Distributed Source Coding Under Logarithmic Loss and its Gaussian Counterparts

Achievable rate distortion region for the quadratic Gaussian multi-terminal source coding was recently solved by Wagner, Tavildar, and Viswanath [1]. Although it is a very important result, the proofs are somewhat ad-hoc and hard to be generalized. Recently, Courtade and Weissman [2] established the complete achievable rate region of two-encoder multi-terminal source coding problem under logarithmic loss for any finite alphabet sources. In this project, we show it is natural to extend logarithmic loss to any sources, and in general it provides a tighter outer bound for corresponding source coding problems in the quadratic Gaussian settings. Our conjecture is the logarithmic loss results would provide a unified framework to establish rate regions of various quadratic Gaussian source coding problems, and we have shown that for the quadratic Gaussian source coding with rate-limited side information problem, logarithmic loss indeed achieved this goal.