How to visualize multiterminal source coding

In the six decades since Shannon, source coding research has witnessed tremendous progress. Major milestones include Slepian and Wolf generalization of Shannon one-terminal lossless problem to the multiterminal setting, and Wyner and Ziv quantification of the effect of decoder side information on Shannon rate-distortion problem. Yet, the present state of source coding theory still remains unsatisfactory. For instance, given a well-characterized problem, one often does not know the effect of adding one extra source, or the effect of availability of decoder side information. Further mystery: why the two-source lossy coding problem due to Berger and Tung remains unsolved, whereas a similar Berger-Yeung problem, where one of the sources is perfectly reconstructed, is easily solved? In this backdrop, we shall propose a canonical theory of multiterminal source coding that brings a variety of problems under a unified framework, and a corresponding method of graphical visualization. As a consequence, multiterminal problems are divided into amenable and intransigent categories, thereby solving certain longstanding problems, and explaining why some of the problems are hard to solve. Additionally, the effect of additional sources and decoder side information is quantified in an arbitrary multiterminal setting.