Achieving the Stationary Feedback Capacity for Gaussian Channels

AbstractIn this paper, we study a Gaussian channel with memory and wit h noiseless feedback, for which we present a coding scheme to achieve the stationary feedback capacity (the maximum information rate over all stationaryinput distributions, conjectured to be the asymptotic feed back capacity). The coding scheme essentially implements the celebrated Kalman filter algorithm; is equiv alent to an estimation system over the same channel without feedback; and reveals that the achievable informat ion rate of the feedback communication system can be alternatively given by the decay rate of the Cramer-Rao boun d of the associated estimation system. Thus, combined with the control theoretic characterizations of feedback c ommunication (proposed by Elia), this implies that the fundamental limitations in feedback communication, estim a on, and control coincide. In addition, the proposed coding scheme simplifies the coding complexity and shortens he coding delay, and its construction amounts to solving a finite-dimensional optimization problem. We also pr vide a further simplification to the optimal input distribution developed by Yang, Kavcic, and Tatikonda.