On the Feedback Capacity of Power-Constrained Gaussian Noise Channels With Memory

摘要

For a stationary additive Gaussian-noise channel with a rational noise powerspectrum of a finite-order $L$, we derive two new results for the feedbackcapacity under an average channel input power constraint. First, we show that avery simple feedback-dependent Gauss-Markov source achieves the feedbackcapacity, and that Kalman-Bucy filtering is optimal for processing thefeedback. Based on these results, we develop a new method for optimizing thechannel inputs for achieving the Cover-Pombra block-length-$n$ feedbackcapacity by using a dynamic programming approach that decomposes thecomputation into $n$ sequentially identical optimization problems where eachstage involves optimizing $O(L^2)$ variables. Second, we derive the explicitmaximal information rate for stationary feedback-dependent sources. In general,evaluating the maximal information rate for stationary sources requires solvingonly a few equations by simple non-linear programming. For first-orderautoregressive and/or moving average (ARMA) noise channels, this optimizationadmits a closed form maximal information rate formula. The maximal informationrate for stationary sources is a lower bound on the feedback capacity, and itequals the feedback capacity if the long-standing conjecture, that stationarysources achieve the feedback capacity, holds.