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Probl. Peredachi Inf., 2016, Volume 52, Issue 4, Pages 3–13 (Mi ppi2218)  

Information Theory

On some extremal problems for mutual information and entropy

V. V. Prelov

Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia

Abstract: The problem of determining the maximum mutual information $I(X;Y)$ and minimum entropy $H(X,Y)$ of a pair of discrete random variables $X$ and $Y$ is considered under the condition that the probability distribution of $X$ is fixed and the error probability $\mathrm{Pr}\{Y\ne X\}$ takes a given value $\varepsilon$, $0\le\varepsilon\le1$. Precise values for these quantities are found, which in several cases allows us to obtain explicit formulas for both the maximum information and minimum entropy in terms of the probability distribution of $X$ and the parameter $\varepsilon$.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-08051
Supported in part by the Russian Foundation for Basic Research, project no. 15-01-08051.


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English version:
Problems of Information Transmission, 2016, 52:4, 319–328

Bibliographic databases:

UDC: 621.391.1+519.72
Received: 01.12.2015
Revised: 14.10.2016

Citation: V. V. Prelov, “On some extremal problems for mutual information and entropy”, Probl. Peredachi Inf., 52:4 (2016), 3–13; Problems Inform. Transmission, 52:4 (2016), 319–328

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  • Проблемы передачи информации Problems of Information Transmission
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