论文标题
带有状态和内存的通道反馈错误指数上的上限
Upper Bounds on the Feedback Error Exponent of Channels With States and Memory
论文作者
论文摘要
作为一类国家依赖的通道，Markov通道长期以来一直在信息理论中进行了研究，以表征反馈能力和误差指数。本文研究了此类通道的更一般的变体，在这种变种中，国家通过一般随机过程演变而成，不一定是马尔可夫或阵行。假定状态是发射器和接收器未知的，但是已知潜在的概率分布。对于此设置，我们在反馈误差指数上获得了上限，并具有可变长度代码的反馈容量。边界以定向的相互信息和定向相对熵表示。误差指数上的界限被简化为burnashev的离散无内存通道的表达。我们的方法依赖于Martingales理论的工具来分析根据过去通道输出的消息的熵定义的随机过程。
As a class of state-dependent channels, Markov channels have been long studied in information theory for characterizing the feedback capacity and error exponent. This paper studies a more general variant of such channels where the state evolves via a general stochastic process, not necessarily Markov or ergodic. The states are assumed to be unknown to the transmitter and the receiver, but the underlying probability distributions are known. For this setup, we derive an upper bound on the feedback error exponent and the feedback capacity with variable-length codes. The bounds are expressed in terms of the directed mutual information and directed relative entropy. The bounds on the error exponent are simplified to Burnashev's expression for discrete memoryless channels. Our method relies on tools from the theory of martingales to analyze a stochastic process defined based on the entropy of the message given the past channel's outputs.
