Perfect Codes Correcting a Single Burst of Limited-Magnitude Errors

Hengjia Wei; Moshe Schwartz

doi:10.1109/ISIT50566.2022.9834644

Perfect Codes Correcting a Single Burst of Limited-Magnitude Errors

Hengjia Wei, Moshe Schwartz

Department of Electrical & Computer Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

Motivated by applications to DNA-storage, flash memory, and magnetic recording, we study perfect burst-correcting codes for the limited-magnitude error channel. These codes are lattices that tile the integer grid with the appropriate error ball. We construct two classes of such perfect codes correcting a single burst of length 2 for (1, 0)-limited-magnitude errors, both for cyclic and non-cyclic bursts. We also present a generic construction that requires a primitive element in a finite field with specific properties. We then show that in various parameter regimes such primitive elements exist, and hence, infinitely many perfect burst-correcting codes exist.

Original language	English
Title of host publication	2022 IEEE International Symposium on Information Theory, ISIT 2022
Publisher	Institute of Electrical and Electronics Engineers
Pages	1809-1814
Number of pages	6
ISBN (Electronic)	9781665421591
DOIs	https://doi.org/10.1109/ISIT50566.2022.9834644
State	Published - 1 Jan 2022
Event	2022 IEEE International Symposium on Information Theory, ISIT 2022 - Espoo, Finland Duration: 26 Jun 2022 → 1 Jul 2022

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
Volume	2022-June
ISSN (Print)	2157-8095

Conference

Conference	2022 IEEE International Symposium on Information Theory, ISIT 2022
Country/Territory	Finland
City	Espoo
Period	26/06/22 → 1/07/22

ASJC Scopus subject areas

Theoretical Computer Science
Information Systems
Modeling and Simulation
Applied Mathematics

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10.1109/ISIT50566.2022.9834644

Cite this

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title = "Perfect Codes Correcting a Single Burst of Limited-Magnitude Errors",

abstract = "Motivated by applications to DNA-storage, flash memory, and magnetic recording, we study perfect burst-correcting codes for the limited-magnitude error channel. These codes are lattices that tile the integer grid with the appropriate error ball. We construct two classes of such perfect codes correcting a single burst of length 2 for (1, 0)-limited-magnitude errors, both for cyclic and non-cyclic bursts. We also present a generic construction that requires a primitive element in a finite field with specific properties. We then show that in various parameter regimes such primitive elements exist, and hence, infinitely many perfect burst-correcting codes exist.",

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Wei, H & Schwartz, M 2022, Perfect Codes Correcting a Single Burst of Limited-Magnitude Errors. in 2022 IEEE International Symposium on Information Theory, ISIT 2022. IEEE International Symposium on Information Theory - Proceedings, vol. 2022-June, Institute of Electrical and Electronics Engineers, pp. 1809-1814, 2022 IEEE International Symposium on Information Theory, ISIT 2022, Espoo, Finland, 26/06/22. https://doi.org/10.1109/ISIT50566.2022.9834644

Perfect Codes Correcting a Single Burst of Limited-Magnitude Errors. / Wei, Hengjia; Schwartz, Moshe.
2022 IEEE International Symposium on Information Theory, ISIT 2022. Institute of Electrical and Electronics Engineers, 2022. p. 1809-1814 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2022-June).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - Motivated by applications to DNA-storage, flash memory, and magnetic recording, we study perfect burst-correcting codes for the limited-magnitude error channel. These codes are lattices that tile the integer grid with the appropriate error ball. We construct two classes of such perfect codes correcting a single burst of length 2 for (1, 0)-limited-magnitude errors, both for cyclic and non-cyclic bursts. We also present a generic construction that requires a primitive element in a finite field with specific properties. We then show that in various parameter regimes such primitive elements exist, and hence, infinitely many perfect burst-correcting codes exist.

AB - Motivated by applications to DNA-storage, flash memory, and magnetic recording, we study perfect burst-correcting codes for the limited-magnitude error channel. These codes are lattices that tile the integer grid with the appropriate error ball. We construct two classes of such perfect codes correcting a single burst of length 2 for (1, 0)-limited-magnitude errors, both for cyclic and non-cyclic bursts. We also present a generic construction that requires a primitive element in a finite field with specific properties. We then show that in various parameter regimes such primitive elements exist, and hence, infinitely many perfect burst-correcting codes exist.

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Perfect Codes Correcting a Single Burst of Limited-Magnitude Errors

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