Toward a Fundamental Theory of Gaussian Source-Channel Networks

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Research over the past six decades has led to a deep understanding of the point-to-point communication problem. However, the architecture of modern communication systems typically involves networks, rather than isolated direct connections of individual sources to individual destinations. The long-term goal of this research program is to develop a similarly comprehensive understanding of complex communication networks. As an important step toward this goal, the proposed research is intended to provide a theoretical framework for characterizing fundamental performance limits of Gaussian source-channel networks (i.e., network models that consist of vector Gaussian channels with quadratic cost constraint and vector Gaussian sources with quadratic distortion measure) and the structure of associated coding schemes. This theoretical framework is envisaged to contain three major components: reduction techniques, extremal inequalities, and nonlinear methods. Specifically, reduction techniques are used to convert the given Gaussian source-channel network to an equivalent model with a statistical structure that is more amenable to analysis, then the performance limit of the equivalent model is bounded with the aid of extremal inequalities, and finally nonlinear methods are invoked to prove the tightness of the resulting bound. The proposed research will enrich the fundamentals of network information theory through the introduction of new analysis techniques and the solution of important open problems. It will also advance the understanding of complex networked systems, suggesting both specific coding schemes and broad architectural principles. The development of reduction techniques has the potential to provide a bridge between information theory and theoretical computer science. Extremal inequalities obtained through this project are of independent mathematical interest and are likely to find applications beyond information theory. On the education front, this project will provide a valuable research and learning environment for graduate students in the rapidly progressing field of network information theory, and contribute to course development and training of undergraduate students.