Weight Distributions of Regular Low-Density Parity-Check Codes over Finite Fields
Shengtian Yang, Thomas Honold, Yan Chen, Zhaoyang Zhang, Peiliang Qiu
TL;DR
This paper provides a detailed asymptotic analysis of the weight distribution in regular LDPC codes over finite fields, revealing fundamental properties and establishing bounds on minimum distance.
Contribution
It introduces a precise asymptotic approximation for small-weight distributions and generalizes results on minimum distance for regular LDPC codes.
Findings
Asymptotic approximation for small-weight distribution
Qualitative properties of growth rate of weight distribution
Bounds on minimum distance of regular LDPC codes
Abstract
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.
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