CIF: Small: Bridging the Inequality Gap

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Inequalities are a vital component of information theory and comprise one of the most versatile mathematical tools in an information theorist's toolbox. Breakthroughs in obtaining strong information inequalities have invariably led to significant progress on longstanding open problems in information theory, and in turn contribute to the advancement of computer science, probability theory, and combinatorics. This project aims to advance the state-of-the-art knowledge of information inequalities by identifying and addressing key gaps in the existing literature. Being able to provide a better characterization of information inequalities and narrowing existing gaps can greatly increase our understanding of what is feasible in many computationally intractable problems in computer science and mathematics. The project will also support the educational goals of the investigator by training multiple graduate students working at the interface of engineering and mathematics.The project consists of a specific set of research questions that will uncover novel theoretical aspects of information inequalities and will lead to new mathematical strategies to establish novel inequalities. The work will be divided into the following sub-projects, each with a distinct set of research objectives: (1) Perform stability analyses of fundamental information inequalities; (2) Develop a principled approach for establishing new information inequalities by leveraging sub-additivity properties in information theory; and (3) Explore applications of stability results and proof strategies to areas beyond information theory, such as probability, queuing theory, and combinatorics.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.