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

This article is cited in 1 scientific paper (total in 1 paper)

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}


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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  mathnet  crossref  mathscinet  isi  elib
  • Проблемы передачи информации Problems of Information Transmission
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