Connections between the Error Probability and the r-wise Hamming Distances

Hsuan Yin Lin, Stefan M. Moser, Po-Ning Chen

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

An extension from the pairwise Hamming distance to the r-wise Hamming distance is presented. It can be used to fully characterize the maximum-likelihood decoding (MLD) error of an arbitrary code over the binary erasure channel (BEC). By noting that good codes always have large minimum r-wise Hamming distances for all r, a new design criterion for a code is introduced: the minimum r-wise Hamming distance. We then prove an upper bound for the minimum r-wise Hamming distance of an arbitrary code, called the generalized Plotkin bound, and provide a class of (nonlinear) codes that achieve the bound for every r.

Original languageEnglish
Title of host publicationProceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages130-134
Number of pages5
ISBN (Electronic)9784885523182
DOIs
StatePublished - 8 Mar 2019
Event15th International Symposium on Information Theory and Its Applications, ISITA 2018 - Singapore, Singapore
Duration: 28 Oct 201831 Oct 2018

Publication series

NameProceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018

Conference

Conference15th International Symposium on Information Theory and Its Applications, ISITA 2018
CountrySingapore
CitySingapore
Period28/10/1831/10/18

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