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IEEE International Symposium on Information Theory (ISIT)

Weight distributions of non-binary multi-edge type LDPC code ensembles

Giuliano Garrammone, David Declercq, M.P.C. Fossorier

Published Jun 1, 2015• 2 citations
Publisher

Abstract

The non-binary codeword weight distribution and its growth rate are developed for non-binary multi-edge type ensembles of low-density parity-check codes. Moreover, an analysis of the growth rate for small weights is provided. The derived expressions can serve as powerful and flexible tools to analyze and design the non-binary low-density parity-check codes that fall within the multi-edge type framework.

DOI
10.1109/isit.2015.7282982

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The non-binary codeword weight distribution and its growth rate are developed for non-binary multi-edge type ensembles of low-density parity-check codes. Moreover, an analysis of the growth rate for small weights is provided. The derived expressions can serve as powerful and flexible tools to analyze and design the non-binary low-density parity-check codes that fall within the multi-edge type framework.
Non-binary multi-edge type ensembles of low-density parity-check codes are analyzed in terms of non-binary codeword weight distribution and its growth rate. In particular, an exact expression of the growth rate for small weights is developed. As a side result, the stopping set distributions of these ensembles are developed. Examples of weight distributions are provided, showing that the derived closed-form expressions can be easily evaluated. The obtained results can thus be exploited to analyze and design non-binary low-density parity-check codes that fall within the multi-edge type framework such as, but not limited to, protograph-based codes.
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.