Distributed source coding for satellite communications

Inspired by mobile satellite communications systems, we consider a source coding system which consists of multiple sources, multiple encoders, and multiple decoders. Each encoder has access to a certain subset of the sources, each decoder has access to certain subset of the encoders, and each decoder reconstructs a certain subset of the sources almost perfectly. The connectivity between the sources and the encoders, the connectivity between the encoders and the decoders, and the reconstruction requirements for the decoders are all arbitrary. Our goal is to characterize the admissible coding rate region. Despite the generality of the problem, we have developed an approach which enables us to study all cases on the same footing. We obtain inner and outer bounds of the admissible coding rate region in terms of Γ_N * and Γ¯_N*, respectively, which are fundamental regions in the entropy space defined by Yeung (1991). So far, there has not been a full characterization of Γ_N*, so these bounds cannot be evaluated explicitly except for some special cases. Nevertheless, we obtain an alternative outer bound which can be evaluated explicitly. We show that this bound is tight for all the special cases for which the admissible coding rate region is known. The model we study in this paper is more general than all previously reported models on multilevel diversity coding, and the tools we use are new in multiuser information theory