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 Probl. Peredachi Inf., 2003, Volume 39, Issue 1, Pages 166–175 (Mi ppi211)

A Criterion of Extractability of the Mutual Information for a Triple of Strings

A. E. Romashchenko

Abstract: We say that the mutual information of a triple of binary strings $a$, $b$, $c$ can be extracted if there exists a string $d$ such that $a$, $b$, and $c$ are independent given $d$, and $d$ is simple conditional to each of the strings $a$, $b$, and $c$. It is proved that the mutual information between $a$, $b$, and $c$ can be extracted if and only if the values of the conditional mutual informations $I(a:b|c)$, $I(a:c|b)$, and $I(b:c|a)$ are negligible. The proof employs a non-Shannon-type information inequality (a generalization of the recently discovered Zhang–Yeung inequality).

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English version:
Problems of Information Transmission, 2003, 39:1, 148–157

Bibliographic databases:

UDC: 621.391.1:519.722:510.5

Citation: A. E. Romashchenko, “A Criterion of Extractability of the Mutual Information for a Triple of Strings”, Probl. Peredachi Inf., 39:1 (2003), 166–175; Problems Inform. Transmission, 39:1 (2003), 148–157

Citation in format AMSBIB
\Bibitem{Rom03} \by A.~E.~Romashchenko \paper A Criterion of Extractability of the Mutual Information for a Triple of Strings \jour Probl. Peredachi Inf. \yr 2003 \vol 39 \issue 1 \pages 166--175 \mathnet{http://mi.mathnet.ru/ppi211} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2101671} \zmath{https://zbmath.org/?q=an:1077.94008} \transl \jour Problems Inform. Transmission \yr 2003 \vol 39 \issue 1 \pages 148--157 \crossref{https://doi.org/10.1023/A:1023690701161} 

• http://mi.mathnet.ru/eng/ppi211
• http://mi.mathnet.ru/eng/ppi/v39/i1/p166

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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. An. A. Muchnik, A. E. Romashchenko, “Stability of properties of Kolmogorov complexity under relativization”, Problems Inform. Transmission, 46:1 (2010), 38–61
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