Bounded Estimation Over Finite-State Channels: Relating Topological Entropy and Zero-Error Capacity

• 成果类型: Article
• 署名作者: Saberi, Amir; Farokhi, Farhad; Nair, Girish N.
• 署名单位: University of Melbourne
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3120674
• 发表日期: 2022
• 页码: 4029-4044
• 关键词: Channel estimation; State estimation; entropy; Stochastic processes; estimation error; Memoryless systems; mathematical models; control over communications; estimation; finite-state channel; topological entropy and zero-error capacity

摘要

We investigate state estimation of linear systems over channels having a finite state not known by the transmitter or receiver. We show that similar to memoryless channels, zero-error capacity is the right figure of merit for achieving bounded estimation errors. We then consider finite-state, worst-case versions of the common erasure, and additive noise channels models, 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. Separate necessary and sufficient conditions for bounded linear state estimation errors via such channels are obtained. These estimation conditions bring together the topological entropies of the linear system and the discrete channel.