On Wyner's Common Information in the Gaussian Case

2019/12/15 by Sula, Erixhen, Gastpar, Michael
#FOS: Computer and information sciences #Information Theory (cs.IT)

paper · doi:10.48550/arxiv.1912.07083

Abstract

Wyner's Common Information and a natural relaxation are studied in the special case of Gaussian random variables. The relaxation replaces conditional independence by a bound on the conditional mutual information. The main contribution is the proof that Gaussian auxiliaries are optimal, leading to a closed-form formula. As a corollary, the proof technique also establishes the optimality of Gaussian auxiliaries for the Gaussian Gray-Wyner network, a long-standing open problem.

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