Error correction capability of column-weight-three LDPC codes under the Gallager A algorithm-part II

IEEE Transactions on Information Theory

Volumn 56, Issue 6, 2010, Pages 2626-2639

  Chilappagari, Shashi Kiran ^a   Nguyen, Dung Viet ^b   Vasic, Bane ^b   Marcellin, Michael W ^b  

^a MARVELL SEMICONDUCTOR INC   (United States)

^b University of Arizona   (United States)

Author keywords

Error floor; Gallager A algorithm; Girth; Low density parity check (LDPC) codes; Trapping sets

Indexed keywords

ERROR FLOOR; GALLAGER A ALGORITHM; GIRTH; LOW-DENSITY PARITY-CHECK (LDPC) CODES; TRAPPING SETS;

ALGORITHMS; BLOCK CODES; CODING ERRORS; ERROR CORRECTION; FLOORS;

FREQUENCY SELECTIVE FADING;

EID: 77957556478     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2010.2046203     Document Type: Article

References (23)

1. R. G. Gallager, Low Density Parity Check Codes. Cambridge, MA: MIT Press, 1963.
2. R. M. Tanner, "A recursive approach to low complexity codes," IEEE Trans. Inf. Theory, vol.IT-27, no.5, pp. 533-547, May 1981.
3. T. J. Richardson and R. Urbanke, "The capacity of low-density parity-check codes under message-passing decoding," IEEE Trans Inf. Theory, vol.47, no.2, pp. 599-618, Feb. 2001. (Pubitemid 32318092)
4. T. J. Richardson, M. Shokrollahi, and R. Urbanke, "Design of capacityapproaching irregular low-density parity-check codes," IEEE Trans Inf. Theory, vol.47, no.2, pp. 638-656, Feb. 2001. (Pubitemid 32318094)
5. D. J. C. MacKay and M. J. Postol, "Weaknesses of Margulis and Ramanujan-Margulis low-density parity-check codes," in Proc. MFCSIT, 2003, vol.74 [Online]. Available: http://www.inference.phy.cam.ac.uk/mackay/abstracts/ margulis.html, Elsevier, Galway, ser. Electronic Notes in Theoretical Computer Science
6. T. J. Richardson, "Error floors of LDPC codes," in Proc. 41st Annu. Allerton Conf. Communications, Control and Computing, 2003, pp. 1426-1435 [Online]. Available: http://www.hpl.hp.com/personal/Pascal-Vontobel/ pseudocodewords/papers
7. M. Ivkovic, S. K. Chilappagari, and B. Vasic, "Eliminating trapping sets in low-density parity-check codes by using Tanner graph covers," IEEE Trans. Inf. Theory, vol.54, no.8, pp. 3763-3768, Aug. 2008.
8. V. V. Zyablov and M. S. Pinsker, "Estimation of the error-correction complexity for Gallager low-density codes," Probl. Inf. Transmission, vol.11, no.1, pp. 18-28, 1976.
9. M. Sipser and D. Spielman, "Expander codes," IEEE Trans. Inf. Theory, vol.42, no.6, pp. 1710-1722, Nov. 1996.
10. D. Burshtein and G. Miller, "Expander graph arguments for message- passing algorithms," IEEE Trans. Inf. Theory, vol.47, no.2, pp. 782-790, Mar. 2001.
11. D. Burshtein, "On the error correction of regular LDPC codes using the flipping algorithm," IEEE Trans. Inf. Theory, vol.54, no.2, pp. 517-530, Feb. 2008.
12. J. Feldman, M.Wainwright, and D. Karger, "Using linear programming to decode binary linear codes," IEEE Trans. Inf. Theory, vol.51, no.3, pp. 954-972, Mar. 2005.
13. J. Feldman, T. Malkin, R. A. Servedio, C. Stein, and M. J.Wainwright, "LP decoding corrects a constant fraction of errors," IEEE Trans. Inf. Theory, vol.53, no.1, pp. 82-89, Jan. 2007.
14. C. Daskalakis, A. G. Dimakis, R. M. Karp, and M. J. Wainwright, "Probabilistic analysis of linear programming decoding," IEEE Trans. Inf. Theory, vol.54, no.8, pp. 3565-3578, Aug. 2008.
15. S. K. Chilappagari, D. V. Nguyen, B. Vasic, and M. W. Marcellin, "On trapping sets and guaranteed error correction capability of LDPC codes and GLDPC codes," IEEE Trans. Inf. Theory vol.56, no.4, pp. 1600-1611, Apr. 2010.
16. C. Di, D. Proietti, T. Richardson, E. Telatar, and R. Urbanke, "Finite length analysis of low-density parity-check codes on the binary erasure channel," IEEE Trans. Inf. Theory, vol.48, pp. 1570-1579, 2002. (Pubitemid 34759861)
17. A. Orlitsky, R. Urbanke, K. Viswanathan, and J. Zhang, "Stopping sets and the girth of Tanner graphs," in Proc. IEEE Int. Symp. Information Theory, 2002, p. 2.
18. S. K. Chilappagari and B. Vasic, "Error correction capability of column-weight-three LDPC codes," IEEE Trans. Inf. Theory, vol.55, no.5, pp. 2055-2061, May 2009.
19. S. K. Chilappagari, A. R. Krishnan, and B. Vasic, "LDPC codes which can correct three errors under iterative decoding," in Proc. IEEE Inf. Theory Workshop, May 2008, pp. 406-410.
20. A. Shokrollahi, "An introduction to low-density parity-check codes," in Theoretical Aspects of Computer Science: Advanced Lectures. New York: Springer-Verlag, 2002, pp. 175-197.
21. S. K. Chilappagari, M. Chertkov, M. G. Stepanov, and B. Vasic, "Instanton- based techniques for the analysis and reduction of error floors of LDPC codes," presented at the IEEE JSACon Capacity Approaching Codes, 2009 [Online]. Available: http://arxiv.org/abs/0903.1624
22. G. A. Margulis, "Explicit constructions of graphs without short cycles and low density codes," Combinatorica, vol.2, no.1, pp. 71-78, 1982.
23. J. Rosenthal and P. O. Vontobel, "Constructions of LDPC codes using Ramanujan graphs and ideas from Margulis," in Proc. 38th Annu. Allerton Conf. Communication, Control, and Computing, 2000, pp. 248-257.