CIF:Small: Aspects of the Interplay Between Information Theory and Signal Processing: Extremal Problems and Applications

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Many key problems in signal processing and wireless communications can be formulated as extremal optimization problems, whose solutions require a careful integration of results located at the interface of different fields such as information theory, signal processing, statistics, and optimization. This project addresses extremal optimization problems located at the interface between information theory and signal processing. This project focuses on two major research problems: extension of De Bruijn's identity and development of extremal information theoretic inequalities. Successful completion of this project helps to advance the state-of-the-art results in the optimization of communications networks performance and security of communication channels (evaluating the secrecy capacity of wiretap channels, designing of energy efficient secure transmissions), design of robust communications systems (designing min-max optimal training sequences for channel estimation and synchronization), and robust signal estimation and detection algorithms (for smart grid, radar, sonar, and wireless communications applications). This project consists of two closely intertwined research thrusts: developing new extensions and applications of De Bruijn's identity, and development of novel extremal information theoretic inequalities with applications in the design of wireless communications systems with improved performance. At a broader scale, this project will impact positively the economy and society through the development of more efficient technologies for communication networks, power grids, wireless sensing and monitoring devices, biomedical devices, and radar and sonar systems. This project will be also integrated with the educational mission of investigator's university and will be largely disseminated to the community through journal papers, conference and workshop presentations, and editing of journal special issues.