The Common Information of N Dependent Random Variables

Details The Common Information of N Dependent Random Variables The Common Information of N Dependent Random Variables

2010-10-18

arxiv.org/abs/1010.3613v1

Computer Science

Information Theory

8 pages, 4 figures,presented at the Forty-Eighth Annual Allerton Conference on Communication, Control, and Computing, Septembe

Scientific paper

This paper generalizes Wyner's definition of common information of a pair of random variables to that of $N$ random variables. We prove coding theorems that show the same operational meanings for the common information of two random variables generalize to that of $N$ random variables. As a byproduct of our proof, we show that the Gray-Wyner source coding network can be generalized to $N$ source squences with $N$ decoders. We also establish a monotone property of Wyner's common information which is in contrast to other notions of the common information, specifically Shannon's mutual information and G\'{a}cs and K\"{o}rner's common randomness. Examples about the computation of Wyner's common information of $N$ random variables are also given.

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