Reconstruction of Sequences Distorted by Two Insertions
Information Theory
2023-02-21 v1 Combinatorics
math.IT
Abstract
Reconstruction codes are generalizations of error-correcting codes that can correct errors by a given number of noisy reads. The study of such codes was initiated by Levenshtein in 2001 and developed recently due to applications in modern storage devices such as racetrack memories and DNA storage. The central problem on this topic is to design codes with redundancy as small as possible for a given number of noisy reads. In this paper, the minimum redundancy of such codes for binary channels with exactly two insertions is determined asymptotically for all values of . Previously, such codes were studied only for channels with single edit errors or two-deletion errors.
Cite
@article{arxiv.2302.09798,
title = {Reconstruction of Sequences Distorted by Two Insertions},
author = {Zuo Ye and Xin Liu and Xiande Zhang and Gennian Ge},
journal= {arXiv preprint arXiv:2302.09798},
year = {2023}
}