Equidistant codes meeting the Plotkin bound are Not optimal on the binary symmetric channel

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

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

8 Scopus citations

Abstract

In this paper, we re-introduce from our previous work [1] a new family of nonlinear codes, called weak flip codes, and show that its subfamily fair weak flip codes belongs to the class of equidistant codes, satisfying that any two distinct codewords have identical Hamming distance. It is then noted that the fair weak flip codes are related to the binary nonlinear Hadamard codes as both code families maximize the minimum Hamming distance and meet the Plotkin upper bound under certain blocklengths. Although the fair weak flip codes have the largest minimum Hamming distance and achieve the Plotkin bound, we find that these codes are by no means optimal in the sense of average error probability over binary symmetric channels (BSC). In parallel, this result implies that the equidistant Hadamard codes are also nonoptimal over BSCs. Such finding is in contrast to the conventional code design that aims at the maximization of the minimum Hamming distance. The results in this paper are proved by examining the exact error probabilities of these codes on BSCs, using the column-wise analysis on the codebook matrix.

Original languageEnglish
Title of host publication2013 IEEE International Symposium on Information Theory, ISIT 2013
Pages3015-3019
Number of pages5
DOIs
StatePublished - 19 Dec 2013
Event2013 IEEE International Symposium on Information Theory, ISIT 2013 - Istanbul, Turkey
Duration: 7 Jul 201312 Jul 2013

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8095

Conference

Conference2013 IEEE International Symposium on Information Theory, ISIT 2013
Country/TerritoryTurkey
CityIstanbul
Period7/07/1312/07/13

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