数字电路互信息分析

Mutual information analysis for digital circuits

信息论是研究信息流通系统的有效工具,其信息熵表征了信息的不确定度,互信息表征了通信前后系统不确定度的减少量.通信中常用互信息来表征通信系统的处理能力,并且其与信道容量以及电路功率息息相关,因此本论文考虑利用信息论的观点分析数字电路.通过对电路抽象建模,将电路分为了对称信道、非对称信道、无反馈以及反馈电路4种模型.分别讨论了不同模型下,互信息的变化趋势以及影响因素,并证明出反馈对电路具有容错增益以及互信息增益.本文的分析方法适用于其他电路,且由于不涉及具体的电路形式,可以为之后的电路设计提供理论基础.

Information theory is an effective tool to study information flow systems. The information entropy is a measure of the average uncertainty in the random variable, and the mutual information is a measure of the dependence between two random variables. As the mutual information, which is often used to characterize the processing capability in the communication system, is closely related to the channel capacity and circuit power,we use the information theory to analyze the digital circuits in this paper. We discussed variation trend of mutual information and its influence factors for four typical circuit models, symmetric, asymmetric, feedback and nonfeedback circuits. We also proved that the circuit with feedback has fault tolerance and mutual information gain.The analysis method is suitable for other circuits, and it can provide a theoretical basis for circuit design.