Codes in the Damerau Distance for DNA Storage

TL;DR

This paper introduces new code constructions for DNA storage that can correct deletions, transpositions, and combined errors within the Damerau metric, enhancing error correction capabilities in DNA data encoding.

Contribution

It presents the first code constructions capable of correcting single deletions, adjacent transpositions, and their combinations in the Damerau metric for DNA storage applications.

Findings

Codes correcting single deletion or transposition are constructed.

Extended codes correct both deletions and multiple transpositions.

Joint block deletion and transposition correction codes are developed.

Abstract

Motivated by applications in DNA-based storage, we introduce the new problem of code design in the Damerau metric. The Damerau metric is a generalization of the Levenshtein distance which, in addition to deletions, insertions and substitution errors also accounts for adjacent transposition edits. We first provide constructions for codes that may correct either a single deletion or a single adjacent transposition and then proceed to extend these results to codes that can simultaneously correct a single deletion and multiple adjacent transpositions. We conclude with constructions for joint block deletion and adjacent block transposition error-correcting codes.