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

This article is cited in 2 scientific papers (total in 2 papers)

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
Received: 21.01.2014
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  mathnet  crossref  isi  elib
    2. V. V. Prelov, “On extreme values of the Rényi entropy under coupling of probability distributions”, Problems Inform. Transmission, 55:1 (2019), 46–52  mathnet  crossref  crossref  isi  elib
  • Проблемы передачи информации Problems of Information Transmission
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