Sula, ErixhenGastpar, Michael2022-02-142022-02-142022-02-142022-02-0110.1109/TIT.2021.3128187https://infoscience.epfl.ch/handle/20.500.14299/185339WOS:000745528100041This 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.Computer Science, Information SystemsEngineering, Electrical & ElectronicComputer ScienceEngineeringrandom variablesreceiversoptimizationmutual informationsource codingcovariance matricesentropygray-wyner networkwyner's common informationgaussianwater fillingconditional independencenetwork information theorytext::journal::journal article::research article