Zero-Error Feedback Capacity for Bounded Stabilization and Finite-State Additive Noise Channels

This article studies the zero-error feedback capacity of {\em causal} discrete channels with memory. First, by extending the classical zero-error feedback capacity concept, a new notion of {\em uniform zero-error feedback capacity} $C_{0f}$ for such channels is introduced. Using this notion a tight condition for {bounded} stabilization of unstable {noisy} linear systems via causal channels is obtained, assuming no {channel} state information at either end of the channel.