Capacity-approaching protograph codes

IEEE Journal on Selected Areas in Communications

Volumn 27, Issue 6, 2009, Pages 876-888

  Divsalar, Dariush ^a   Dolinar, Sam ^a   Jones, Christopher R ^a   Andrews, Kenneth ^a  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Decoder Implementation; Iterative decoding threshold; LDPC codes; Protograph codes; Rate compatible codes; Weight enumeration

Indexed keywords

DECODER IMPLEMENTATION; LDPC CODES; PROTOGRAPH CODES; RATE-COMPATIBLE CODE; WEIGHT ENUMERATION;

CODES (SYMBOLS); CODING ERRORS; ERROR CORRECTION;

ITERATIVE DECODING;

EID: 77952682688     PISSN: 07338716     EISSN: None     Source Type: Journal    
DOI: 10.1109/JSAC.2009.090806     Document Type: Article

References (45)

1. R. G. Gallager, Low Density Parity Check Codes. Cambridge, MA: MIT Press, 1963.
2. C. Berrou and A. Glavieux, "Near optimum error correcting coding and decoding: Turbo-codes, " IEEE Trans. Commun., Vol. 44, pp. 1261-1271, October 1996.
3. M. R. Tanner, "A recursive approach to low complexity codes, " IEEE Trans. Inform. Theory, vol. 27, pp. 533-547, 1981.
4. D.J.C. MacKay, R.M. Neal, "Near Shannon limit performance of low density parity check codes, " Electronics Letters, Vol. 32, Issue 18, 29 Aug. 1996, p. 1645.
5. T. Richardson, A. Shokrollahi, and R. Urbanke, "Design of capacityapproaching irregular low-density parity-check codes, " IEEE Trans. Inform. Theory, vol. 47, pp. 619-637, 2001.
6. M. Luby, M. Mitzenmacher, A. Shokrollahi, and D. Spielman, "Analysis of low density codes and improved designs using irregular graphs, " IEEE Trans. Inform. Theory, vol. 47, pp. 585-598, 2001.
7. T. Richardson and R. Urbanke, "The capacity of low-density parity check codes under message-passing decoding, " IEEE Trans. Inform. Theory, vol. 47, pp. 599-618, 2001.
8. Y. Kou, S. Lin, and M.P.C. Fossorier, "Low-density parity-check codes based on finite geometries: a rediscovery and new results, " IEEE Trans. Inform. Theory, vol. 47, Nov., 2001, pp. 2711-2736.
9. F. R. Kschischang, "Codes defined on graphs, " IEEE Commun. Mag., Vol. 41, Issue 8, Aug., 2003, pages 118-125.
10. T. Richardson, "Multi-Edge Type LDPC Codes, " presented at the Workshop honoring Prof. Bob McEliece on his 60th birthday, California Institute of Technology, Pasadena, California, May 24-25, 2002.
11. T. Richardson and R. Urbanke, "The Renaissance of Gallager's Low-Density Parity-Check Codes, " IEEE Commun. Mag., pages 126-131, August, 2003.
12. Jeremy Thorpe, "Low Density Parity Check (LDPC) Codes Constructed from Protographs, " JPL IPN Progress Report 42-154, August 15, 2003.
13. Richardson, et al., "Methods and apparatus for decoding LDPC codes, " United States Patent 6, 633, 856, October 14, 2003.
14. D. Divsalar, H. Jin, and R. McEliece, "Coding theorems for Turbo-like codes, " in Proc. 1998 Allerton Conference, 1998.
15. H. Jin, A. Khandekar, and R. McEliece, "Irregular repeat-accumulate codes, " in Proc. 2nd International Symposium on Turbo Codes, 2000.
16. A. Abbasfar, D. Divsalar, and K. Yao, "Accumulate Repeat Accumulate Codes, " (abstract) 2004 IEEE Intl. Symp. on Inform. Theory, Chicago, IL, June 27-July 2, 2004, and IEEE Globecom 2004, Dallas, Texas, 29 November-3 December, 2004.
17. S. Y. Chung, "On the Construction of Some Capacity-Approaching Coding Schemes, " Ph.D. dissertation, Massachusetts Institute of Technology, Cambridge, Massachusetts, Sept. 2000.
18. S.L. Fogal, R. McEliece, J. Thorpe "Enumerators for Protograph Ensembles of LDPC Codes, " 2005 IEEE Intl. Symp. on Inform. Theory, Adelaide, Australia, 4-9 September, 2005.
19. D. Divsalar, "Ensemble Weight Enumerators for Protograph LDPC Codes, " Proceedings of 2006 IEEE International Symposium on Information Theory, Seattle, Washington, July 9-14, 2006.
20. S. Abu-Surra, W. E. Ryan, and D. Divsalar, "Ensemble Enumerators for Protograph-Based Generalized LDPC Codes, " Proceedings of IEEE Globecom 2007, Washington, DC, November 26-30, 2007.
21. R. Ikegaya, K. Kasai, T. Shibuya, K. Sakaniwa, "Asymptotic weight and stopping set distributions for detailedly represented irregular LDPC code ensembles, " Proc. International Symposium on Information Theory, 27 June-2 July 2004, page 208.
