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

Error-correcting Codes for Short Tandem Duplication and Substitution Errors