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IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences

Weight Distributions of Non-binary LDPC Codes

Kenta Kasai, Charly Poulliat, David Declercq, Kohichi Sakaniwa

Published Jan 1, 2011• 22 citations
Publisher

Abstract

In this paper, we study the average symbol and bit-weight distributions for ensembles of non-binary low-density parity-check codes defined on GF(2p). Moreover, we derive the asymptotic exponential growth rate of the weight distributions in the limit of large codelength. Interestingly, we show that the normalized typical minimum distance does not monotonically increase with the size of the field.

DOI
10.1587/transfun.e94.a.1106

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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.