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Technical Program

Paper Detail

Paper IDD1-S1-T1.2
Paper Title Feedack Capacity of MIMO Gaussian Channels
Authors Oron Sabag, Victoria Kostina, Babak Hassibi, Caltech, United States
Session D1-S1-T1: Gaussian Channels with Feedback
Chaired Session: Monday, 12 July, 22:00 - 22:20
Engagement Session: Monday, 12 July, 22:20 - 22:40
Abstract Finding a computable expression for the feedback capacity of channels with non-white Gaussian, additive noise is a long standing open problem. In this paper, we solve this problem in the case where the channel has multiple-inputs and multiple-outputs (MIMO) and the noise process is generated as the output of a state-space model (a hidden Markov model). The main result is a computable characterization of the feedback capacity as a finite-dimensional convex optimization problem. Our solution subsumes all previous solutions to the feedback capacity including the auto-regressive moving-average (ARMA) noise process of first order, even if it is a non-stationary process. The capacity problem can be viewed as the problem of maximizing the measurements' entropy-rate of a controlled (policy-dependent) state-space subject to a power constraint. Our approach is to formulate the finite-block version of this problem as a \emph{sequential convex optimization problem} which leads in turn to a single-letter and computable upper bound. By optimizing over a family of time-invariant policies (corresponds to the channel inputs distribution), a tight lower bound is realized. We show that one of optimization constraints in the capacity characterization boils down to a Riccati equation, revealing an interesting relation between explicit capacity formulae and Riccati equations that appear frequently in control theory.