The necessity and sufficiency of anytime capacity for control over a noisy communication link

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 system. While classical capacity is not enough, another operational sense of capacity called "anytime capacity" is shown to be necessary for the stabilization of an unstable process. 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. The sufficiency result is then generalized to cases without any explicit feedback between the observer and the controller.