Optimal Codes Correcting a Single Indel / Edit for DNA-Based Data Storage

TL;DR

This paper develops efficient coding schemes for correcting single indels or edits in DNA-based data storage, achieving near-optimal redundancy and introducing the first GC-balanced codes capable of correcting such errors.

Contribution

It introduces the first order-optimal linear-time encoders for single indel and edit correction over quaternary alphabets, including GC-balanced codes for DNA storage.

Findings

Linear-time encoders correct a single indel or edit with minimal redundancy.

New GC-balanced codes can correct a single indel or edit in DNA sequences.

Redundancy is reduced compared to previous codes, improving efficiency.

Abstract

An indel refers to a single insertion or deletion, while an edit refers to a single insertion, deletion or substitution. In this paper, we investigate codes that combat either a single indel or a single edit and provide linear-time algorithms that encode binary messages into these codes of length n. Over the quaternary alphabet, we provide two linear-time encoders. One corrects a single edit with log n + O(log log n) redundancy bits, while the other corrects a single indel with log n + 2 redundant bits. These two encoders are order-optimal. The former encoder is the first known order-optimal encoder that corrects a single edit, while the latter encoder (that corrects a single indel) reduces the redundancy of the best known encoder of Tenengolts (1984) by at least four bits. Over the DNA alphabet, we impose an additional constraint: the GC-balanced constraint and require that exactly half of the symbols of any DNA codeword to be either C or G. In particular, via a modification of Knuth's balancing technique, we provide a linear-time map that translates binary messages into GC-balanced codewords and the resulting codebook is able to correct a single indel or a single edit. These are the first known constructions of GC-balanced codes that correct a single indel or a single edit.