We review how Shannon's classical notion of capacity is not enough to characterize a noisy communication channel if we intend to use that channel as a part of a feedback loop to stabilize an unstable linear system. While classical capacity is not enough, another parametric sense of capacity called "anytime capacity" is shown to be necessary for the stabilization of an unstable process. The rate required is given by the log of the system gain and the sense of reliability required comes from the sense of stability desired. A consequence of this necessity result is a sequential generalization of the Schalkwijk/Kailath scheme for communication over the AWGN channel with feedback.In cases of sufficiently rich information patterns between the encoder and decoder, we show that adequate anytime capacity is also sufficient for there to exist a stabilizing controller. These sufficiency results are then generalized to cases with noisy observations and without any explicit feedback between the observer and the controller. Both necessary and sufficient conditions are extended to the continuous time case as well.In part II, the vector-state generalizations are established. Here, it is the magnitudes of the unstable eigenvalues that play an essential role. The channel is no longer summarized by a single number, or even a single function. Instead, the concept of the anytime-rate-region is introduced in which we ask for the region of rates that the channel can support while still meeting different reliability targets for parallel bitstreams. For cases where there is no explicit feedback of the noisy channel outputs, the intrinsic delay of the control system tells us what the feedback delay needs to be while evaluating the anytime reliability of the channel.

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