TY - GEN

T1 - Stochastic interpretation for the Arimoto algorithm

AU - Tridenski, Sergey

AU - Zamir, Ram

N1 - Publisher Copyright:
© 2015 IEEE.

PY - 2015/6/24

Y1 - 2015/6/24

N2 - 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.

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

KW - Gallager error exponent

KW - channel input adaptation

KW - natural type selection

UR - http://www.scopus.com/inward/record.url?scp=84938914942&partnerID=8YFLogxK

U2 - 10.1109/ITW.2015.7133141

DO - 10.1109/ITW.2015.7133141

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AN - SCOPUS:84938914942

T3 - 2015 IEEE Information Theory Workshop, ITW 2015

BT - 2015 IEEE Information Theory Workshop, ITW 2015

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2015 IEEE Information Theory Workshop, ITW 2015

Y2 - 26 April 2015 through 1 May 2015

ER -