On codes decoding a constant fraction of errors on the BSC

Jan Hązła; Alex Samorodnitsky; Ori Sberlo

doi:10.1145/3406325.3451015

On codes decoding a constant fraction of errors on the BSC

Jan Hązła
, Alex Samorodnitsky
, Ori Sberlo

The Rachel and Selim Benin School of Engineering and Computer Science

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

12 Scopus citations

Abstract

We strengthen the results from a recent work by the second author, achieving bounds on the weight distribution of binary linear codes that are successful under block-MAP (as well as bit-MAP) decoding on the BEC. We conclude that a linear code that is successful on the BEC can also decode over a range of binary memoryless symmetric (BMS) channels. In particular, applying the result of Kudekar, Kumar, Mondelli, Pfister, ?a?o?lu and Urbanke from STOC 2016, we prove that a Reed-Muller code of positive rate R decodes errors on the p with high probability if p < 1/2 - ?2-R(1-2-R).

Original language	English
Title of host publication	STOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing
Editors	Samir Khuller, Virginia Vassilevska Williams
Publisher	Association for Computing Machinery
Pages	1479-1488
Number of pages	10
ISBN (Electronic)	9781450380539
DOIs	https://doi.org/10.1145/3406325.3451015
State	Published - 15 Jun 2021
Event	53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021 - Virtual, Online, Italy Duration: 21 Jun 2021 → 25 Jun 2021

Publication series

Name	Proceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)	0737-8017

Conference

Conference	53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021
Country/Territory	Italy
City	Virtual, Online
Period	21/06/21 → 25/06/21

Bibliographical note

Publisher Copyright:
© 2021 ACM.

Keywords

Reed - Muller codes
capacity-achieving codes
weight enumerator

Access to Document

10.1145/3406325.3451015

Cite this

Hązła, J., Samorodnitsky, A., & Sberlo, O. (2021). On codes decoding a constant fraction of errors on the BSC. In S. Khuller, & V. V. Williams (Eds.), STOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing (pp. 1479-1488). (Proceedings of the Annual ACM Symposium on Theory of Computing). Association for Computing Machinery. https://doi.org/10.1145/3406325.3451015

Hązła, Jan ; Samorodnitsky, Alex ; Sberlo, Ori. / On codes decoding a constant fraction of errors on the BSC. STOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing. editor / Samir Khuller ; Virginia Vassilevska Williams. Association for Computing Machinery, 2021. pp. 1479-1488 (Proceedings of the Annual ACM Symposium on Theory of Computing).

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title = "On codes decoding a constant fraction of errors on the BSC",

abstract = "We strengthen the results from a recent work by the second author, achieving bounds on the weight distribution of binary linear codes that are successful under block-MAP (as well as bit-MAP) decoding on the BEC. We conclude that a linear code that is successful on the BEC can also decode over a range of binary memoryless symmetric (BMS) channels. In particular, applying the result of Kudekar, Kumar, Mondelli, Pfister, ?a?o?lu and Urbanke from STOC 2016, we prove that a Reed-Muller code of positive rate R decodes errors on the p with high probability if p < 1/2 - ?2-R(1-2-R).",

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Hązła, J, Samorodnitsky, A & Sberlo, O 2021, On codes decoding a constant fraction of errors on the BSC. in S Khuller & VV Williams (eds), STOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing. Proceedings of the Annual ACM Symposium on Theory of Computing, Association for Computing Machinery, pp. 1479-1488, 53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021, Virtual, Online, Italy, 21/06/21. https://doi.org/10.1145/3406325.3451015

On codes decoding a constant fraction of errors on the BSC. / Hązła, Jan; Samorodnitsky, Alex; Sberlo, Ori.
STOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing. ed. / Samir Khuller; Virginia Vassilevska Williams. Association for Computing Machinery, 2021. p. 1479-1488 (Proceedings of the Annual ACM Symposium on Theory of Computing).

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

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N2 - We strengthen the results from a recent work by the second author, achieving bounds on the weight distribution of binary linear codes that are successful under block-MAP (as well as bit-MAP) decoding on the BEC. We conclude that a linear code that is successful on the BEC can also decode over a range of binary memoryless symmetric (BMS) channels. In particular, applying the result of Kudekar, Kumar, Mondelli, Pfister, ?a?o?lu and Urbanke from STOC 2016, we prove that a Reed-Muller code of positive rate R decodes errors on the p with high probability if p < 1/2 - ?2-R(1-2-R).

AB - We strengthen the results from a recent work by the second author, achieving bounds on the weight distribution of binary linear codes that are successful under block-MAP (as well as bit-MAP) decoding on the BEC. We conclude that a linear code that is successful on the BEC can also decode over a range of binary memoryless symmetric (BMS) channels. In particular, applying the result of Kudekar, Kumar, Mondelli, Pfister, ?a?o?lu and Urbanke from STOC 2016, we prove that a Reed-Muller code of positive rate R decodes errors on the p with high probability if p < 1/2 - ?2-R(1-2-R).

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Hązła J, Samorodnitsky A, Sberlo O. On codes decoding a constant fraction of errors on the BSC. In Khuller S, Williams VV, editors, STOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing. Association for Computing Machinery. 2021. p. 1479-1488. (Proceedings of the Annual ACM Symposium on Theory of Computing). doi: 10.1145/3406325.3451015

On codes decoding a constant fraction of errors on the BSC

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