Feedback Capacity and a Variant of the Kalman Filter with ARMA Gaussian Noises: Explicit Bounds and Feedback Coding Design
This work addresses the feedback capacity problem in communication theory, providing an alternative perspective and potentially tighter bounds, though it appears incremental as it builds on existing results.
The paper tackles the problem of determining feedback capacity for channels with ARMA Gaussian noises by relating it to a variant of the Kalman filter, resulting in explicit lower bounds and recursive coding schemes to achieve these bounds.
In this paper, we relate a feedback channel with any finite-order autoregressive moving-average (ARMA) Gaussian noises to a variant of the Kalman filter. In light of this, we obtain relatively explicit lower bounds on the feedback capacity for such colored Gaussian noises, and the bounds are seen to be consistent with various existing results in the literature. Meanwhile, this variant of the Kalman filter also leads to explicit recursive coding schemes with clear structures to achieve the lower bounds. In general, our results provide an alternative perspective while pointing to potentially tighter bounds for the feedback capacity problem.