Generalized and doubly generalized LDPC codes with random component codes for the binary erasure channel

IEEE Transactions on Information Theory

Volumn 56, Issue 4, 2010, Pages 1651-1672

  Paolini, Enrico ^a   Fossorier, Marc P C ^b   Chiani, Marco ^a  

^a UNIVERSITY OF BOLOGNA   (Italy)

^b Cergy Pontoise University   (France)

Author keywords

Binary erasure channel; Channel coding; EXIT chart; Information functions; Iterative decoding; Low density parity check (LDPC) codes; Split information functions

Indexed keywords

BINARY ERASURE CHANNEL; EXIT-CHARTS; INFORMATION FUNCTION; INFORMATION FUNCTIONS; LOW-DENSITY PARITY-CHECK (LDPC) CODES; LOW-DENSITY PARITY-CHECK CODES;

ASYMPTOTIC ANALYSIS; CHANNEL CODING; CONVOLUTIONAL CODES; EVOLUTIONARY ALGORITHMS; FUNCTION EVALUATION;

ITERATIVE DECODING;

EID: 77950252868     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2010.2040938     Document Type: Article

References (39)

1. R. Gallager, Low-Density Parity-Check Codes. Cambridge, MA: M.I.T. Press, 1963.
2. T. Richardson, M. Shokrollahi, and R. Urbanke, "Design of capacityapproaching irregular low-density parity-check codes," IEEE Trans. Inf. Theory, vol.47, pp. 619-637, Feb. 2001.
3. S. Y. Chung, G. D. Forney, T. J. Richardson, and R. Urbanke, "On the design of low-density parity-check codes within 0.0045 db of the Shannon limit," IEEE Commun. Lett., vol.5, no.2, pp. 58-60, Feb. 2001.
4. M. Luby, M. Mitzenmacher, M. Shokrollahi, and D. Spielman, "Efficient erasure correcting codes," IEEE Trans. Inf. Theory, vol.47, no.2, pp. 569-584, Feb. 2001.
5. P. Oswald and M. Shokrollahi, "Capacity-achieving sequences for the erasure channel," IEEE Trans. Inf. Theory, vol.48, no.12, pp. 364-373, Dec. 2002.
6. M. Shokrollahi, "New sequences of linear time erasure codes approaching the channel capacity," in Proc. Int. Symp. Appl. Algebra, Algebraic Algorithms, Error Correcting Codes, M. Fossorier, H. Imai, S. Lin, and A. Poli, Eds., Berlin, Germany, 1999, Lecture Notes in Computer Science, pp. 65-76.
7. T. Richardson, "Error floors of LDPC codes," in Proc. Forty-First Allerton Conf. Commun., Contr. Comput., Monticello, IL, Oct. 2003, pp. 1426-1435.
8. M. Chiani and A. Ventura, "Design and performance evaluation of some high-rate irregular low-density parity-check codes," in Proc. 2001 IEEE Global Telecommun. Conf., San Antonio, TX, Nov. 2001, vol.2, pp. 990-994.
9. A. Amraoui, A. Montanari, and R. Urbanke, "How to find good finite-length codes: From art towards science," European Trans. Telecommun., vol.18, no.5, pp. 491-508, Aug. 2007.
10. C. Di, R. Urbanke, and T. Richardson, "Weight distribution of lowdensity parity-check codes," IEEE Trans. Inf. Theory, vol.52, no.11, pp. 4839-4855, Nov. 2006.
11. C. Di, D. Proietti, I. E. Telatar, T. J. Richardson, and R. Urbanke, "Finite-length analysis of low-density parity-check codes on the binary erasure channel," IEEE Trans. Inf. Theory, vol.48, no.6, pp. 1570-1579, June 2002.
12. R. M. Tanner, "A recursive approach to low complexity codes," IEEE Trans. Inf. Theory, vol.27, no.5, pp. 533-547, Sep. 1981.
13. M. Lentmaier and K. Zigangirov, "On generalized low-density paritycheck codes based on Hamming component codes," IEEE Commun. Lett., vol.3, no.8, pp. 248-250, Aug. 1999.
14. J. Boutros, O. Pothier, and G. Zemor, "Generalized low density (Tanner) codes," in Proc. 1999 IEEE Int. Conf. Commun., Vancouver, Canada, Jun. 1999, vol.1, pp. 441-445.
15. C. Measson and R. Urbanke, "Further analytic properties of EXIT-like curves and applications," in Proc. 2003 IEEE Int. Symp. Inf. Theory, Yokohama, Japan, Jun./Jul. 2003, p. 266.
16. I. Djordjevic, O. Milenkovic, and B. Vasic, "Generalized low-density parity-check codes for optical communication systems," J. Lightw. Technol., vol.23, no.5, pp. 1939-1946, May 2005.
