It is known that for a discrete channel with correlated additive noise, the ordinary capacity with or without feedback both equal log $q - mathcal{H}left( Z ight)$, where $mathcal{H}left( Z ight)$is the entropy rate of the noise process Z and q is the alphabet size. In this paper, a class of finite-state additive noise channels is introduced. It is shown that the zero-error feedback capacity of such channels is either zero or C0f = log q - h(Z), where h(Z) is the topological entropy of the noise process. Moreover, the zero-error capacity without feedback is lower-bounded by log q - 2h(Z). We explicitly compute the zero-error feedback capacity for several examples, including channels with isolated errors and a Gilbert-Elliot channel.
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