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Weight Distributions of Regular Low-Density Parity-Check Codes over Finite Fields (1010.2030v3)
Published 11 Oct 2010 in cs.IT and math.IT
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.
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