Single-Deletion Single-Substitution Correcting Codes

Ilia Smagloy; Lorenz Welter; Antonia Wachter-Zeh; Eitan Yaakobi

doi:10.1109/TIT.2023.3319088

Single-Deletion Single-Substitution Correcting Codes

Ilia Smagloy, Lorenz Welter, Antonia Wachter-Zeh, Eitan Yaakobi

Computer Science

Technion - Israel Institute of Technology

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

Abstract

Correcting insertions/deletions as well as substitution errors simultaneously plays an important role in DNA-based storage systems as well as in classical communications. This paper deals with the fundamental task of constructing codes that can correct a single insertion or deletion along with a single substitution. A non-asymptotic upper bound on the size of non-binary single-deletion s-substitution correcting codes is derived, showing that the non-asymptotic redundancy of such a code of length n has to be at least (s+1) log_q n. An explicit construction of binary single-deletion single-substitution correcting codes with at most 6 log n + 8 redundancy bits is presented.

Original language	English
Pages (from-to)	7659-7671
Number of pages	13
Journal	IEEE Transactions on Information Theory
Volume	69
Issue number	12
DOIs	https://doi.org/10.1109/TIT.2023.3319088
State	Published - 1 Dec 2023

Keywords

Error-correcting codes
synchronization errors

All Science Journal Classification (ASJC) codes

Information Systems
Computer Science Applications
Library and Information Sciences

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10.1109/TIT.2023.3319088

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abstract = "Correcting insertions/deletions as well as substitution errors simultaneously plays an important role in DNA-based storage systems as well as in classical communications. This paper deals with the fundamental task of constructing codes that can correct a single insertion or deletion along with a single substitution. A non-asymptotic upper bound on the size of non-binary single-deletion s-substitution correcting codes is derived, showing that the non-asymptotic redundancy of such a code of length n has to be at least (s+1) logq n. An explicit construction of binary single-deletion single-substitution correcting codes with at most 6 log n + 8 redundancy bits is presented.",

keywords = "Error-correcting codes, synchronization errors",

author = "Ilia Smagloy and Lorenz Welter and Antonia Wachter-Zeh and Eitan Yaakobi",

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AU - Smagloy, Ilia

AU - Welter, Lorenz

AU - Wachter-Zeh, Antonia

AU - Yaakobi, Eitan

PY - 2023/12/1

Y1 - 2023/12/1

N2 - Correcting insertions/deletions as well as substitution errors simultaneously plays an important role in DNA-based storage systems as well as in classical communications. This paper deals with the fundamental task of constructing codes that can correct a single insertion or deletion along with a single substitution. A non-asymptotic upper bound on the size of non-binary single-deletion s-substitution correcting codes is derived, showing that the non-asymptotic redundancy of such a code of length n has to be at least (s+1) logq n. An explicit construction of binary single-deletion single-substitution correcting codes with at most 6 log n + 8 redundancy bits is presented.

AB - Correcting insertions/deletions as well as substitution errors simultaneously plays an important role in DNA-based storage systems as well as in classical communications. This paper deals with the fundamental task of constructing codes that can correct a single insertion or deletion along with a single substitution. A non-asymptotic upper bound on the size of non-binary single-deletion s-substitution correcting codes is derived, showing that the non-asymptotic redundancy of such a code of length n has to be at least (s+1) logq n. An explicit construction of binary single-deletion single-substitution correcting codes with at most 6 log n + 8 redundancy bits is presented.

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KW - synchronization errors

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JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

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ER -

Single-Deletion Single-Substitution Correcting Codes

Abstract

Keywords

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