CIF:Medium:Collaborative Research: Geometric Network Information Theory

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The proliferation of communication networks means that their efficiency and security now affects almost all aspects of our daily lives. At the societal level, reliable and efficient networks are of central importance to technological development, national economic growth and national defense. In light of this, the problem of understanding fundamental information limits of networked devices is more acute now than ever. Unfortunately, it has been a longstanding challenge in information theory to systematically extend its success beyond classical point-to-point exchanges of information. Despite significant research effort since the inception of the field in 1948, the information limits for most network settings, even for networks as fundamental as a three node relay channel, have remained open to date.This project aims to change the way many network problems are analyzed today in information theory. Traditional information-theoretic approaches for quantifying fundamental performance limits of networks often fail because the current toolset of information theory is not sufficiently refined to characterize tensions that emerge in networks due to competing objectives. Looking beyond traditional methods, this project will study the role that inequalities from geometric and functional analysis can play in characterizing tensions between information measures. The research project will be complemented with a strong inter-university education program, which includes joint and collaborative student and post-doctoral researcher advising.