On the Feedback Capacity of Power Constrained Gaussian Noise Channels with Memory

—For a stationary additive Gaussian-noise channel with a rational noise power spectrum of a finite-order L, we derive two new results for the feedback capacity under an average channel input power constraint. First, we show that a very simple feedback-dependent Gauss–Markov source achieves the feedback capacity, and that Kalman–Bucy filtering is optimal for processing the feedback. Based on these results, we develop a new method for optimizing the channel inputs for achieving the Cover–Pombra block-length- n feedback capacity by using a dynamic programming approach that decomposes the computation into n sequentially identical optimization problems where each stage involves optimizing O(L2 ) variables. Second, we derive the explicit maximal information rate for stationary feedback-dependent sources. In general, evaluating the maximal information rate for stationary sources requires solving only a few equations by simple nonlinear programming. For first-order autoregressive an...

• Type: Journal
• Year: 2007
• Where: CORR
• Authors: Shaohua Yang, Aleksandar Kavcic, Sekhar Tatikonda
• Keywords: CORR 2007, Education, Feedback Capacity, Maximal Information Rate, Stationary Additive Gaussian-noise