On Wyner's Common Information in the Gaussian Case

Erixhen Sula; Michael Gastpar

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arXiv · 1912.07083

On Wyner's Common Information in the Gaussian Case

Erixhen Sula·Michael Gastpar

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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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Erixhen Sula, Michael Gastpar. 2019-12-15. On Wyner's Common Information in the Gaussian Case. https://arxiv.org/abs/1912.07083

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