Non-binary Codes for Correcting a Burst of at Most t Deletions

TL;DR

This paper introduces new non-binary codes capable of correcting bursts of deletions in sequences, including permutations, advancing error correction methods for DNA storage and related fields.

Contribution

The paper presents the first non-binary codes for correcting burst deletions of length up to t, including permutation sequences, with the largest known code sizes for these parameters.

Findings

Codes correct bursts of up to 2 deletions for q-ary alphabets

Extension to bursts of length t where t is a constant

Largest known codes for these parameters

Abstract

The problem of correcting deletions has received significant attention, partly because of the prevalence of these errors in DNA data storage. In this paper, we study the problem of correcting a consecutive burst of at most $t$ deletions in non-binary sequences. We first propose a non-binary code correcting a burst of at most 2 deletions for $q$-ary alphabets. Afterwards, we extend this result to the case where the length of the burst can be at most $t$ where $t$ is a constant. Finally, we consider the setup where the sequences that are transmitted are permutations. The proposed codes are the largest known for their respective parameter regimes.