English

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

Information Theory 2021-06-07 v6 Machine Learning Systems and Control Signal Processing Systems and Control math.IT Optimization and Control

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.

Keywords

Cite

@article{arxiv.2001.03108,
  title  = {Feedback Capacity and a Variant of the Kalman Filter with ARMA Gaussian Noises: Explicit Bounds and Feedback Coding Design},
  author = {Song Fang and Quanyan Zhu},
  journal= {arXiv preprint arXiv:2001.03108},
  year   = {2021}
}

Comments

Note that this is an extended version of the original submission "A Connection between Feedback Capacity and Kalman Filter for Colored Gaussian Noises"