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 Probl. Peredachi Inf., 2014, Volume 50, Issue 3, Pages 3–18 (Mi ppi2141)

Information Theory

On one extreme value problem for entropy and error probability

V. V. Prelov

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

Abstract: The problem of determining both the maximum and minimum entropy of a random variable $Y$ as well as the maximum absolute value of the difference between entropies of $Y$ and another random variable $X$ is considered under the condition that the probability distribution of $X$ is fixed and the error probability (i.e., the probability of noncoincidence of random values of $X$ and $Y$) is given. A precise expression for the minimum entropy of $Y$ is found. Some conditions under which the entropy of $Y$ takes its maximum value are pointed out. In other cases, some lower and upper bounds are obtained for the maximum entropy of $Y$ as well as for the maximum absolute value of the difference between entropies of $Y$ and $X$.

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English version:
Problems of Information Transmission, 2014, 50:3, 203–216

Bibliographic databases:

UDC: 621.391.1+519.72
Revised: 19.06.2014

Citation: V. V. Prelov, “On one extreme value problem for entropy and error probability”, Probl. Peredachi Inf., 50:3 (2014), 3–18; Problems Inform. Transmission, 50:3 (2014), 203–216

Citation in format AMSBIB
\Bibitem{Pre14} \by V.~V.~Prelov \paper On one extreme value problem for entropy and error probability \jour Probl. Peredachi Inf. \yr 2014 \vol 50 \issue 3 \pages 3--18 \mathnet{http://mi.mathnet.ru/ppi2141} \transl \jour Problems Inform. Transmission \yr 2014 \vol 50 \issue 3 \pages 203--216 \crossref{https://doi.org/10.1134/S003294601403016} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000343931900001} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84910022857} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. V. V. Prelov, “On some extremal problems for mutual information and entropy”, Problems Inform. Transmission, 52:4 (2016), 319–328
2. V. V. Prelov, “On extreme values of the Rényi entropy under coupling of probability distributions”, Problems Inform. Transmission, 55:1 (2019), 46–52
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