An Explicit Formula for the Zero-Error Feedback Capacity of a Class of Finite-State Additive Noise Channels
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It is known that for a discrete channel with correlated additive noise, the ordinary capacity with or without feedback both equal log q-ℋ (Z), where ℋ(Z) 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 C_0f =log q -h (Z), where h (Z) is the topological entropy of the noise process. A topological condition is given when the zero-error capacity is zero, with or without feedback. Moreover, the zero-error capacity without feedback is lower-bounded by log q-2 h (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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