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 language | English |
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Title of host publication | 2015 IEEE Information Theory Workshop, ITW 2015 |
Publisher | Institute of Electrical and Electronics Engineers Inc. |
ISBN (Electronic) | 9781479955268 |
DOIs | |
State | Published - 24 Jun 2015 |
Externally published | Yes |
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 |
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Conference
Conference | 2015 IEEE Information Theory Workshop, ITW 2015 |
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Country/Territory | Israel |
City | Jerusalem |
Period | 26/04/15 → 1/05/15 |
Bibliographical note
Publisher Copyright:© 2015 IEEE.
Keywords
- Arimoto-Blahut algorithm
- Gallager error exponent
- channel input adaptation
- natural type selection