Stochastic interpretation for the Arimoto algorithm

Sergey Tridenski; Ram Zamir

doi:10.1109/ITW.2015.7133141

Stochastic interpretation for the Arimoto algorithm

Sergey Tridenski, Ram Zamir

School of Electrical Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Scopus citations

Abstract

The Arimoto algorithm computes the Gallager function max_Q 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 Q_k(x), the next distribution Q_k+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 language	English
Title of host publication	2015 IEEE Information Theory Workshop, ITW 2015
Publisher	Institute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)	9781479955268
DOIs	https://doi.org/10.1109/ITW.2015.7133141
State	Published - 24 Jun 2015
Event	2015 IEEE Information Theory Workshop, ITW 2015 - Jerusalem, Israel Duration: 26 Apr 2015 → 1 May 2015

Publication series

Name	2015 IEEE Information Theory Workshop, ITW 2015

Conference

Conference	2015 IEEE Information Theory Workshop, ITW 2015
Country/Territory	Israel
City	Jerusalem
Period	26/04/15 → 1/05/15

Keywords

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

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10.1109/ITW.2015.7133141

Cite this

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title = "Stochastic interpretation for the Arimoto algorithm",

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.",

keywords = "Arimoto-Blahut algorithm, Gallager error exponent, channel input adaptation, natural type selection",

author = "Sergey Tridenski and Ram Zamir",

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year = "2015",

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doi = "10.1109/ITW.2015.7133141",

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AU - Zamir, Ram

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AB - 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.

KW - Arimoto-Blahut algorithm

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KW - natural type selection

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Stochastic interpretation for the Arimoto algorithm

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Keywords

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