Repeat-Free Codes

Ohad Elishco; Ryan Gabrys; Eitan Yaakobi; Muriel Medard

doi:10.1109/TIT.2021.3092056

Repeat-Free Codes

Ohad Elishco, Ryan Gabrys, Eitan Yaakobi, Muriel Medard

Department of Communication Systems Engineering

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

In this paper we consider the problem of encoding data into repeat-free sequences in which sequences are imposed to contain any k -tuple at most once (for predefined k ). First, the capacity of the repeat-free constraint are calculated. Then, an efficient algorithm, which uses two bits of redundancy, is presented to encode length- n sequences for k=2+2log (n). This algorithm is then improved to support any value of k of the form k=alog (n) , for 1< a , while its redundancy is o(n). We also calculate the capacity of repeat-free sequences when combined with local constraints which are given by a constrained system, and the capacity of multi-dimensional repeat-free codes.

Original language	English
Article number	9465135
Pages (from-to)	5749-5764
Number of pages	16
Journal	IEEE Transactions on Information Theory
Volume	67
Issue number	9
DOIs	https://doi.org/10.1109/TIT.2021.3092056
State	Published - 1 Sep 2021

Keywords

DNA sequences
Information theory
capacity
constrained coding
encoder construction
error-correcting codes

ASJC Scopus subject areas

Information Systems
Computer Science Applications
Library and Information Sciences

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AU - Gabrys, Ryan

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AU - Medard, Muriel

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AB - In this paper we consider the problem of encoding data into repeat-free sequences in which sequences are imposed to contain any k -tuple at most once (for predefined k ). First, the capacity of the repeat-free constraint are calculated. Then, an efficient algorithm, which uses two bits of redundancy, is presented to encode length- n sequences for k=2+2log (n). This algorithm is then improved to support any value of k of the form k=alog (n) , for 1< a , while its redundancy is o(n). We also calculate the capacity of repeat-free sequences when combined with local constraints which are given by a constrained system, and the capacity of multi-dimensional repeat-free codes.

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Repeat-Free Codes

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Keywords

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