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

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

2007-01-16

arxiv.org/abs/cs/0701099v1

Computer Science

Information Theory

Transaction on Information Theory, accepted version, first version submitted on Oct 22, 2003

Scientific paper

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 $O(L^2)$ 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 non-linear programming. For first-order autoregressive and/or moving average (ARMA) noise channels, this optimization admits a closed form maximal information rate formula. The maximal information rate for stationary sources is a lower bound on the feedback capacity, and it equals the feedback capacity if the long-standing conjecture, that stationary sources achieve the feedback capacity, holds.

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