Single-Error Detection and Correction for Duplication and Substitution Channels

TL;DR

This paper investigates DNA-inspired channels that mutate stored data via duplications and substitutions, proposing codes capable of detecting and correcting these errors under specific mutation scenarios.

Contribution

It introduces new error-detecting and error-correcting codes tailored for channels with duplication and substitution mutations, considering two different substitution models.

Findings

Codes can correct any number of tandem duplications of fixed length

Codes can handle at most one substitution during mutations

Effective error detection and correction in DNA storage channels

Abstract

Motivated by mutation processes occurring in in-vivo DNA-storage applications, a channel that mutates stored strings by duplicating substrings as well as substituting symbols is studied. Two models of such a channel are considered: one in which the substitutions occur only within the duplicated substrings, and one in which the location of substitutions is unrestricted. Both error-detecting and error-correcting codes are constructed, which can handle correctly any number of tandem duplications of a fixed length $k$, and at most a single substitution occurring at any time during the mutation process.