22. C. Di, A. Montanari, R. Urbanke, "Weight distributions of LDPC code ensembles: combinatorics meets statistical physics, " Proc. International Symposium on Information Theory, 27 June-2 July 2004, page 102.
23. A. Orlitsky, K. Viswanathan, and J. Zhang, "Stopping set distribution of LDPC code ensembles, " IEEE Trans. Inform. Theory, vol. 51, pp. 929-953, Mar. 2005.
24. D. Burshtein, G. Miller, "Asymptotic enumeration methods for analyzing LDPC codes, " IEEE Trans. Inform. Theory, Volume 50, Issue 6, June 2004 Page(s):1115-1131
25. S. Litsyn, V. Shevelev, "Distance distributions in ensembles of irregular low-density parity-check codes, " IEEE Trans. Inform. Theory, Volume 49, Issue 12, Dec., 2003, pp. 3140-3159.
26. S. Litsyn, V. Shevelev, "On ensembles of low-density parity-check codes: asymptotic distance distributions, " IEEE Trans. Inform. Theory, Volume 48, Issue 4, April 2002, pp. 887-908.
27. I. Sason, E. Telatar and R. Urbanke, "Asymptotic input-output weight distributions and thresholds of convolutional and turbo-like codes, " IEEE Trans. Inform. Theory , vol. 48, no. 12, pp. 3052-3061, December 2002.
28. H. Pfister, I. Sason and R. Urbanke, "Capacity-achieving ensembles for the binary erasure channel with bounded complexity, " IEEE Trans. Inform. Theory , vol. 51, no. 7, pp. 2352-2379, July 2005.
29. J. P. Tillich, "The average weight distribution of Tanner code ensembles and a way to modify them to improve their weight distribution, " Proc. International Symposium on Information Theory, 27 June-2 July 2004, page 7.
30. D. Divsalar, E. Biglieri, "Upper Bounds to Error Probabilities of Coded Systems Beyond the Cutoff Rate, " IEEE Trans. Commun., vol. 51, No. 12, December 2003.
31. D. Divsalar, C. Jones, "Protograph LDPC Codes with Node Degrees at Least 3, " Global Telecommunications Conference (GLOBECOM), Nov. 2006.
32. EPFL, "Degree distribution optimizer for irregular unstructured LDPC codes (LdpcOpt), " (http://ipgdemos.epfl.ch/ldpcopt/)
33. Xiao-Yu Hu, E. Eleftheriou, D. M. Arnold, "Progressive edge-growth Tanner graphs, " IEEE Global Telecommunications Conference, GLOBECOM 2001, Volume 2, 25-29 Nov. 2001, pp. 995-1001.
34. T. Tian, C. Jones, J. Villasenor, R. D. Wesel, "Characterization and selective avoidance of cycles in irregular LDPC code construction, " IEEE Trans. Commun., Aug., 2004, pp. 1242-1247.
35. D. Divsalar, S. Dolinar, C. Jones, "Construction of Protograph LDPC Codes with Linear Minimum Distance, " International Symposium on Information Theory (ISIT), July. 2006.
36. D. Divsalar, C. Jones, S. Dolinar, J. Thorpe, "Protograph Based LDPC Codes with Minimum Distance Linearly Growing with Block Size, " IEEE Globecom 2005.
37. C. Di, R. Urbanke, T. Richardson, "Weight distributions: how deviant can you be?" Proc. 2001 IEEE International Symposium on Information Theory, 2001. 24-29 June 2001, p. 50.
38. C. Jones, S. Dolinar, K. Andrews, D. Divsalar, Y. Zhang, W. Ryan, "Functions and Architectures for LDPC Decoding, " Information Theory Workshop, Sept. 2007, pp. 577-583.
39. J. Haguenauer, E. Offer, and L. Papke, "Iterative decoding of binary block and convolutional codes, " IEEE Trans. Inform. Theory, vol. 42, no. 2, pp. 429-445, Mar. 1996.
40. E. Eleftheriou, T. Mittelholzer, and A. Dholakia, "A reduced-complexity decoding algorithm for low-density parity-check codes, " IEE Electron. Letters, vol. 37, pp. 102-104, Jan. 2001.
41. D. J. C. MacKay, "Good error-correcting codes based on very sparse matrices", IEEE Trans. Inform. Theory, vol. 45, no. 3, pp. 399-431, Mar. 1999.
42. X. Hu, E. Eleftheriou, D. Arnold, A. Dholakia, "Efficient implementations for the sun-product algorithm for decoding LDPC codes", Proc. IEEE International Conference on Communications, 2001.
43. J. Chen, A. Dholakia, E. Eleftheriou, M.P.C. Fossorier, H. Xiao-Yu, "Reduced-Complexity Decoding of LDPC Codes", IEEE Trans. Commun., vol. 53, pp. 1288-1299, Aug. 2005.
44. C. Jones, E. Valles, M. Smith, and J. Villasenor, "Approximate-Min constraint node updating for LDPC code decoding", Proc. IEEE Military Communications Conference (MILCOM), vol. 1, pp. 157-162, Oct. 2004.
45. D. E. Knuth, The Art of Computer Programming, Reading, MA. Addison Wesley, 1973, vol. 3, pp. 181-242.