Feedback Capacity and a Variant of the Kalman Filter with ARMA Gaussian Noises: Explicit Bounds and Feedback Coding Design

• URL: http://arxiv.org/abs/2001.03108v6
• Date: Thu, 3 Jun 2021 22:40:32 GMT
• Title: Feedback Capacity and a Variant of the Kalman Filter with ARMA Gaussian Noises: Explicit Bounds and Feedback Coding Design
• Authors: Song Fang and Quanyan Zhu
• Abstract summary: We obtain relatively explicit lower bounds on the feedback capacity for colored Gaussian noises. Our results provide an alternative perspective while pointing to potentially tighter bounds for the feedback capacity problem.
• Score: 23.249999313567624
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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