-ziv coding scheme and its application to the quadratic gaussian ceo problem,” IEEE Transactions on Information Theory, vol. 54, no. 4, pp. 1586–1603, April 2008.

[18] H. Behroozi and M. R. Soleymani, “Distortion sum-rate performance of successive coding strategy in quadratic gaussian ceo problem,” IEEE Transactions on Wireless Communications, vol. 6, no. 12, pp. 4361–4365, December 2007.

[19] V. Kostina, and B. Hassibi, "The CEO problem with inter-block memory", IEEE Transactions on Information Theory, vol. 67, no. 12, pp. 7752-7768, 2021.

[20] T. Filler and J. Fridrich, “Binary quantization using belief propagation with decimation over factor graphs of ldgm codes,” in Allerton Conference on Control, Computing, and Communication, September 2007.

[21] A. D. Liveris, Z. Xiong, and C. N. Georghiades, “Compression of binary sources with side information at the decoder using ldpc codes,” IEEE Communications Letters, vol. 6, no. 10, pp. 440–442, Oct 2002.

[22] H. Esmaeeli and M. Rezaei. “Methods and Criteria for Evaluating Controllability of Video Bit Rate in HEVC-SCC,” International Journal of Industrial Electronics Control and Optimization vol. 4, no. 3, pp. 313-320, 2021.

[23] X. He, X. Zhou, P. Komulainen, M. Juntti, and T. Matsumoto, “A lower bound analysis of hamming distortion for a binary ceo problem with joint source-channel coding,” IEEE Transactions on Communications, vol. 64, no. 1, pp. 343–353, Jan 2016.

[24] T. Filler and J. Fridrich, “Binary quantization using belief propagation with decimation over factor graphs of ldgm codes,” in Allerton Conference on Control, Computing, and Communication, September 2007.

[25] T. Filler, “Minimizing embedding impact in steganography using low density codes,” Master’s thesis, SUNY Binghamton, Jul. 2007.
[26] M. J. Wainwright, E. Maneva, and E. Martinian, “Lossy source compression using low-density generator matrix codes: Analysis and algorithms,” IEEE Transactions on Information Theory, vol. 56, no. 3, pp. 1351–1368, March 2010.

[27] P. L. Dragotti and M. Gastpar, Distributed source coding: Theory, Algorithms and Applications. Elsevier, 2009.

[28] S. S. Pradhan and K. Ramchandran, “Distributed source coding using syndromes (discus): design and construction,” IEEE Transactions on Information Theory, vol. 49, no. 3, pp. 626–643, Mar 2003.

[29] S. Yuxuan, S. Shuo, and W. Yongpeng, "Rate-Distortion Analysis for Semantic-Aware Multi-Terminal Source Coding Problem", arXiv preprint arXiv:2303.06391, 2023.

[30] M. Sartipi and F. Fekri, “Lossy distributed source coding using ldpc codes,” IEEE Communications Letters, vol. 13, no. 2, pp. 136–138, February 2009.

[31] D. H. Schonberg, “Practical distributed source coding and its application to the compression of encrypted data,” Ph.D. dissertation, Univ. California, Berkeley, 2007.