论文标题
有限状态通道的有限状态估计：拓扑熵和零误差容量
Bounded State Estimation over Finite-State Channels: Relating Topological Entropy and Zero-Error Capacity
论文作者
论文摘要
我们研究了线性系统对具有有限状态的线性系统的状态估计，发射器或接收器不知道。我们表明，与无内存通道类似，零误差容量是实现有限估计误差的正确值。然后，我们考虑了有限的，最坏情况的常见擦除和添加噪声通道模型，其中噪声由有限状态的机器控制，没有任何统计结构。其零误差容量上的上限和下边界得出了与通道动力学的{\ em拓扑熵}的联系。通过此类通道获得了有界线性状态估计误差的单独和充分条件。这些估计条件汇集了线性系统和离散通道的拓扑熵。
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 {\em 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.
