On decoding of low-density parity-check codes over the binary erasure channel

IEEE Transactions on Information Theory

Volumn 50, Issue 3, 2004, Pages 439-454

  Pishro Nik, Hossein ^a   Fekri, Faramarz ^a  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Bipartite graphs; Erasure channel; Improved decoding; Iterative decoding; Low density parity check (LDPC) codes; Maximum likelihood (ML) decoding; Performance bound

Indexed keywords

ALGORITHMS; BIT ERROR RATE; BOUNDARY CONDITIONS; CODES (SYMBOLS); COMMUNICATION CHANNELS (INFORMATION THEORY); COMPUTATIONAL COMPLEXITY; COMPUTER SIMULATION; GRAPH THEORY;

BINARY ERASURE CHANNEL; BIPARTITE GRAPHS; IMPROVED DECODING; LOW DENSITY PARITY CHECK CODES; MAXIMUM LIKELIHOOD DECODING; PERFORMANCE BOUND;

DECODING;

EID: 1842429214     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2004.824918     Document Type: Article

References (20)

1. M. Luby, M. Mitzenmacher, M. Shokrollahi, and D. Spielman, "Efficient erasure correcting codes," IEEE Trans. Inform. Theory, vol. 47, pp. 569-584, Feb. 2001.
2. C. Di, D. Proietti, I. E. Telatar, T. Richardson, and R. Urbanke, "Finite-length analysis of low-density parity-check codes on the binary erasure channel," IEEE Trans. Inform. Theory, vol. 48, pp. 1570-1579, June 2002.
3. M. A. Shokrollahi, "Capacity-achieving sequences," IMA Volumes in Mathematics and its Applications, vol. 123, pp. 153-166, 2000.
4. ____, "New sequences of linear time erasure codes approaching the channel capacity," AAECC, pp. 65-76, 1999.
5. P. Oswald and M. A. Shokrollahi, "Capacity-achieving sequences for the erasure channel," IEEE Trans. Inform. Theory, vol. 48, pp. 3019-3028, Dec. 2002.
6. T. J. Richardson and R. L. Urbanke, "The capacity of low-density parity-check codes under message-passing decoding," IEEE Trans. Inform. Theory, vol. 47, pp. 599-618, Feb. 2001.
7. T. J. Richardson, M. A. Shokrollahi, and R. L. Urbanke, "Design of capacity-approaching irregular low-density parity-check codes," IEEE Trans. Inform. Theory, vol. 47, pp. 619-637, Feb. 2001.
8. H. Pishro-Nik and F. Fekri, "Improved decoding algorithms for low-density parity-check codes," in Proc. 3rd Int. Symp. Turbo Codes and Related Topics, Brest, France, Sept. 2003.
9. D. J. C. MacKay, "Good error-correcting codes based on very sparse matrices," IEEE Trans. Inform. Theory, vol. 45, pp. 399-431, Mar. 1999.
10. 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, pp. 2696-2710, Nov. 2001.
11. D. Burshtein, M. Krivelevich, S. Litsyn, and G. Miller, "Upper bounds on the rate of ldpc codes," IEEE Trans. Inform. Theory, vol. 48, pp. 2437-2449, Sept. 2002.
12. R. M. Tanner, "A recursive approach to low complexity codes," IEEE Trans. Inform. Theory, vol. IT-27, pp. 533-547, Sept. 1981.
13. S. Litsyn and V. Shevelev, "On ensembles of low-density parity-check codes: Asymptotic distance distributions," IEEE Trans. Inform. Theory, vol. 48, pp. 887-908, Apr. 2002.
14. D. Burshtein and G. Miller, "Asymptotic enumeration method for analyzing LDPC codes," IEEE Trans. Inform. Theory, submitted for publication.
15. R. G. Galleger, Low-Density Parity-Check Codes. Cambridge, MA: MIT Press, 1963.
16. C. Di, T. Richardson, and R. Urbanke, "Weight distributions: How deviant can you be?," in Proc. 2001 IEEE Int. Symp. Information Theory, Washington, DC, 2001, p. 50.
17. R. Urbanke. Unpublished research. [Online]. Available: http://lthcwww.epfl.ch/research/ldpcopt/
18. S. Litsyn and V. Shevelev, "Distance distributions in ensembles of irregular low-density parity-check codes," IEEE Trans. Inform. Theory, submitted for publication.
19. I. Sason and R. Urbanke, "Parity-check density versus performance of binary linear block codes over memoryless symmetric channels," IEEE Trans. Inform. Theory, vol. 49, pp. 1611-1635, July 2003.
20. T. Richardson, A. Shokrollahi, and R. Urbanke, "Finite-length analysis of low-density parity-check ensembles for the binary erasure channel," in Proc. 2002 IEEE Int. Symp. Information Theory, Lausanne, Switzerland, June/July 2001, p. 1.