The goal of this research project is to develop a Many-User Information Theory, which studies the fundamental information limits of models with a large number of sources, transmitters and/or receivers, whose population size is comparable or even larger than the coding blocklength. This new theory is deeply rooted in the classical Single-user and Multiuser Information Theory, which characterizes the performance of communication systems (often of a single user) by studying the asymptotic regime of infinite coding blocklength with a fixed (often small) number of users. For systems whose number of users is comparable to or larger than the blocklength, Multiuser Information Theory generally offers only limited results. In particular, sending the number of users to infinity after the blocklength goes to infinity may not yield the same result as sending the two to infinity simultaneously according to a certain relationship. In the new Many-User Information Theory, an additional dimension, namely, the user dimension, is simultaneously sent to infinity with the blocklength. Specific examples of many-user models include the many-access channel, the many-broadcast channel, and models with many correlated sources, among others. A crucial component of this research is to seek a new notion of capacity and capacity region in the many-user paradigm, as the traditional notion of rate in bits per symbol or per channel use becomes ill-suited for the task.
This research project will push the envelope of Information Theory. Transformative results will be developed in all three major subfields, namely, source coding, channel coding, and rate-distortion theory. Ideally, Many-User Information Theory will provide much needed guidance for the design of emerging and future communication systems, such as sensor networks and machine-to-machine communication systems, and will eventually affect many aspects of people's lives, including healthcare, transportation, smart grid, smart home, smart city, and public safety. Many-User Information Theory is also likely to cross-fertilize with other branches of mathematical and physical sciences, including probability theory, statistics, and statistical physics. The project also provides many opportunities for undergraduate students, including those from underrepresented groups, to gain experience in STEM research.
