Stochastic interpretation for the Arimoto algorithm

Sergey Tridenski, Ram Zamir

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

Abstract

The Arimoto algorithm computes the Gallager function maxQ E0(ρ, Q) for a given channel P (y / x) and parameter ρ, by means of alternating maximization. Along the way, it generates a sequence of input distributions Q1(x), Q2(x),⋯, that converges to the maximizing input Q∗(x). We propose a stochastic interpretation for the Arimoto algorithm. We show that for a random (i.i.d.) codebook with a distribution Qk(x), the next distribution Qk+1(x) in the Arimoto algorithm is equal to the type (Q′) of the feasible transmitted codeword that maximizes the conditional Gallager exponent (conditioned on a specific transmitted codeword type Q′). This interpretation is a first step toward finding a stochastic mechanism for on-line channel input adaptation.

Original languageEnglish
Title of host publication2015 IEEE Information Theory Workshop, ITW 2015
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9781479955268
DOIs
StatePublished - 24 Jun 2015
Event2015 IEEE Information Theory Workshop, ITW 2015 - Jerusalem, Israel
Duration: 26 Apr 20151 May 2015

Publication series

Name2015 IEEE Information Theory Workshop, ITW 2015

Conference

Conference2015 IEEE Information Theory Workshop, ITW 2015
Country/TerritoryIsrael
CityJerusalem
Period26/04/151/05/15

Keywords

  • Arimoto-Blahut algorithm
  • Gallager error exponent
  • channel input adaptation
  • natural type selection

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