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On computation of information via variation and inequalities for the entropy function

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Abstract

This paper supplements the author’s paper [1]. We obtain an explicit formula which in a special case allows us to calculate the maximum of mutual information of several random variables via the variational distance between the joint distribution of these random variables and the product of their marginal distributions. We establish two new inequalities for the binary entropy function, which are related to the problem considered here.

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References

  1. Prelov, V.V., Mutual Information of Several Random Variables and Its Estimation via Variation, Probl. Peredachi Inf., 2009, vol. 45, no. 4, pp. 3–17 [Probl. Inf. Trans. (Engl. Transl.), 2009, vol. 45, no. 4, pp. 295–308].

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  2. Pinsker, M.S., On Estimation of Information via Variation, Probl. Peredachi Inf., 2005, vol. 41, no. 2, pp. 3–8 [Probl. Inf. Trans. (Engl. Transl.), 2005, vol. 41, no. 2, pp. 71–75].

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  3. Prelov, V.V., On Inequalities between Mutual Information and Variation, Probl. Peredachi Inf., 2007, vol. 43, no. 1, pp. 15–27 [Probl. Inf. Trans. (Engl. Transl.), 2007, vol. 43, no. 1, pp. 12–23].

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  4. Prelov, V.V. and van der Meulen, E.C., Mutual Information, Variation, and Fano’s Inequality, Probl. Peredachi Inf., 2008, vol. 44, no. 3, pp. 19–32 [Probl. Inf. Trans. (Engl. Transl.), 2008, vol. 44, no. 3, pp. 185–197].

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Authors and Affiliations

  1. Kharkevich Institute for Information Transmission Problems, RAS, Moscow, Russia

    V. V. Prelov

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

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Original Russian Text © V.V. Prelov, 2010, published in Problemy Peredachi Informatsii, 2010, Vol. 46, No. 2, pp. 24–29.

Supported in part by the Russian Foundation for Basic Research, project no. 09-01-00536.

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Prelov, V.V. On computation of information via variation and inequalities for the entropy function. Probl Inf Transm 46, 122–126 (2010). https://doi.org/10.1134/S003294601002002X

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  • DOI: https://doi.org/10.1134/S003294601002002X

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