Channel dispersion and moderate deviations limits for memoryless channels

Yury Polyanskiy, Sergio Verdu

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

42 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
CountryUnited 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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  • Cite this

    Polyanskiy, Y., & Verdu, S. (2010). Channel dispersion and moderate deviations limits for memoryless channels. In 2010 48th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2010 (pp. 1334-1339). [5707068] (2010 48th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2010). https://doi.org/10.1109/ALLERTON.2010.5707068