Fri, 28-May-2021 / 1:00pm / TBA
I will present a channel capacity problem that received much attention in information theory that we recently solved using control theory and convex optimization methods. The channel is the additive Gaussian noise (AGN) with feedback. When the AGN is white, i.e. AWGN, the capacity is given by the well-known formula C = 0.5 \log (1+SNR). However, if the noise is not white, finding an explicit capacity expression is not simple due to the memory inherited from the noise process to the optimal channel inputs and outputs processes. Our main result is a closed-form formula for the feedback capacity, given by a convex optimization problem, for the general case where: the channel noise is generated by any linear state-space, and the channel has multiple inputs and multiple outputs (MIMO). I will highlight the interesting relations between the capacity problem and notions that naturally appear in control and Kalman filtering such as Riccati equations and LMIs.
Oron Sabag is a postdoctoral fellow in the Department of Electrical Engineering at Caltech. He received his B.Sc. (cum laude), the M.Sc. (summa cum laude) and the Ph.D. in Electrical and Computer Engineering from the Ben-Gurion University of the Negev, Israel, in 2013, 2016 and 2019, respectively. His research interests include information theory, control theory and reinforcement learning. Honors include the ISEF postdoctoral fellowship, Lachish Fellowship, ISIT-2017 best student paper award, SPCOM-2016 best student paper award, the Feder Family Award for outstanding research in communications and the Kaufman award.
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