Sequential Characterizations of Cover and Pombra Gaussian Feedback Capacity: Generalizations to MIMO Channels via Sufficient Statistic

The multiple-input multiple output (MIMO) generalization of Cover's and Pombra's Gaussian feedback capacity is considered. An equivalent sequential characterization of the finite block or transmission feedback information (FTFI) capacity is derived, with the optimal channel input processes expressed as functional of a sufficient statistic and a Gaussian orthogonal innovations process. From the new representations follows that the Cover and Pombra characterization of the FTFI capacity is expressed as a functional of two generalized matrix difference Riccati equations (DRE) of filtering theory of Gaussian systems. The new characterization, although, more complex than existing formulas that appeared in the literature, its sequential optimization formulation offers computational advantages, especially for MIMO channels.