Exposing Pseudoweight Layers in Regular LDPC Code Ensembles

TL;DR

This paper analyzes the asymptotic growth rate of the pseudoweight distribution in regular LDPC code ensembles, providing a method involving nonlinear equations and simulation results for low-degree graph covers.

Contribution

It introduces a novel approach to evaluate the asymptotic pseudoweight growth rate for regular LDPC codes using nonlinear equations and demonstrates its effectiveness through simulations.

Findings

Growth rate can be evaluated via 2M+1 nonlinear equations

Simulation results validate the theoretical approach

Analysis applies to low-degree graph covers

Abstract

A solution is presented for the asymptotic growth rate of the AWGN-pseudoweight distribution of regular low-density parity-check (LDPC) code ensembles for a selected graph cover degree M >= 1. The evaluation of the growth rate requires solution of a system of 2M+1 nonlinear equations in 2M+1 unknowns. Simulation results for the pseudoweight distribution of two regular LDPC code ensembles are presented for graph covers of low degree.