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Feedback communication is studied from a control-theoretic perspective,mapping the communication problem to a control problem in which the controlsignal is received through the same noisy channel as in the communicationproblem, and the (nonlinear and time-varying) dynamics of the system determinea subclass of encoders available at the transmitter. The MMSE capacity isdefined to be the supremum exponential decay rate of the mean square decodingerror. This is upper bounded by the information-theoretic feedback capacity,which is the supremum of the achievable rates. A sufficient condition isprovided under which the upper bound holds with equality. For the special classof stationary Gaussian channels, a simple application of Bode's integralformula shows that the feedback capacity, recently characterized by Kim, isequal to the maximum instability that can be tolerated by the controller undera given power constraint. Finally, the control mapping is generalized to theN-sender AWGN multiple access channel. It is shown that Kramer's code for thischannel, which is known to be sum rate optimal in the class of generalizedlinear feedback codes, can be obtained by solving a linear quadratic Gaussiancontrol problem.

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