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On one extreme value problem for entropy and error probability

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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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Authors and Affiliations

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

    V. V. Prelov

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  1. V. V. Prelov
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Correspondence to V. V. Prelov.

Additional information

Original Russian Text © V.V. Prelov, 2014, published in Problemy Peredachi Informatsii, 2014, Vol. 50, No. 3, pp. 3–18.

Supported in part by the Russian Foundation for Basic Research, project no. 12-01-00905-a.

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Prelov, V.V. On one extreme value problem for entropy and error probability. Probl Inf Transm 50, 203–216 (2014). https://doi.org/10.1134/S003294601403016

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  • DOI: https://doi.org/10.1134/S003294601403016

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