Problems of Information Transmission

, Volume 54, Issue 3, pp 229–244 | Cite as

On Some Optimization Problems for the Rényi Divergence

  • V. V. PrelovEmail author
Information Theory


We consider the problem of determining the maximum and minimum of the Rényi divergence Dλ(P||Q) and Dλ(Q||P) for two probability distribution P and Q of discrete random variables X and Y provided that the probability distribution P and the parameter α of α-coupling between X and Y are fixed, i.e., provided that Pr{X = Y } = α.


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  1. 1.
    Rényi, A., On Measures of Entropy and Information, Proc. 4th Berkeley Sympos. on Mathematical Statistics and Probability, Berkely, CA, USA, June 20–July 30, 1960, Neyman, J., Ed., Berkely: Univ. of California Press, 1961, vol. 1: Contributions to the Theory of Statistics, pp. 547–561.Google Scholar
  2. 2.
    van Erven, T. and Harremoës, P., Rényi Divergence and Kullback–Leibler Divergence, IEEE Trans. Inform. Theory, 2014, vol. 60, no. 7, pp. 3797–3820.MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Aczél, J. and Daróczy, Z., On Measures of Information and Their Characterization, New York: Academic, 1975.zbMATHGoogle Scholar
  4. 4.
    Prelov, V.V., Coupling of Probability Distributions and an Extremal Problem for the Divergence, Probl. Peredachi Inf., 2015, vol. 51, no. 2, pp. 114–121 [Probl. Inf. Transm. (Engl. Transl.), 2015, vol. 51, no. 2, pp. 192–199].MathSciNetzbMATHGoogle Scholar

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© Pleiades Publishing, Inc. 2018

Authors and Affiliations

  1. 1.Kharkevich Institute for Information Transmission ProblemsRussian Academy of SciencesMoscowRussia

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