Hamming codes as error-reducing codes

William Rurik, Arya Mazumdar

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

Abstract

Hamming codes are the first nontrivial family of error-correcting codes that can correct one error in a block of binary symbols. In this paper we extend the notion of error-correction to error-reduction and present several decoding methods with the goal of improving the error-reducing capabilities of Hamming codes. First, the error-reducing properties of Hamming codes with standard decoding are demonstrated and explored. We show a lower bound on the average number of errors present in a decoded message when two errors are introduced by the channel for general Hamming codes. Other decoding algorithms are investigated experimentally, and it is found that these algorithms improve the error reduction capabilities of Hamming codes beyond the aforementioned lower bound of standard decoding.

Original languageEnglish (US)
Title of host publication2016 IEEE Information Theory Workshop, ITW 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages404-408
Number of pages5
ISBN (Electronic)9781509010905
DOIs
StatePublished - Oct 21 2016
Event2016 IEEE Information Theory Workshop, ITW 2016 - Cambridge, United Kingdom
Duration: Sep 11 2016Sep 14 2016

Publication series

Name2016 IEEE Information Theory Workshop, ITW 2016

Other

Other2016 IEEE Information Theory Workshop, ITW 2016
CountryUnited Kingdom
CityCambridge
Period9/11/169/14/16

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