Codes in the Damerau Distance for DNA Storage
Information Theory
2018-05-02 v3 math.IT
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.
Cite
@article{arxiv.1601.06885,
title = {Codes in the Damerau Distance for DNA Storage},
author = {Ryan Gabrys and Eitan Yaakobi and Olgica Milenkovic},
journal= {arXiv preprint arXiv:1601.06885},
year = {2018}
}