TY - GEN

T1 - On codes decoding a constant fraction of errors on the BSC

AU - Hązła, Jan

AU - Samorodnitsky, Alex

AU - Sberlo, Ori

N1 - Publisher Copyright:
© 2021 ACM.

PY - 2021/6/15

Y1 - 2021/6/15

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).

KW - Reed - Muller codes

KW - capacity-achieving codes

KW - weight enumerator

UR - http://www.scopus.com/inward/record.url?scp=85108175282&partnerID=8YFLogxK

U2 - 10.1145/3406325.3451015

DO - 10.1145/3406325.3451015

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AN - SCOPUS:85108175282

T3 - Proceedings of the Annual ACM Symposium on Theory of Computing

SP - 1479

EP - 1488

BT - STOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing

A2 - Khuller, Samir

A2 - Williams, Virginia Vassilevska

PB - Association for Computing Machinery

T2 - 53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021

Y2 - 21 June 2021 through 25 June 2021

ER -