Title :
Multivariate Mutual Information Inspired by Secret-Key Agreement
Author :
Chung Chan ; Al-Bashabsheh, Ali ; Ebrahimi, Javad B. ; Kaced, Tarik ; Tie Liu
Author_Institution :
Inst. of Network Coding & the Shenzhen Res. Inst., Chinese Univ. of Hong Kong, Hong Kong, China
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.
Keywords :
information theory; learning (artificial intelligence); multiterminal networks; private key cryptography; Dilworth truncation; Shannon mutual information; cointersecting submodular functions; information theory; machine learning; mathematical underpinnings; multiterminal secret-key agreement; multivariate mutual information; source model; Communication system security; Entropy; Mutual information; Network coding; Physical layer; Random variables; Source coding; Telecommunication services; Upper bound; Dilworth truncation; multivariate mutual information; omnivocality; principal partition; principle lattices of partitions; secret-key agreement; submodularity;
Journal_Title :
Proceedings of the IEEE
DOI :
10.1109/JPROC.2015.2458316