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This paper presents explicit solutions for two related non-convex information extremization problems due to Gray and Wyner in the Gaussian case. The first problem is the Gray-Wyner network subject to a sum-rate constraint on the two private links. Here, our argument establishes the optimality of Gaussian codebooks and hence, a closed-form formula for the optimal rate region. The second problem is Wyner's common information and a generalization thereof, where conditional independence is generalized to a limit on the conditional mutual information. We present full explicit solutions for the scalar as well as the vector case.
Negar Kiyavash, Seyed Jalal Etesami, Kun Zhang
Michael Christoph Gastpar, Amedeo Roberto Esposito