Computing the Rate Distortion Region for the CEO Problem With Independent Sources

Abstract

A method for numerically calculating the rate distortion region for the central estimation officer (CEO) problem when the sources are independent is derived by generalizing the Blahut-Arimoto algorithm. Unlike the traditional rate distortion function computation problem, the Lagrangian for the CEO rate distortion region can be nonconvex. When the Lagrangian is convex, the presented algorithm is converged from every initialization to the global optimum under some additional uniqueness conditions. When the Lagrangian is nonconvex, the convergent value obtained by the algorithm can be initialization dependent. To handle these nonconvex cases, an explicit nonrandom initialization that is in the region of attraction of the global optimum for low distortions is provided. Some example problems motivated by remote lossy function computation in sensor networks and wireless resource controllers highlight that both the convex and nonconvex cases occur in practice and the utility of the algorithm in computing their rate distortion regions.