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IEEE International Symposium on Information Theory (ISIT)

Weight distribution for non-binary cluster LDPC code ensemble

T. Nozaki, Masaki Maehara, Kenta Kasai, Kohichi Sakaniwa

Published Jul 1, 2013• 2 citations
Publisher

Abstract

In this paper, we derive the average weight distributions for the irregular non-binary cluster low-density parity-check (LDPC) code ensembles. Moreover, we give the exponential growth rate of the average weight distribution in the limit of large code length. We show that there exist (2, dc)-regular non-binary cluster LDPC code ensembles whose normalized typical minimum distances are strictly positive.

DOI
10.1109/isit.2013.6620742

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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.