Unified Theory of Source Coding: Part II -- Multiterminal Problems

In the first paper of this two part communication, we solved in a unified framework a variety of two terminal source coding problems with noncooperative encoders, thereby consolidating works of Shannon, Slepian-Wolf, Wyner, Ahlswede-Körner, Wyner-Ziv, Berger et al. and Berger-Yeung. To achieve such unification we made use of a fundamental principle that dissociates bulk of the analysis from the distortion criterion at hand (if any) and extends the typicality arguments of Shannon and Wyner-Ziv. In this second paper, we generalize the fundamental principle for any number of sources and on its basis exhaustively solve all multiterminal source coding problems with noncooperative encoders and one decoder. The distortion criteria, when applicable, are required to apply to single letters and be bounded. Our analysis includes cases where side information is, respectively, partially available, completely available and altogether unavailable at the decoder. As seen in our first paper, the achievable regions permit infinite order information-theoretic descriptions. We also show that the entropy-constrained multiterminal estimation problem can be solved as a special case of our theory.