Distributed Simulation of Continuous Random Variables

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Distributed Simulation of Continuous Random Variables

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Creation Date: Jul 10, 2016

Published In: Jul 2016

Paper Type: Conference Paper

Book Title: Proceedings of the 2016 IEEE International Symposium on Information Theory

Address: Barcelona, Spain

Abstract:

We establish the first known upper bound on the exact and Wyner's common information of n continuous random variables in terms of the dual total correlation between them (which is a generalization of mutual information). In particular, we show that when the pdf of the random variables is log-concave, there is a constant gap of n2 log e + 9n log n between this upper bound and the dual total correlation lower bound that does not depend on the distribution. The upper bound is obtained using a computationally efficient dyadic decomposition scheme for constructing a discrete common randomness variable W from which the n random variables can be simulated in a distributed manner. We then bound the entropy of W using a new measure, which we refer to as the erosion entropy.

IEEE Explore link: http://ieeexplore.ieee.org/document/7541362/

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