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.
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 has systematically explored the fundamental relationship between the two theories, and studied their application to the design and optimization of future communication systems. This research is divided into two parts. Part I was inspired by fundamental formulas which relate the mutual information and estimation errors in Gaussian and Poisson channels. The project has lead to discovery of new connections of this nature in other useful models and to the characterization of capacity of multiple antenna systems with interfering users. Many new results from this project have been included along with classical results in a research monograph titled 'The interplay of information measures and estimation measures,' to be published in the series of Foundations and Trends in Communications and Information Theory. Part II of the research was concerned with communication systems which explore spaces of increasingly high dimensions for efficiency (e.g., in coding, spreading, multiplexing). The research was inspired by heuristic results (via statistical physics) which show that the multiple dimensions of the input signal to a linear system decouple asymptotically. New large-system results have been obtained using statistical physics techniques as well as rigorous analysis. Applications have been identified in compressed sensing, neighbor discovery and message exchange in wireless networks. The PI and team have found the capacity-achieving signaling scheme for Gaussian channels with duty-cycle constraint. The PI and team have proposed a new MIMO switching scheme and evaluated its performance. This project has contributed to a rich environment for the training of several students in research. The scope of information science curricula at Northwestern has also been broadened during the course of the project.
