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Cambridge University Press eBooks

Weight Distribution and Minimum Distance of LDPC Codes

Enrico Paolini, Gianluigi Liva, Balázs Matuz, Marco Chiani

Published Feb 25, 2026• 0 citations
Publisher

Abstract

Weight distribution of LDPC codes: More advanced topics on LDPC codes are covered by Chapter 5, which is focused on structural properties of these codes related to their weight distributions. This chapter addresses weight distributions of unstructured and partially structured LDPC code ensembles as well as weight distribution exponents. It also addresses ensemble expurgation and minimum distance analysis for LDPC codes.

DOI
10.1017/9781316443354.006

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Weight distribution of LDPC codes: More advanced topics on LDPC codes are covered by Chapter 5, which is focused on structural properties of these codes related to their weight distributions. This chapter addresses weight distributions of unstructured and partially structured LDPC code ensembles as well as weight distribution exponents. It also addresses ensemble expurgation and minimum distance analysis for LDPC codes.
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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.