Distributed Simulation of Continuous Random Variables

Cheuk Ting Li; Abbas El Gamal

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arXiv · 1601.05875

Distributed Simulation of Continuous Random Variables

Cheuk Ting Li·Abbas El Gamal

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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.

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Cheuk Ting Li, Abbas El Gamal. 2016-01-22. Distributed Simulation of Continuous Random Variables. https://arxiv.org/abs/1601.05875

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