17. M. Lentmaier,D. Truhachev, K. Zigangirov, and D. Costello, "An analysis of the block error probability performance of iterative decoding," IEEE Trans. Inf. Theory, vol.51, no.11, pp. 3834-3855, Nov. 2005.
18. N. Miladinovic and M. Fossorier, "Generalized LDPC codes and generalized stopping sets," IEEE Trans. Commun., vol.56, no.2, pp. 201-212, Feb. 2008.
19. F. Kuo and L. Hanzo, "Symbol-flipping based decoding of generalized low-density parity-check codes over GF(q)," in Proc. 2006 IEEE Wireless Commun. Netw. Conf., Las Vegas, NV, Apr. 2006, vol.3, pp. 1207-1211.
20. S. Abu-Surra, G. Liva, and W. Ryan, "Low-floor Tanner codes via Hamming-node or RSCC-node doping," in Proc. of Int. Symp. Applied Algebra, Algebraic Algoritmhs, and Error Correcting Codes, M. Fossorier, H. Imai, S. Lin, and A. Poli, Eds., Berlin, Germany, 2006, Lecture Notes in Computer Science, pp. 245-254.
21. J. Chen and R. M. Tanner, "A hybrid coding scheme for the Gilbert- Elliott channel," IEEE Trans. Commun., vol.54, no.10, pp. 1787-1796, Oct. 2006.
22. G. Liva, W. Ryan, and M. Chiani, "Quasi-cyclic generalized LDPC codes with low error floors," IEEE Trans. Commun., vol.56, no.1, pp. 49-57, Jan. 2008.
23. 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.
24. Y.Wang and M. Fossorier, "Doubly generalized LDPC codes over the AWGNchannel," IEEE Trans. Commun., vol.57, no.5, pp. 1312-1319, May 2009.
25. Y. Wang and M. Fossorier, "EXIT chart analysis for doubly generalized LDPC codes," in Proc. 2006 IEEE Global Telecommun. Conf., San Francisco, CA, Nov. 2006, pp. 1-6.
26. S. Dolinar, "Design and iterative decoding of networks of many small codes," in Proc. 2003 IEEE Int. Symp. Inf. Theory, Yokohama, Japan, Jun./Jul. 2003, p. 346.
27. G. Zemor, "On expander codes," IEEE Trans. Inf. Theory, vol.47, no.2, pp. 835-837, Feb. 2001.
28. A. Barg and G. Zemor, "Distance properties of expander codes," IEEE Trans. Inf. Theory, vol.52, no.1, pp. 78-90, Jan. 2006.
29. S. Abu-Surra, G. Liva, and W. Ryan, "Design of generalized LDPC codes and their decoders," in Proc. 2007 IEEE Commun. TheoryWorkshop, Sedona, AZ, May 2007, p. 2.
30. S. Ten Brink, "Convergence behavior of iteratively decoded parallel concatenated codes," IEEE Trans. Commun., vol.49, no.10, pp. 1727-1737, Oct. 2001.
31. A. Ashikhmin, G. Kramer, and S. Ten Brink, "Extrinsic information transfer functions: Model and erasure channel properties," IEEE Trans. Inf. Theory, vol.50, no.11, pp. 2657-2673, Nov. 2004.
32. E. Sharon, A. Ashikhmin, and S. Litsyn, "Analysis of low-density parity-check codes based on EXIT functions," IEEE Trans. Commun., vol.54, no.8, pp. 1407-1414, Aug. 2006.
33. T. Helleseth, T. Kløve, and V. I. Levenshtein, "On the information function of an error-correcting code," IEEE Trans. Inf. Theory, vol.43, no.2, pp. 549-557, Mar. 1997.
34. E. Paolini, M. Fossorier, and M. Chiani, "Doubly-generalized LDPC codes: Stability bound over the BEC," IEEE Trans. Inf. Theory, vol.55, no.3, pp. 1027-1046, Mar. 2009.
35. A. Barg, Complexity Issues in Coding Theory, Handbook on Coding Theory, (Part I: Algebraic Coding). Amsterdam, The Netherlands: North Holland, 1998.
36. K. Price, R. Storn, and J. Lampinen, Differential Evolution: A Practical Approach to Global Optimization. Berlin, Germany: Springer- Verlag, 2005.
37. Handbook of Evolutionary Computation, T. Back, D. Fogel, and Z. Michalewicz, Eds. Bristol, U.K.: IOP Publishing Ltd., 1997.
38. K. Price and R. Storn, "Differential evolution-A simple and efficient heuristic for global optimization over continuous spaces," J. Global Optimization, vol.11, no.4, pp. 341-359, Dec. 1997.
39. M. Shokrollahi and R. Storn, "Design of efficient erasure codes with differential evolution," in Proc. IEEE Int. Symp. Inf. Theory, Sorrento, Italy, Jun. 2000, p. 5.