Growth Rate of the Weight Distribution of Doubly-Generalized LDPC Codes: General Case and Efficient Evaluation

TL;DR

This paper introduces a new efficient numerical method for evaluating the growth rate of the weight distribution in irregular doubly-generalized LDPC codes, enabling exact analysis even for complex code ensembles.

Contribution

It develops the first efficient numerical technique for exact growth rate evaluation of D-GLDPC codes, involving solving a 4x4 polynomial system.

Findings

The method accurately computes growth rates for D-GLDPC codes.

Application to example ensembles demonstrates the technique's effectiveness.

Abstract

The growth rate of the weight distribution of irregular doubly-generalized LDPC (D-GLDPC) codes is developed and in the process, a new efficient numerical technique for its evaluation is presented. The solution involves simultaneous solution of a 4 x 4 system of polynomial equations. This represents the first efficient numerical technique for exact evaluation of the growth rate, even for LDPC codes. The technique is applied to two example D-GLDPC code ensembles.