Expurgated infinite constellations at finite dimensions

Amir Ingber*, Ram Zamir

*Corresponding author for this work

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

Abstract

We revisit the setting of a Gaussian channel without power constraints, proposed by Poltyrev, where the codewords are points in Euclidean space and their density is considered instead of the communication rate. We refine the expurgation technique (proposed by Poltyrev for the derivation of the error exponent) to the finite dimensions case and obtain a finite-dimensional achievability bound. While the expurgation exponent improves upon the random coding exponent only for certain rates (below a rate known as δ ex), we show that for finite dimensions the expurgation technique is useful for a broader range of rates. In addition, we present precise asymptotical analysis of the expurgation bound and find the sub-exponential terms, which turn out to be non-negligible.

Original languageEnglish
Title of host publication2012 IEEE International Symposium on Information Theory Proceedings, ISIT 2012
Pages130-134
Number of pages5
DOIs
StatePublished - 2012
Event2012 IEEE International Symposium on Information Theory, ISIT 2012 - Cambridge, MA, United States
Duration: 1 Jul 20126 Jul 2012

Publication series

NameIEEE International Symposium on Information Theory - Proceedings

Conference

Conference2012 IEEE International Symposium on Information Theory, ISIT 2012
Country/TerritoryUnited States
CityCambridge, MA
Period1/07/126/07/12

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