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

Ben-Gurion University of the Negev, Technion - Israel Institute of Technology

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

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	American 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
DNA sequences
Decoding
Encoding
Information theory
Organisms
Probability distribution
Redundancy
Wireless communication
capacity
constrained coding
encoder construction
error-correcting codes

All Science Journal Classification (ASJC) codes

Information Systems
Computer Science Applications
Library and Information Sciences

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10.1109/TIT.2021.3092056

Cite this

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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.",

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AU - Medard, Muriel

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KW - Decoding

KW - Encoding

KW - Information theory

KW - Organisms

KW - Probability distribution

KW - Redundancy

KW - Wireless communication

KW - capacity

KW - constrained coding

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Repeat-Free Codes

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Keywords

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