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Probl. Peredachi Inf., 2008, Volume 44, Issue 3, Pages 19–32 (Mi ppi1277)  

This article is cited in 7 scientific papers (total in 7 papers)

Information Theory

Mutual Information, Variation, and Fano's Inequality

V. V. Prelova, E. C. van der Meulenb

a A. A. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences
b Katholieke Universiteit Leuven

Abstract: Some upper and lower bounds are obtained for the maximum of the absolute value of the difference between the mutual information $|I(X;Y)-I(X';Y')|$ of two pairs of discrete random variables $(X,Y)$ and $(X',Y')$ via the variational distance between the probability distributions of these pairs. In particular, the upper bound obtained here substantially generalizes and improves the upper bound of [1]. In some special cases, our upper and lower bounds coincide or are rather close. It is also proved that the lower bound is asymptotically tight in the case where the variational distance between $(X,Y)$ and $(X',Y')$ tends to zero.

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English version:
Problems of Information Transmission, 2008, 44:3, 185–197

Bibliographic databases:

UDC: 621.391.1:519.2
Received: 15.05.2008

Citation: V. V. Prelov, E. C. van der Meulen, “Mutual Information, Variation, and Fano's Inequality”, Probl. Peredachi Inf., 44:3 (2008), 19–32; Problems Inform. Transmission, 44:3 (2008), 185–197

Citation in format AMSBIB
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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, “Mutual information of several random variables and its estimation via variation”, Problems Inform. Transmission, 45:4 (2009), 295–308  mathnet  crossref  mathscinet  zmath  isi
    2. V. V. Prelov, “On computation of information via variation and inequalities for the entropy function”, Problems Inform. Transmission, 46:2 (2010), 122–126  mathnet  crossref  mathscinet  isi
    3. V. V. Prelov, “Generalization of a Pinsker problem”, Problems Inform. Transmission, 47:2 (2011), 98–116  mathnet  crossref  mathscinet  isi
    4. Sason I., “Entropy Bounds for Discrete Random Variables via Maximal Coupling”, IEEE Trans. Inf. Theory, 59:11 (2013), 7118–7131  crossref  mathscinet  isi  elib
    5. V. V. Prelov, “On one extreme value problem for entropy and error probability”, Problems Inform. Transmission, 50:3 (2014), 203–216  mathnet  crossref  isi
    6. Anderson R.P., Porfiri M., “Assessing Significance of Information Flow in High Dimensional Dynamical Systems With Few Data”, 7Th Annual Dynamic Systems and Control Conference, 2014, Vol 2, Amer Soc Mechanical Engineers, 2014, V002T24A002  isi
    7. V. V. Prelov, “On some extremal problems for mutual information and entropy”, Problems Inform. Transmission, 52:4 (2016), 319–328  mathnet  crossref  isi  elib
  • Проблемы передачи информации Problems of Information Transmission
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