Control-theoretic Approach to Communication with Feedback: Fundamental Limits and Code Design

Feedback communication is studied from a control-theoretic perspective, mapping the communication problem to a control problem in which the control signal is received through the same noisy channel as in the communication problem, and the (nonlinear and time-varying) dynamics of the system determine a subclass of encoders available at the transmitter. The MMSE capacity is defined to be the supremum exponential decay rate of the mean square decoding error. This is upper bounded by the information-theoretic feedback capacity, which is the supremum of the achievable rates. A sufficient condition is provided under which the upper bound holds with equality. For the special class of stationary Gaussian channels, a simple application of Bode's integral formula shows that the feedback capacity, recently characterized by Kim, is equal to the maximum instability that can be tolerated by the controller under a given power constraint. Finally, the control mapping is generalized to the N-sender AWGN multiple access channel. It is shown that Kramer's code for this channel, which is known to be sum rate optimal in the class of generalized linear feedback codes, can be obtained by solving a linear quadratic Gaussian control problem.Comment: Submitted to IEEE Transactions on Automatic Contro

Fundamental limits in Gaussian channels with feedback: confluence of communication, estimation, and control

The emerging study of integrating information theory and control systems theory has attracted tremendous attention, mainly motivated by the problems of control under communication constraints, feedback information theory, and networked systems. An often overlooked element is the estimation aspect; however, estimation cannot be studied isolatedly in those problems. Therefore, it is natural to investigate systems from the perspective of unifying communication, estimation, and control;This thesis is the first work to advocate such a perspective. To make Matters concrete, we focus on communication systems over Gaussian channels with feedback. For some of these channels, their fundamental limits for communication have been studied using information theoretic methods and control-oriented methods but remain open. In this thesis, we address the problems of characterizing and achieving the fundamental limits for these Gaussian channels with feedback by applying the unifying perspective;We establish a general equivalence among feedback communication, estimation, and feedback stabilization over the same Gaussian channels. As a consequence, we see that the information transmission (communication), information processing (estimation), and information utilization (control), seemingly different and usually separately treated, are in fact three sides of the same entity. We then reveal that the fundamental limitations in feedback communication, estimation, and control coincide: The achievable communication rates in the feedback communication problems can be alternatively given by the decay rates of the Cramer-Rao bounds (CRB) in the associated estimation problems or by the Bode sensitivity integrals in the associated control problems. Utilizing the general equivalence, we design optimal feedback communication schemes based on the celebrated Kalman filtering algorithm; these are the first deterministic, optimal communication schemes for these channels with feedback (except for the degenerated AWGN case). These schemes also extend the Schalkwijk-Kailath (SK) coding scheme and inherit its useful features, such as reduced coding complexity and improved performance. Hence, this thesis demonstrates that the new perspective plays a significant role in gaining new insights and new results in studying Gaussian feedback communication systems. We anticipate that the perspective could be extended to more general problems and helpful in building a theoretically and practically sound paradigm that unifies information, estimation, and control

A space communications study Final report, 15 Sep. 1966 - 15 Sep. 1967

Investigation of signal to noise ratios and signal transmission efficiency for space communication system