Multivariate Mutual Information Inspired by Secret-Key Agreement

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Author(s)

  • Chung CHAN
  • Ali AL-BASHABSHEH
  • Javad B. EBRAHIMI
  • Tarik KACED
  • Tie LIU

Detail(s)

Original languageEnglish
Pages (from-to)1883-1913
Journal / PublicationProceedings of the IEEE
Volume103
Issue number10
Online published16 Sept 2015
Publication statusPublished - Oct 2015
Externally publishedYes

Abstract

The capacity for multiterminal secret-key agreement inspires a natural generalization of Shannon's mutual information from two random variables to multiple random variables. Under a general source model without helpers, the capacity is shown to be equal to the normalized divergence from the joint distribution of the random sources to the product of marginal distributions minimized over partitions of the random sources. The mathematical underpinnings are the works on co-intersecting submodular functions and the principle lattices of partitions of the Dilworth truncation. We clarify the connection to these works and enrich them with information-theoretic interpretations and properties that are useful in solving other related problems in information theory as well as machine learning.

Research Area(s)

  • Dilworth truncation, multivariate mutual information, omnivocality, principal partition, principle lattices of partitions, secret-key agreement, submodularity

Citation Format(s)

Multivariate Mutual Information Inspired by Secret-Key Agreement. / CHAN, Chung; AL-BASHABSHEH, Ali; EBRAHIMI, Javad B. et al.
In: Proceedings of the IEEE, Vol. 103, No. 10, 10.2015, p. 1883-1913.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review