Distance Spectrum Formula for the Largest Minimum Hamming Distance of Finite-Length Binary Block Codes

Ling Hua Chang, Carol Wang, Po-Ning Chen, Yunghsiang S. Han, Vincent Y.F. Tan

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

1 Scopus citations

Abstract

In this paper, an exact distance spectrum formula for the largest minimum Hamming distance of finite-length binary block codes is presented. The exact formula indicates that the largest minimum distance of finite-length block codes can be fully characterized by the information spectrum of the Hamming distance between two independent and identically distributed (i.i.d.) random codewords. The distance property of finite-length block codes is then connected to the distance spectrum. A side result of this work is a new lower bound to the largest minimum distance of finite-length block codes. Numerical examinations show that the new lower bound improves the finite-length Gilbert-Varshamov lower bound and can reach the minimum distance of existing finite-length block codes.

Original languageEnglish
Title of host publication2017 IEEE Information Theory Workshop, ITW 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages419-423
Number of pages5
ISBN (Electronic)9781509030972
DOIs
StatePublished - Nov 2017
Event2017 IEEE Information Theory Workshop, ITW 2017 - Kaohsiung, Taiwan
Duration: 6 Nov 201710 Nov 2017

Publication series

NameInformation Theory Workshop
PublisherIEEE
ISSN (Print)2475-420X

Conference

Conference2017 IEEE Information Theory Workshop, ITW 2017
CountryTaiwan
CityKaohsiung
Period6/11/1710/11/17

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