Applications of an Exact Formula for the Largest Minimum Distance of Block Codes

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

*Corresponding author for this work

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

Abstract

An exact information spectrum-type formula for the maximum size of finite length block codes subject to a minimum pairwise distance constraint is presented. This formula can be applied to codes for a broad class of distance measures, which only requires having the minimum value between a point and itself. As revealed by the formula, the largest code size is fully characterized by the information spectrum of the distance between two independent and identically distributed (i.i.d.) random codewords drawn from an optimal distribution. Under an arbitrary uniformly bounded distance measure, the asymptotic largest code rate (in the block length n) attainable for a sequence of (n, M, nδ)-codes is given exactly by the maximum large deviation rate function of the normalized distance between two i.i.d. random codewords.

Original languageEnglish
Title of host publication2018 52nd Annual Conference on Information Sciences and Systems, CISS 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages1
ISBN (Electronic)9781538605790
DOIs
StatePublished - 21 May 2018
Event52nd Annual Conference on Information Sciences and Systems, CISS 2018 - Princeton, United States
Duration: 21 Mar 201823 Mar 2018

Publication series

Name2018 52nd Annual Conference on Information Sciences and Systems, CISS 2018

Conference

Conference52nd Annual Conference on Information Sciences and Systems, CISS 2018
CountryUnited States
CityPrinceton
Period21/03/1823/03/18

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