Topics in network information representation and communication

Network information representation and communication are fundamental problems with important practical applications. In this dissertation, some topics in network information representation and communication are studied. Specifically, our recent research progress on determining the rate region for some multiple description problems and the capacity region for the Gaussian interference channel is presented. The first problem is a data compression problem, and the second is a data transmission problem.;In the first part of this dissertation, the multiple description problem of vector Gaussian sources with two levels of receivers is discussed. A novel information-theoretic inequality that is used to lower-bound the achievable multiple-description rates is derived, and a joint Gaussian scheme is shown to be the optimal compression scheme for the multiple description of a vector Gaussian source with two levels of receivers, under quadratic distortion constraints. The robustness of this description scheme is also discussed.;In the second part of this dissertation, the problem of determining the capacity region of the Gaussian interference channel is discussed. New outer bounds on capacity are derived, and a very simple power-splitting scheme is shown to be within 1 bits/s/Hz of the capacity of the channel for all values of the channel parameters. The point-to-point classical notion of degrees of freedom is naturally generalized to interference-limited scenarios.