Construction of Near-Optimum Burst Erasure Correcting Low-Density Parity-Check Codes

TL;DR

This paper introduces a new algorithm called PSS for optimizing LDPC codes to effectively correct both independent erasures and burst erasures, enhancing their performance on erasure channels.

Contribution

The paper presents the PSS algorithm for improving LDPC code parity-check matrices to better handle burst erasures without sacrificing performance on memory-less channels.

Findings

PSS algorithm improves burst erasure correction in LDPC codes.

Optimized codes maintain performance on memory-less erasure channels.

Numerical results demonstrate effectiveness across various LDPC codes.

Abstract

In this paper, a simple, general-purpose and effective tool for the design of low-density parity-check (LDPC) codes for iterative correction of bursts of erasures is presented. The design method consists in starting from the parity-check matrix of an LDPC code and developing an optimized parity-check matrix, with the same performance on the memory-less erasure channel, and suitable also for the iterative correction of single bursts of erasures. The parity-check matrix optimization is performed by an algorithm called pivot searching and swapping (PSS) algorithm, which executes permutations of carefully chosen columns of the parity-check matrix, after a local analysis of particular variable nodes called stopping set pivots. This algorithm can be in principle applied to any LDPC code. If the input parity-check matrix is designed for achieving good performance on the memory-less erasure channel, then the code obtained after the application of the PSS algorithm provides good joint correction of independent erasures and single erasure bursts. Numerical results are provided in order to show the effectiveness of the PSS algorithm when applied to different categories of LDPC codes.