Unified-Theory-of-Source-Coding-Part-II-–-Multiterminal-Problems.pdfVIP

Unified Theory of Source Coding: Part II – Multiterminal Problems Soumya Jana University of Illinois at Urbana-Champaign Email: {jana}@uiuc.edu Abstract 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-K¨orner, Wyner-Ziv, Berger et al. and Berger-Yeung. To achieve such unification we made use of a funda- mental 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 noncoopera- tive 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 informa- tion 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 multi- terminal estimation problem can be solved as a special case of our theory. 1 1 Introduction In the first paper of this two part communication [1], we solved in a unified framework a variety of two terminal source coding problems with noncooperative encoders, consolidating works of Shannon [2, 3], Slepian-Wolf [4], Wyner [5], Ahlswede-K¨orner [6], Wyner-Ziv [7], Berger et al. [8] and Berger-Yeung [9]. In particular, we derived a fund