Construction of universal codes using LDPC matrices and their error exponents

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

Volumn E90-A, Issue 9, 2007, Pages 1830-1839

  Miyake, Shigeki ^a   Maruyama, Mitsuru ^a  

^a NTT Network Innovation Laboratories   (Japan)

Author keywords

Error exponent; LDPC matrices; Minimum entropy decoding; Universal code

Indexed keywords

DECODING; ERROR CORRECTION; ERRORS;

CORRELATED SOURCES; DECODING ERRORS; ENTROPY DECODING; ERROR EXPONENT; NOISY CHANNEL MODELS; SUM-PRODUCT DECODING; UNIVERSAL CODES; UNIVERSAL CODING;

CODES (SYMBOLS);

EID: 52349109081     PISSN: 09168508     EISSN: 17451337     Source Type: Journal    
DOI: 10.1093/ietfec/e90-a.9.1830     Document Type: Conference Paper

References (21)

1. C. Berrou, A. Glavieux, and P. Thitimajshima, "Near Shannon limit error-correcting coding and decoding: Turbo codes," Proc. 1993 Int. Conf. Commun., pp. 1064-1070, 1993.
2. G. Caire, S. Shamai, and S. Verdú, "Lossless data compression with error correction codes," Proc. 2003 IEEE Int. Symp. Inform. Theory, p. 22, 2003.
3. G. Caire, S. Shamai, and S. Verdú, "Universal data compression with LDPC codes," Proc. Third Int. Symp. Turbo Codes and Related Topics, pp. 55-58, 2003.
4. G. Caire, S. Shamai, and S. Verdú, "Noiseless data compression with low density parity check codes," DIMACS Series in Discrete Mathematics and Theoretical Computer Science: Advances in Network Information Theory, vol. 66, pp. 263-284, American Mathematical Society, 2004.
5. T. P. Coleman, M. Medard, and M. Effros, "Polynomial complexity universal block decoding with exponential error probability decay," submitted to IEEE Trans. Inform. Theory.
6. I. Csiszár and J. Körner, Information Theory: Coding Theorems for Discrete Memoryless Systems, Academic Press, 1981.
7. I. Csiszár, "Linear codes for sources and source networks: Error exponents, universal coding," IEEE Trans. Inform. Theory, vol. 28, no. 4, pp. 585-592, 1982.
8. q," IEEE Trans. Inform. Theory, vol. 51, no. 5, pp. 1871-1879, 2005.
9. R. G. Gallager, "Low density parity check codes," IRE Trans. Inform. Theory, vol. 8, pp. 21-28, 1962.
10. R. G. Gallager, Low Density Parity Check Codes, no. 21 in Research Monograph Series, MIT Press, Cambridge, MA, 1963.
11. D. J. C. MacKay, "Good error-correcting codes based on very sparse matrices," IEEE Trans. Inform. Theory, vol. 45, no. 2, pp. 399-431, 1999.
12. Y. Matsunaga and H. Yamamoto, "A coding theorem for lossy data compression by LDPC codes," IEEE Trans. Inform. Theory, vol. 49, no. 9, pp. 2225-2229, 2003.
13. G. Miller and D. Burshtein, "Bounds on the maximum-likelihood decoding error probability of low-density parity-check codes," IEEE Trans. Inform. Theory, vol. 47, no. 7, pp. 2696-2710, 2001.
14. q by LDPC code," Proc. 2006 IEEE Int. Symp. Inform. Theory, pp. 813-816, 2006.
15. J. Muramatsu, T. Uyematsu, and T. Wadayama, "Low density parity check matrices for coding of correlated sources," IEEE Trans. Inform. Theory, vol. 51, no. 10, pp. 3645-3654, 2005.
16. J. Rissanen, "Universal coding, information, prediction, and estimation," IEEE Trans. Inform. Theory, vol. 30, no. 4, pp. 629-636, 1984.
17. N. Shulman and M. Feder, "Random coding techniques for nonrandom codes," IEEE Trans. Inform. Theory, vol. 45, no. 6, pp. 2101-2104, 1999.
18. K. Visweswariah, S. R. Kulkarni, and S. Verdú, "Universal variableto-fixed length source codes," IEEE Trans. Inform. Theory, vol. 47, no. 4, pp. 1461-1472, 2001.
19. Z. Xiong, A. D. Liveris, and S. Cheng, "Distributed source coding for sensor networks," IEEE Signal Process. Mag., vol. 21, pp. 80-94, 2004.
20. J. Ziv and A. Lempel, "A universal algorithm for sequential data compression," IEEE Trans. Inform. Theory, vol. 23, no. 3, pp. 337-343, 1977.
21. J. Ziv and A. Lempel, "Compression of individual sequences by variable rate coding," IEEE Trans. Inform. Theory, vol. 24, no. 5, pp. 530-536, 1978.