On the Feedback Capacity of Power Constrained Gaussian Noise Channels with Memory
<|reference_start|>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 $O(L^2)$ 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.<|reference_end|>
@article{yang2007on,
    title={On the Feedback Capacity of Power Constrained Gaussian Noise Channels
  with Memory},
    author={Shaohua Yang, Aleksandar Kavcic, Sekhar Tatikonda},
    journal={arXiv preprint arXiv:cs/0701099},
    year={2007},
    archivePrefix={arXiv},
    eprint={cs/0701099},
    primaryClass={cs.IT math.IT}
}