Low-Density Parity-Check Codes Which Can Correct Three Errors Under Iterative Decoding

TL;DR

This paper establishes conditions under which low-density parity-check (LDPC) codes with specific column weights can reliably correct three errors using iterative hard-decision decoding, and provides a construction method for such codes.

Contribution

It introduces necessary and sufficient conditions for column-weight three and four LDPC codes to correct three errors, along with a construction technique and performance simulations.

Findings

Conditions for correcting three errors in LDPC codes are established.

A construction method for codes meeting these conditions is proposed.

Simulation results demonstrate the effectiveness of the constructed codes.

Abstract

In this paper, we give necessary and sufficient conditions for low-density parity-check (LDPC) codes with column-weight three to correct three errors when decoded using hard-decision message-passing decoding. Additionally, we give necessary and sufficient conditions for column-weight-four codes to correct three errors in four iterations of hard-decision message-passing decoding. We then give a construction technique which results in codes satisfying these conditions. We also provide numerical assessment of code performance via simulation results.