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

Abstract

This article studies the zero-error feedback capacity of causal discrete channels with memory. First, by extending the classical zero-error feedback capacity concept, a new notion of uniform zero-error feedback capacity C0f 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. Furthermore, the zero-error feedback capacity of a class of additive noise channels is investigated. It is known that for a discrete channel with correlated additive noise, the ordinary capacity with or without feedback is equal log q-Hch, where H..