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 |
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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 | |
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 |
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ISSN (Print) | 0737-8017 |
Conference
Conference | 53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021 |
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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