Codes in the Damerau Distance for DNA Storage

Ryan Gabrys; Eitan Yaakobi; Olgica Milenkovic

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arXiv · 1601.06885

Codes in the Damerau Distance for DNA Storage

Ryan Gabrys·Eitan Yaakobi·Olgica Milenkovic

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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.

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Ryan Gabrys, Eitan Yaakobi, Olgica Milenkovic. 2016-01-26. Codes in the Damerau Distance for DNA Storage. https://arxiv.org/abs/1601.06885

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