Correcting a Fraction of Errors in Nonbinary Expander Codes with Linear Programming

TL;DR

This paper introduces a linear-programming decoder for nonbinary expander codes that guarantees maximum-likelihood certification and can correct a significant fraction of errors.

Contribution

The paper presents a novel LP decoder for nonbinary expander codes with proven error correction capabilities and maximum-likelihood certification.

Findings

Decoder corrects errors up to ~1/4 of the product of relative minimum distances

Decoder has maximum-likelihood certificate properties

Effective for nonbinary expander codes

Abstract

A linear-programming decoder for \emph{nonbinary} expander codes is presented. It is shown that the proposed decoder has the maximum-likelihood certificate properties. It is also shown that this decoder corrects any pattern of errors of a relative weight up to approximately 1/4 \delta_A \delta_B (where \delta_A and \delta_B are the relative minimum distances of the constituent codes).