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.

中文翻译：

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有限状态通道上的有界状态估计：关联拓扑熵和零误差容量

我们研究了有限状态擦除和加性噪声通道上线性系统的有界状态估计，其中噪声由没有任何统计结构的有限状态机控制。导出了它们的零误差容量的上限和下限，揭示了与通道动力学的拓扑熵的联系。介绍了一些示例，并根据其特定特征导出了单独的容量界限，并与拓扑熵的界限进行了比较。然后通过将非随机无记忆通道的先前结果扩展到有限状态通道，获得通过此类通道进行有界误差线性状态估计的必要和充分条件。这些估计条件将线性系统和离散通道的拓扑熵结合在一起。