Bounded state Estimation over Finite-State Channels: Relating Topological Entropy and Zero-Error Capacity
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We investigate bounded state estimation of linear systems over finite-state erasure and additive noise channels in which the noise is governed by a finite-state machine without any statistical structure. Upper and lower bounds on their zero-error capacities are derived, revealing a connection with the topological entropy of the channel dynamics. Some examples are introduced and separate capacity bounds based on their specific features are derived and compared with bounds from topological entropy. Necessary and sufficient conditions for linear state estimation with bounded errors via such channels are then obtained, by extending previous results for nonstochastic memoryless channels to finite-state channels. These estimation conditions bring together the topological entropies of the linear system and the discrete channel.
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