论文标题
一类有限状态添加噪声通道的零回馈能力的明确公式
An Explicit Formula for the Zero-Error Feedback Capacity of a Class of Finite-State Additive Noise Channels
论文作者
论文摘要
众所周知，对于具有相关添加剂噪声的离散通道，带有反馈的普通容量都等于$ \ log q- \ m natercal {h}（z）$，其中$ \ nathcal {h}（z）$是噪声过程$ z $和$ q $的熵率。在本文中，引入了一类有限状态添加噪声通道。结果表明，此类通道的零反馈容量为零或$ c_ {0f} = \ log q -h（z）$，其中$ h（z）$是噪声过程的{\ em拓扑熵}。当零误差容量为零，有或没有反馈时，给出拓扑条件。此外，没有反馈的零误差容量被$ \ log Q-2 H（Z）$降低。我们明确地计算了几个示例的零回馈能力，包括具有孤立误差的通道和吉尔伯特·埃利奥特通道。
It is known that for a discrete channel with correlated additive noise, the ordinary capacity with or without feedback both equal $ \log q-\mathcal{H} (Z) $, where $ \mathcal{H}(Z) $ is the entropy rate of the noise process $ Z $ and $ q $ is the alphabet size. In this paper, a class of finite-state additive noise channels is introduced. It is shown that the zero-error feedback capacity of such channels is either zero or $C_{0f} =\log q -h (Z) $, where $ h (Z) $ is the {\em topological entropy} of the noise process. A topological condition is given when the zero-error capacity is zero, with or without feedback. Moreover, the zero-error capacity without feedback is lower-bounded by $ \log q-2 h (Z) $. We explicitly compute the zero-error feedback capacity for several examples, including channels with isolated errors and a Gilbert-Elliot channel.
