Optimally Decoding Two-Dimensional Reed-Solomon Codes Against Deletion Errors

TL;DR

This paper introduces an optimal decoding algorithm for two-dimensional Reed-Solomon codes capable of correcting deletion errors up to the theoretical limit, addressing a key open problem in error correction.

Contribution

It presents the first efficient decoding algorithm for 2D RS codes that corrects deletions up to the half-Singleton bound, optimizing field operations.

Findings

Decoding algorithm corrects deletions up to the half-Singleton bound.

Algorithm is optimal in terms of field operations.

Addresses a significant open problem in error correction for RS codes.

Abstract

Constructing Reed-Solomon (RS) codes that can correct insertion and deletion (ins-del) errors has been the focus of several recent studies. However, efficient decoding algorithms for such codes have received less attention and remain a significant open problem. In this work, we take a first step toward addressing this problem by designing a decoding algorithm for the case of $2$-dimensional RS codes that can correct deletions up to the half-Singleton bound and is optimal in terms of field operations.