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首页> 外文期刊>Information Theory, IEEE Transactions on >Directed Information, Causal Estimation, and Communication in Continuous Time
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Directed Information, Causal Estimation, and Communication in Continuous Time

机译：连续时间内的定向信息，因果估计和交流

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摘要

A notion of directed information between two continuous-time processes is proposed. A key component in the definition is taking an infimum over all possible partitions of the time interval, which plays a role no less significant than the supremum over “space” partitions inherent in the definition of mutual information. Properties and operational interpretations in estimation and communication are then established for the proposed notion of directed information. For the continuous-time additive white Gaussian noise channel, it is shown that Duncan's classical relationship between causal estimation error and mutual information continues to hold in the presence of feedback upon replacing mutual information by directed information. A parallel result is established for the Poisson channel. The utility of this relationship is demonstrated in computing the directed information rate between the input and output processes of a continuous-time Poisson channel with feedback, where the channel input process is constrained to be constant between events at the channel output. Finally, the capacity of a wide class of continuous-time channels with feedback is established via directed information, characterizing the fundamental limit on reliable communication.
机译：提出了两个连续时间过程之间的有向信息的概念。定义中的关键组成部分是对时间间隔的所有可能分区进行最小化，其作用不亚于互信息定义中固有的“空间”分区的最高部分。然后，针对拟议的定向信息概念建立了估计和通信中的属性和操作解释。对于连续时间加性高斯白噪声信道，证明了在有反馈替换有向信息后，在存在反馈的情况下，邓肯因果估计误差与互信息之间的经典关系继续成立。建立了泊松通道的并行结果。在计算具有反馈的连续时间Poisson通道的输入和输出过程之间的有向信息率时，证明了这种关系的效用，其中通道输入过程被约束为在通道输出事件之间是恒定的。最后，通过定向信息建立了具有反馈功能的各种连续时间信道的容量，这表征了可靠通信的基本限制。

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