Channel dispersion and moderate deviations limits for memoryless channels

Yury Polyanskiy, Sergio Verdu

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

46 Scopus citations

Abstract

Recently, Altug and Wagner [1] posed a question regarding the optimal behavior of the probability of error when channel coding rate converges to the capacity sufficiently slowly. They gave a sufficient condition for the discrete memoryless channel (DMC) to satisfy a moderate deviation property (MDP) with the constant equal to the channel dispersion. Their sufficient condition excludes some practically interesting channels, such as the binary erasure channel and the Z-channel. We extend their result in two directions. First, we show that a DMC satisfies MDP if and only if its channel dispersion is nonzero. Second, we prove that the AWGN channel also satisfies MDP with a constant equal to the channel dispersion. While the methods used by Altug and Wagner are based on the method of types and other DMC-specific ideas, our proofs (in both achievability and converse parts) rely on the tools from our recent work [2] on finite-blocklength regime that are equally applicable to non-discrete channels and channels with memory.

Original languageEnglish (US)
Title of host publication2010 48th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2010
Pages1334-1339
Number of pages6
DOIs
StatePublished - Dec 1 2010
Event48th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2010 - Monticello, IL, United States
Duration: Sep 29 2010Oct 1 2010

Publication series

Name2010 48th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2010

Other

Other48th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2010
Country/TerritoryUnited States
CityMonticello, IL
Period9/29/1010/1/10

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Control and Systems Engineering

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