Arimoto channel coding converse and Rényi divergence

Yury Polyanskiy, Sergio Verdu

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

71 Scopus citations

Abstract

Arimoto [1] proved a non-asymptotic upper bound on the probability of successful decoding achievable by any code on a given discrete memoryless channel. In this paper we present a simple derivation of the Arimoto converse based on the data-processing inequality for Rényi divergence. The method has two benefits. First, it generalizes to codes with feedback and gives the simplest proof of the strong converse for the DMC with feedback. Second, it demonstrates that the sphere-packing bound is strictly tighter than Arimoto converse for all channels, blocklengths and rates, since in fact we derive the latter from the former. Finally, we prove similar results for other (non-Rényi) divergence measures.

Original languageEnglish (US)
Title of host publication2010 48th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2010
Pages1327-1333
Number of pages7
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

Keywords

  • Feedback
  • Information measures
  • Rényi divergence
  • Shannon theory
  • Strong converse

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