CAREER: Information Transmission and Optimal Estimation: Fundamentals and Applications

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Communication technology is a major driving force for advances in the modern society. The fundamental problem of communication is on one hand a problem of signal detection and estimation, and on the other a problem of efficient information representation and transmission.Regarding information theory and estimation theory as two sides of the same coin, this research systematically explores the fundamental relationship between the two theories, and studies their application to the design and optimization of future wired, wireless and optical communication systems.This research is divided into two parts. Part I is inspired by fundamental formulas which relate the mutual information and estimation errors in Gaussian and Poisson channels. The investigators study the operational meaning and generalizations of the formulas; their application to information inequalities; and the general role of estimation in efficient information transmission through time-varying channels. Part II of the research is concerned with communication systems which explore spaces of increasingly high dimensions for efficiency (e.g., in coding, spreading, multiplexing). The research is inspired by heuristic results (via statistical physics) which show that the multiple dimensions of the input signal to a linear system decouple asymptotically. Equipped with rigorous techniques developed for sparse systems, a series of conjectured generalizations of the decoupling result are studied, as well as the self-averaging phenomenon of large systems, which is related to the asymptotic equipartition property in information theory. The program also includes training students in research and broadening the scope of information science curricula at Northwestern.