Error-correcting Codes for Short Tandem Duplication and Substitution Errors

TL;DR

This paper develops error-correcting codes for DNA data storage that can simultaneously correct short tandem duplication and substitution errors, addressing the unique challenges posed by DNA's error patterns.

Contribution

It introduces a novel coding scheme capable of correcting both duplication and substitution errors in DNA sequences, with proven bounds and minimal additional redundancy.

Findings

The code corrects an arbitrary number of duplication errors and one substitution error.

The additional redundancy cost for correcting substitutions is only 0.003 bits/symbol for DNA alphabet.

The approach effectively limits substitution effects to finite substrings, enabling efficient correction.

Abstract

Due to its high data density and longevity, DNA is considered a promising medium for satisfying ever-increasing data storage needs. However, the diversity of errors that occur in DNA sequences makes efficient error-correction a challenging task. This paper aims to address simultaneously correcting two types of errors, namely, short tandem duplication and substitution errors. We focus on tandem repeats of length at most 3 and design codes for correcting an arbitrary number of duplication errors and one substitution error. Because a substituted symbol can be duplicated many times (as part of substrings of various lengths), a single substitution can affect an unbounded substring of the retrieved word. However, we show that with appropriate preprocessing, the effect may be limited to a substring of finite length, thus making efficient error-correction possible. We construct a code for correcting the aforementioned errors and provide lower bounds for its rate. Compared to optimal codes correcting only duplication errors, numerical results show that the asymptotic cost of protecting against an additional substitution is only 0.003 bits/symbol when the alphabet has size 4, an important case corresponding to data storage in DNA.