Feedback Capacity of Parallel ACGN Channels and Kalman Filter: Power Allocation with Feedback

In this paper, we relate the feedback capacity of parallel additive colored Gaussian noise (ACGN) channels to a variant of the Kalman filter. By doing so, we obtain lower bounds on the feedback capacity of such channels, as well as the corresponding feedback (recursive) coding schemes, which are essentially power allocation policies with feedback, to achieve the bounds. The results are seen to reduce to existing lower bounds in the case of a single ACGN feedback channel, whereas when it comes to parallel additive white Gaussian noise (AWGN) channels with feedback, the recursive coding scheme reduces to a feedback "water-filling" power allocation policy.

Fundamental Limits on the Maximum Deviations in Control Systems: How Short Can Distribution Tails be Made by Feedback?

This paper is on the application of information theory to the analysis of fundamental lower bounds on the maximum deviations in feedback control systems, where the plant is linear time-invariant while the controller can generically be any causal functions as long as it stabilizes the plant. It is seen in general that the lower bounds are characterized by the unstable poles (or nonminimum-phase zeros) of the plant as well as the conditional entropy of the disturbance. Such bounds provide fundamental limits on how short the distribution tails in control systems can be made by feedback.

Relativistic Rocket Control (Relativistic Space-Travel Flight Control): Feedback Control of Relativistic Dynamics Propelled by Ejecting Mass

In this short note, we investigate the feedback control of relativistic dynamics propelled by mass ejection, modeling, e.g., the relativistic rocket control or the relativistic (space-travel) flight control. As an extreme case, we also examine the control of relativistic photon rockets which are propelled by ejecting photons.

The Spectral-Domain $\mathcal{W}_2$ Wasserstein Distance for Elliptical Processes and the Spectral-Domain Gelbrich Bound

In this short note, we introduce the spectral-domain $\mathcal{W}_2$ Wasserstein distance for elliptical stochastic processes in terms of their power spectra. We also introduce the spectral-domain Gelbrich bound for processes that are not necessarily elliptical.

Independent Elliptical Distributions Minimize Their $\mathcal{W}_2$ Wasserstein Distance from Independent Elliptical Distributions with the Same Density Generator

This short note is on a property of the $\mathcal{W}_2$ Wasserstein distance which indicates that independent elliptical distributions minimize their $\mathcal{W}_2$ Wasserstein distance from given independent elliptical distributions with the same density generators. Furthermore, we examine the implications of this property in the Gelbrich bound when the distributions are not necessarily elliptical. Meanwhile, we also generalize the results to the cases when the distributions are not independent. The primary purpose of this note is for the referencing of papers that need to make use of this property or its implications.