Multiplicatively repeated nonbinary LDPC codes

IEEE Transactions on Information Theory

Volumn 57, Issue 10, 2011, Pages 6788-6795

  Kasai, Kenta ^a   Declercq, David ^b   Poulliat, Charly ^b   Sakaniwa, Kohichi ^a  

^a Tokyo Institute of Technology ^*  (Japan)

^b ENSEA   (France)

Author keywords

Iterative decoding; low rate code; nonbinary low density parity check code; rate compatible code; repetition code

Indexed keywords

DECODING ALGORITHM; LDPC CODES; LOW-RATE CODE; NON-BINARY; NON-BINARY LDPC CODES; RATE COMPATIBLE CODES; RATE-COMPATIBLE CODE; REPETITION CODE;

CODING ERRORS; COMPUTATIONAL COMPLEXITY; ERROR CORRECTION; ITERATIVE DECODING; SIGNAL ENCODING;

CONCATENATED CODES;

EID: 80053959951     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2011.2162259     Document Type: Article

References (32)

1. K. Kasai, D. Declercq, C. Poulliat, and K. Sakaniwa, "Rate- compatible non-binary LDPC codes concatenated with multiplicative repetition codes," in Proc. 2010 IEEE Int. Symp. Inf. Theory (ISIT), Jun. 2010, pp. 844-848.
2. R. G. Gallager, Low Density Parity Check Codes, ser. ResearchMonograph Series. Cambridge, MA: MIT Press, 1963.
3. T. 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.
4. T. J. Richardson, M. A. Shokrollahi, and R. L. Urbanke, "Design of capacity-approaching irregular low-density parity-check codes," IEEE Trans. Inf. Theory, vol. 47, no. 2, pp. 619-637, Feb. 2001.
5. T. Richardson and R. Urbanke, "Multi-edge type LDPC codes," 2003 [Online]. Available: http://ece.iisc.ernet.in/~vijay/multiedge.pdf
6. D. Divsalar, S. Dolinar, and C. Jones, "Low-rate LDPC codes with simple protograph structure," inProc. 2005 IEEE Int. Symp. Inf.Theory (ISIT), Sep. 2005, pp. 1622-1626.
7. G. Yue, L. Ping, and X. Wang, "Generalized low-density parity-check codes based on Hadamard constraints," IEEE Trans. Inf. Theory, vol. 53, no. 3, pp. 1058-1079, Mar. 2007.
8. S. Haykin, Communication Systems, 4th ed. New York:Wiley, 2001.
9. M. Davey and D. MacKay, "Low-density parity check codes over GF ," IEEE Commun. Lett., vol. 2, no. 6, pp. 165-167, Jun. 1998.
10. W. Chang and J. Cruz, "Nonbinary LDPC codes for 4-kB sectors," IEEE Trans. Magn., vol. 44, no. 11, pp. 3781-3784, Nov. 2008.
11. I. Djordjevic and B. Vasic, "Nonbinary LDPC codes for optical communication systems," IEEE Photon. Technol. Lett., vol. 17, no. 10, pp. 2224-2226, Oct. 2005.
12. B. Zhou, J. Kang, S. Song, S. Lin, K. Abdel-Ghaffar, and M. Xu, "Construction of non-binary quasi-cyclic LDPC codes by arrays and array dispersions," IEEE Trans. Commun., vol. 57, no. 6, pp. 1652-1662, Jun. 2009.
13. M. Arabaci, I. Djordjevic, R. Saunders, and R. Marcoccia, "High-rate nonbinary regular quasi-cyclic LDPC codes for optical communications," J. Lightw. Technol., vol. 27, no. 23, pp. 5261-5267, Dec. 2009.
14. B. Zhou, J. Kang, Y. Tai, S. Lin, and Z. Ding, "High performance nonbinary quasi-cyclic LDPC codes on euclidean geometries LDPC codes on euclidean geometries," IEEE Trans. Commun., vol. 57, no. 5, pp. 1298-1311, May 2009.
15. C. Poulliat, M. Fossorier, and D. Declercq, "Design of regular-LDPC codes over GF using their binary images," IEEE Trans. Commun., vol. 56, no. 10, pp. 1626-1635, Oct. 2008.
16. L. Sassatelli, D. Declercq, and C. Poulliat, "Low-rate non-binary hybrid LDPC codes," in Proc. 5th Int. Symp. Turbo Codes Related Topics, Sep. 2008, pp. 225-230.
17. V. Rathi and R. Urbanke, "Density evolution, threshold and the stability condition for non-binary LDPC codes," IEE Proc.-Commun., vol. 152, no. 6, pp. 1069-1074, 2005.
18. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes. Amsterdam, The Netherlands: Elsevier, 1977.
19. T. Richardson and R. Urbanke, Modern Coding Theory. Cambridge, U.K.: Cambridge Univ. Press, 2008.
20. J. Justesen, "Class of constructive asymptotically good algebraic codes," IEEE Trans. Inf. Theory, vol. IT-18, no. 5, pp. 652-656, Sep. 1972.
21. M. Davey and D. MacKay, "Low density parity check codes over GF ," in Proc. Inf. Theory Workshop, Jun. 1998, pp. 70-71.
22. D. Declercq and M. Fossorier, "Decoding algorithms for nonbinary LDPC codes over GF ," IEEE Trans. Commun., vol. 55, no. 4, pp. 633-643, Apr. 2007.
23. A. Bennatan and D. Burshtein, "On the application of LDPC codes to arbitrary discrete-memoryless channels," IEEE Trans. Inf. Theory, vol. 50, no. 3, pp. 417-438, Mar. 2004.
24. G. Li, I. Fair, and W. Krzymien, "Density evolution for nonbinary LDPC codes under Gaussian approximation," IEEE Trans. Inf. Theory, vol. 55, no. 3, pp. 997-1015, Mar. 2009.
25. D. Klinc, J. Ha, and S. McLaughlin, "Optimized puncturing and shortening distributions for nonbinary LDPC codes over the binary erasure channel," in Proc. 46th Annu. Allerton Conf. Commun., Control, Comput., Sep. 2008, pp. 1053-1058.
26. H. Pfister and I. Sason, "Accumulate repeat accumulate codes: Capacity-achieving ensembles of systematic codes for the erasure channel with bounded complexity," IEEE Trans. Inf. Theory, vol. 53, no. 6, pp. 2088-2115, Jun. 2007.
27. C. Di, D. Proietti, I. Telatar, T. Richardson, and R. Urbanke, "Finitelength analysis of low-density parity-check codes on the binary erasure channel," IEEE Trans. Inf. Theory, vol. 48, no. 6, pp. 1570-1579, Jun. 2002.
28. C. E. Shannon, "Capacity of the band-limited Gaussian channel," Bell System Tech. J., vol. 38, pp. 611-656, May 1959.
29. A. Valembois and M. Fossorier, "Sphere-packing bounds revisited for moderate block lengths," IEEE Trans. Inf. Theory, vol. 50, no. 12, pp. 2998-3014, Dec. 2004.
30. G.Wiechman and I. Sason, "An improved sphere-packing bound for finite-length codes over symmetric memoryless channels," IEEE Trans. Inf. Theory, vol. 54, no. 5, pp. 1962-1990, May 2008.
31. M. Davey, "Error-correction using low-density parity-check codes," Ph.D. dissertation, Univ. Cambridge, Cambridge, U.K., 1999.
32. L. Sassatelli and D. Declercq, "Nonbinary hybrid LDPC codes," IEEE Trans. Inf. Theory, vol. 56, no. 10, pp. 5314-5334, Oct. 2010.