Abstract-We consider the two-encoder multiterminal source coding problem subject to distortion constraints computed under logarithmic loss. We provide a single-letter description of the achievable rate distortion region for arbitrarily correlated sources with finite alphabets. In doing so, we also give the rate distortion region for the CEO problem under logarithmic loss. Notably, the Berger-Tung inner bound is tight in both settings.

Abstract-We consider the two-encoder multiterminal source coding problem subject to distortion constraints computed under logarithmic loss. We provide a single-letter description of the achievable rate distortion region for arbitrarily correlated sources with finite alphabets. In doing so, we also give the rate distortion region for the CEO problem under logarithmic loss. Notably, the Berger-Tung inner bound is tight in both settings.

Consider a connected network of n nodes that all wish to recover k desired packets. Each node begins with a subset of the desired packets and exchanges coded packets with its neighbors. This paper provides necessary and sufficient conditions which characterize the set of all transmission schemes that permit every node to ultimately learn (recover) all k packets. When the network satisfies certain regularity conditions and packets are randomly distributed, this paper provides tight concentration results on the number of transmissions required to achieve universal recovery. For the case of a fully connected network, a polynomial-time algorithm for computing an optimal transmission scheme is derived. An application to secrecy generation is discussed.

We establish existence of Stein kernels for probability measures on R d satisfying a Poincaré inequality, and obtain bounds on the Stein discrepancy of such measures. Applications to quantitative central limit theorems are discussed, including a new CLT in Wasserstein distance W 2 with optimal rate and dependence on the dimension. As a byproduct, we obtain a stable version of an estimate of the Poincaré constant of probability measures under a second moment constraint. The results extend more generally to the setting of converse weighted Poincaré inequalities. The proof is based on simple arguments of calculus of variations.Further, we establish two general properties enjoyed by the Stein discrepancy, holding whenever a Stein kernel exists: Stein discrepancy is strictly decreasing along the CLT, and it controls the skewness of a random vector.

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