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||American 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|
|Number of pages||10|
|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
|Name||Proceedings of the Annual ACM Symposium on Theory of Computing|
|Conference||53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021|
|Period||21/06/21 → 25/06/21|
Bibliographical noteFunding Information:
∗Research partially supported by ISF grant 1724/15. †The research leading to these results has received funding from the Israel Science Foundation (grant number 552/16) and from the Len Blavatnik and the Blavatnik Family foundation.
© 2021 ACM.
- Reed - Muller codes
- capacity-achieving codes
- weight enumerator