二维多态联合概率分布及信息传输理论研究

Two Dimensional Joint Probability Distribution of Multi-states and the Research on the Information Transfers

根据不相关性与独立的等价概念,给出了有限离散随机变量的二维联合概率分布的一种描述方法。将两点值的情况推广到多点离散值的情况,当给出两个随机变量的边缘分布及合适的有限阶幂互协方差函数(或高阶相关系数)时,可得两维联合概率分布列,使两个随机变量的不相关性与独立性有一系统地描述和一个完整的表达形式。经过仿真验证了此方法的有效性。将得到的表示形式应用在数据信道通信的分析中,用信道两端的相关系数来描述输入输出的信息耦合,对信息理论是一个很好的补充。该方法与信息论中的平均互信息、数据处理定理相对应,得到非常美观的公式及非常理想的特性。

According to the theory that the independence is equivalent to the uncorrelation, a description of joint probability distribution of finite discrete random variable is found. Through extending the values of two - state to that of multi - state, when two random variables＇ marginal distributions and right high steps correlative coefficients are given, two dimensional joint probability row can be got to make independence and uncorrelation have an integrated description and expressive form.. This method is verified through simulations. By the way, the expression obtained is applied to the analysis of data channel communications. The in - out information coupling is described by channel＇s port correlative coefficients, which is a fine supplement to the information theory. This method is corresponding with information theory＇s average mutual information and data processing theorem, and a perfect formula and ideal characteristics are obtained.