In this paper, we show a general equivalence between feedback stabilization through an analog communication channel, and a communication scheme based on feedback which is a generalization of that of Schalkwijk and Kailath. We also show that the achievable transmission rate of the scheme is given by the Bode's sensitivity integral formula, which characterizes a fundamental limitation of causal feedback. Therefore, we can now use the many results and design tools from control theory to design feedback communication schemes providing desired communication rates, and to generate lower bounds on the channel feedback capacity. We consider single user Gaussian channels with memory and memory-less multiuser broadcast, multiple access, and interference channels. In all cases, the results we obtain either achieve the feedback capacity, when this is known, recover known best rates, or provide new best achievable rates.
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Manuscript received May 5, 2003; revised December 31, 2003. Recommended by Guest Editors P. Antsaklis and J. Baillieul. This work was supported by the National Science Foundation under the Career Award Grant ECS-0093950. The author is with the Department of Electrical and Computer Engineering, Iowa Sate University, Ames, IA 50010 USA (e-mail: email@example.com). Digital Object Identifier 10.1109/TAC.2004.834119 Fig. 1. LQG optimal control and its interpretation as stabilization over an AWGN channel.