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dc.contributor.authorOrdentlich, Or
dc.contributor.authorPolyanskiy, Yury
dc.date.accessioned2019-08-07T12:22:46Z
dc.date.available2019-08-07T12:22:46Z
dc.date.issued2018-06
dc.identifier.isbn9781538647813
dc.identifier.issn2157-8117
dc.identifier.urihttps://hdl.handle.net/1721.1/121969
dc.description.abstractConsider a binary linear code of length N, minimum distance d-{\min}, transmission over the binary erasure channel with parameter 0 < \epsilon < 1 or the binary symmetric channel with parameter 0 < \epsilon < \frac{1}{2}, and block-MAP decoding. It was shown by Tillich and Zemor that in this case the error probability of the block-MAP decoder transitions 'quickly' from \delta to 1-\delta for any \delta > 0 if the minimum distance is large. In particular the width of the transition is of order O(1/\sqrt{d-{\min}}). We strengthen this result by showing that under suitable conditions on the weight distribution of the code, the transition width can be as small as \Theta(1/N^{\frac{1}{2}-\kappa}), for any \kappa > 0, even if the minimum distance of the code is not linear. This condition applies e.g., to Reed-Mueller codes. Since \Theta(1/N^{\frac{1}{2}}) is the smallest transition possible for any code, we speak of 'almost' optimal scaling. We emphasize that the width of the transition says nothing about the location of the transition. Therefore this result has no bearing on whether a code is capacity-achieving or not. As a second contribution, we present a new estimate on the derivative of the EXIT function, the proof of which is based on the Blowing-Up Lemma.en_US
dc.language.isoen
dc.publisherIEEEen_US
dc.relation.isversionof10.1109/isit.2018.8437453en_US
dc.rightsCreative Commons Attribution-Noncommercial-Share Alikeen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/4.0/en_US
dc.sourcearXiven_US
dc.titleAlmost Optimal Scaling of Reed-Muller Codes on BEC and BSC Channelsen_US
dc.typeArticleen_US
dc.identifier.citationHassani, Hamed, Shrinivas Kudekar, Or Ordentlich, Yury Polyanskiy and Rüdiger Urbanke. "Almost Optimal Scaling of Reed-Muller Codes on BEC and BSC Channels." In 2018 IEEE International Symposium on Information Theory (ISIT), Vail, CO, USA, 17-22 June 2018.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Scienceen_US
dc.relation.journal2018 IEEE International Symposium on Information Theory (ISIT)en_US
dc.eprint.versionOriginal manuscripten_US
dc.type.urihttp://purl.org/eprint/type/ConferencePaperen_US
eprint.statushttp://purl.org/eprint/status/NonPeerRevieweden_US
dc.date.updated2019-07-01T17:40:59Z
dspace.date.submission2019-07-01T17:41:00Z


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