在最坏情况下擦除和对称信道上状态估计
State Estimation over Worst-Case Erasure and Symmetric Channels with Memory
AI总结：
研究了最坏情况下擦除和对称信道的模型，推导了零错误容量的上下界，并通过扩展非随机无记忆信道的先前结果，得到了具有有限记忆的线性状态估计的必要和充分条件，涉及线性系统和信道的拓扑熵。
摘要：
研究了最坏情况下擦除和对称信道的模型，其中每个给定长度的滑动窗口中发生的信道错误数量被限制。推导了它们的零错误容量的上下界，其中下界揭示了信道动态的拓扑熵的联系。然后通过将先前非随机无记忆信道的结果扩展到具有有限记忆的信道，得到了利用此类信道进行具有有界估计误差的线性状态估计的必要和充分条件。这些估计条件涉及线性系统和信道的拓扑熵。
英文摘要：
Worst-case models of erasure and symmetric channels are investigated, in which the number of channel errors occurring in each sliding window of a given length is bounded. Upper and lower bounds on their zero-error capacities are derived, with the lower bounds revealing a connection with the topological entropy of the channel dynamics. Necessary and sufficient conditions for linear state estimation with bounded estimation errors via such channels are then obtained, by extending previous results for non-stochastic memoryless channels to those with finite memory. These estimation conditions involve the topological entropies of the linear system and the channel.
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