Two Problems in Multiterminal Information Theory
This dissertation consists of three parts. The first part considers the archetypical multiterminal source coding problem with logarithmic loss distortion constraints. A single-letter description of the achievable rate distortion region is given for finite-alphabet sources. In the course of doing so, the rate distortion region for the m-encoder CEO problem is also characterized. Several applications and examples are given, and a variety of related problems are discussed.
The second part of this dissertation considers the combinatorial problem of Coded Cooperative Data Exchange. In this problem, data which is originally distributed in a network is exchanged among nodes until universal recovery is achieved (i.e., all terminals recover all data initially present in the network). This dissertation characterizes the minimum number of exchanges which must take place in order to permit universal recovery. Explicit algorithms and tight concentration results are given for several special cases of interest.
Finally, three new lemmas are provided, each of which is interesting in its own right. Applications to multiterminal information theory are discussed.