Distance Distributions in Ensembles of Irregular Low-Density Parity-Check Codes

IEEE Transactions on Information Theory

Volumn 49, Issue 12, 2003, Pages 3140-3159+3353

  Litsyn, Simon ^a   Shevelev, Vladimir ^b  

^a TEL AVIV UNIVERSITY   (Israel)

^b BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

Author keywords

Distance distributions; Low density parity check (LDPC) codes

Indexed keywords

ASYMPTOTIC STABILITY; LINEAR SYSTEMS; MAXIMUM LIKELIHOOD ESTIMATION; OPTIMIZATION; POLYNOMIAL APPROXIMATION; PROBABILITY;

DISTANCE DISTRIBUTION; LOW-DENSITY PARITY-CHECK (LDPC) CODES;

SIGNAL ENCODING;

EID: 0347968063     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2003.820012     Document Type: Article

References (14)

1. R. G. Gallager, Information Theory and Reliable Communication. New York: Wiley, 1968.
2. _, Low Density Parity Check Codes. Cambridge, MA: MIT Press, 1963.
3. I. J. Good and J. F. Crook, "The enumeration of arrays and a generalization related to contingency tables," Discr. Math., vol. 19, no. 1, pp. 23-45, 1977.
4. C. Di, R. Urbanke, and T. Richardson, "Weight distributions: How deviant can you be?," in Proc. Int. Symp. Information Theory (ISIT 2001), Washington, DC, 2001, p. 50.
5. S. Litsyn and V. Shevelev, "On ensembles of low-density parity check codes: Asymptotic distance distributions," IEEE Trans. Inform. Theory, vol. 48, p. 887, Apr. 2002.
6. M. Luby, M. Mitzenmacher, A. Shokrollahi, and D. Spielman, "Analysis of low density codes and improved designs using irregular graphs," in Proc. 30th Annu. ACM Symp. Theory of Computing, 1998, pp. 249-258.
7. D. J. C. MacKay, "Good error-correcting codes based on very sparse matrices," IEEE Trans. Inform. Theory, vol. 45, pp. 399-431, Mar. 1999.
8. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes. Amsterdam, The Netherlands: Elsevier, 1977.
9. 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.
10. P. E. O'Neil, "Asymptotics and random matrices with row-sum and column-sum restrictions," Bull. Amer. Math. Soc., vol. 75, pp. 1276-1282, 1969.
11. 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, Feb. 2001.
12. T. Richardson, A. Shokrollahi, and R. Urbanke, "Design of capacity-approaching irregular low-density parity-check codes," IEEE Trans. Inform. Theory, vol. 47, pp. 619-637, Feb. 2001.
13. I. Sason and S. Shamai (Shitz), "Improved upper bounds on the ensemble performance of ML decoded low density parity check codes," IEEE Commun. Lett., vol. 4, pp. 89-91, Mar. 2000.
14. A. Shokrollahi, "Capacity achieving sequences," in Codes, Systems, and Graphical Models, B. Marcus and J. Rosenthal, Eds. New York: Springer-Verlag, 2000, IMA Series on Mathematics and its Applications, pp. 153-166.