Weight Distributions of Regular Low-Density Parity-Check Codes over Finite Fields
arXiv:1010.2030 · doi:10.1109/TIT.2011.2162642
Abstract
The average weight distribution of a regular low-density parity-check (LDPC) code ensemble over a finite field is thoroughly analyzed. In particular, a precise asymptotic approximation of the average weight distribution is derived for the small-weight case, and a series of fundamental qualitative properties of the asymptotic growth rate of the average weight distribution are proved. Based on this analysis, a general result, including all previous results as special cases, is established for the minimum distance of individual codes in a regular LDPC code ensemble.
15 pages, 5 figures, accepted for publication in IEEE Transactions on Information Theory, July 2011