Distributed Simulation of Continuous Random Variables
Proceedings of the 2016 IEEE International Symposium on Information Theory, Barcelona, Spain, July 2016
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 n 2  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.