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International Symposium on Information Theory and its Applications

Weight distribution of non-binary LDPC codes

Kenta Kasai, Charly Poulliat, David Declercq, Tomoharu Shibuya, Kohichi Sakaniwa

Published Dec 1, 2008• 17 citations
Publisher

Abstract

Weight distributions of binary low-density parity-check (LDPC) codes are well studied. We investigate the average distributions of symbol and binary weight for non-binary LDPC code ensemble. We derive the asymptotic growth rate and its linear approximation for small weight. Moreover, we show the typical minimum distance does not monotonically increase with the size of the field where the codes are defined.

DOI
10.1109/isita.2008.4895508

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Weight distributions of binary low-density parity-check (LDPC) codes are well studied. We investigate the average distributions of symbol and binary weight for non-binary LDPC code ensemble. We derive the asymptotic growth rate and its linear approximation for small weight. Moreover, we show the typical minimum distance does not monotonically increase with the size of the field where the codes are defined.
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.