论文信息 - Upper bounds on the rate of LDPC codes as a function of minimum distance

Upper bounds on the rate of LDPC codes as a function of minimum distance

New upper bounds on the rate of low-density parity-check (LDPC) codes as a function of the minimum distance of the code are derived. These bounds are based on combinatorial arguments and linear programming. They improve on the previous bounds due to Burshtein et al. It is proved that at least for high rate LDPC codes have worse relative minimum distance than the one guaranteed by the Gilbert-Varshamov bound

Simon Litsyn | Yael Ben-Haim

[1] F. MacWilliams,et al. The Theory of Error-Correcting Codes , 1977 .

[2] Alon Orlitsky,et al. Stopping set distribution of LDPC code ensembles , 2003, IEEE Transactions on Information Theory.

[3] R. Urbanke,et al. Weight Distribution of Iterative Coding Systems: How Deviant can You be? , 2001 .

[4] Robert J. McEliece,et al. New upper bounds on the rate of a code via the Delsarte-MacWilliams inequalities , 1977, IEEE Trans. Inf. Theory.

[5] Simon Litsyn,et al. Distance distributions in ensembles of irregular low-density parity-check codes , 2003, IEEE Trans. Inf. Theory.

[6] Simon Litsyn,et al. Survey of binary Krawtchouk polynomials , 1999, Codes and Association Schemes.

[7] Changyan Di. Asymptotic and finite-length analysis of low-density parity-check codes , 2004 .

[8] Simon Litsyn,et al. On ensembles of low-density parity-check codes: Asymptotic distance distributions , 2002, IEEE Trans. Inf. Theory.

[9] Simon Litsyn,et al. On relations between covering radius and dual distance , 1999, IEEE Trans. Inf. Theory.

[10] Robert G. Gallager,et al. Low-density parity-check codes , 1962, IRE Trans. Inf. Theory.

[11] David Burshtein,et al. Asymptotic enumeration methods for analyzing LDPC codes , 2004, IEEE Transactions on Information Theory.

[12] Simon Litsyn,et al. Upper bounds on the rate of LDPC codes as a function of minimum distance , 2002, IEEE Transactions on Information Theory.