Browse > Article
http://dx.doi.org/10.4218/etrij.10.0210.0204

Lossy Source Compression of Non-Uniform Binary Source via Reinforced Belief Propagation over GQ-LDGM Codes  

Zheng, Jianping (State Key Laboratory of Integrated Services Networks, Xidian University)
Bai, Baoming (State Key Laboratory of Integrated Services Networks, Xidian University)
Li, Ying (State Key Laboratory of Integrated Services Networks, Xidian University)
Publication Information
ETRI Journal / v.32, no.6, 2010 , pp. 972-975 More about this Journal
Abstract
In this letter, we consider the lossy coding of a non-uniform binary source based on GF(q)-quantized low-density generator matrix (LDGM) codes with check degree $d_c$=2. By quantizing the GF(q) LDGM codeword, a non-uniform binary codeword can be obtained, which is suitable for direct quantization of the non-uniform binary source. Encoding is performed by reinforced belief propagation, a variant of belief propagation. Simulation results show that the performance of our method is quite close to the theoretic rate-distortion bounds. For example, when the GF(16)-LDGM code with a rate of 0.4 and block-length of 1,500 is used to compress the non-uniform binary source with probability of 1 being 0.23, the distortion is 0.091, which is very close to the optimal theoretical value of 0.074.
Keywords
Source coding; lossy compression; LDGM codes; belief propagation;
Citations & Related Records

Times Cited By Web Of Science : 0  (Related Records In Web of Science)
Times Cited By SCOPUS : 0
연도 인용수 순위
  • Reference
1 A. Braunstein, M. Mézard, and R. Zecchina, "Survey Propagation: An Algorithm for Satisfiability," Random Structures and Algorithms, vol. 27, no. 2, Sept. 2005, pp. 201-226.   DOI   ScienceOn
2 S. Ciliberti, M. Mézard, and R. Zecchina, "Lossy Data Compression with Random Gates," Phys. Rev. Lett., vol. 95, 2005, p. 038701.   DOI   ScienceOn
3 T. Filler and J. Fridrich, "Binary Quantization Using Belief Propagation with Decimation over Factor Graphs of LDGM Codes," Proc. Allerton Conf. Commun., Control, Computing, Monticello, IL, USA, 2007, pp. 495-501.
4 P.A. Regalia, "A Modified Belief Propagation Algorithm for Code Word Quantization," IEEE Trans. Commun., vol. 57, no. 12, Dec. 2009, pp. 3513-3517.   DOI
5 L. Cappellari, "Lossy Source Compression of Non-Uniform Binary Source Using GQ-LDGM Codes," ITW, Dublin, 2010, available: arXiv:1004.2628.
6 Z. Sun et al., "Lossy Source Compression for Non-Uniform Sources Using LDGM Codes," 24th Queen's Biennial Symp. Commun., Kingston, Ontario, Canada, June 2008.
7 A. Braunstein et al., "Encoding for the Blackwell Channel with Reinforced Belief Propagation," Proc. IEEE Int. Symp. Inform. Theory, Nice, 2007, pp. 1891-1895.
8 X.-Y. Hu, Low-Density Low-Complexity Error-Correcting Codes on Sparse Graphs, Doctoral dissertation, Swiss Federal Institute of Technology Lausanne (EPFL), 2002.
9 A. Braunstein, F. Kayhan, and R. Zecchina, "Efficient LDPC Codes over GF(q) for Lossy Data Compression," Proc. IEEE Int. Symp. Inform. Theory, Seoul, Korea, 2009, pp. 1978-1982.
10 X.-Y. Hu, E. Eleftheriou, and D.M. Arnold, "Regular and Irregular Progressive Edge-Growth Tanner Graphs," IEEE Trans. Inform. Theory, vol. 51, no. 1, Jan. 2005, pp. 386-398.
11 E. Martinian and J. Yedidia, "Iterative Quantization Using Codes on Graphs," Proc. Allerton Conf. Commun., Control, Computing, Monticello, IL, USA, 2003, pp. 110-122.
12 M. J. Wainwright, E. Maneva, and E. Martinian, "Lossy Source Compression Using Low-Density Generator Matrix Codes: Analysis and Algorithms," IEEE Trans. Inf. Theory, vol. 56, no. 3, June 2010, pp. 1351-1368.   DOI
13 T. Murayama, "Thouless-Anderson-Palmer Approach for Lossy Compression," J. Phys. Rev. E: Stat. Nonlin. Soft Matter Phys., vol. 69, 2004, p. R035105.   DOI