Communications and Signal Processing Seminar
Problems in the Intersection of Informaton Theory and Control
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In this talk we consider problems in information theory and channel coding that can be formulated and solved utilizing ideas from stochastic control, decentralized optimization, and dynamic teams/games. The presence of feedback is what makes the interaction between information theory and control interesting and fruitful.
We start with the investigation of the capacity of point-to-point channels with memory and feedback. Casting the problem as a centralized stochastic control problem leads to a single-letter characterization of the capacity with a well-defined and intuitive auxiliary variable. We discuss how this approach can be used to shed light on one of the still open problems in information theory: a single-letter characterization of the capacity for the discrete memoryless Multiple Access Channel (MAC) with feedback.
We then turn to the problem of designing deterministic transmission schemes (channel codes) that provably achieve the capacity of the aforementioned channels. We develop a generalization of the Posterior Matching (PM) scheme and show that it has close connections with the real-time communication problem over the same channel. We generalize the PM scheme to a fully sequential version of the well-known Cover&Leung scheme for the MAC with feedback.
We will conclude with a discussion on how these problems changes in the presence of users that do not form a team, but act strategically.