广义熵和广义互信息的编码意义

本文首先简要介绍了作者早时修想出的预测熵,广义熵和广义互信息,然后讨论了预测熵,广义熵和广义互信息的编码意义,定义了限误差信息率Ｒ（ＡＪ）,证明广义熵是给定误差限广义信息量Ｉ（ｘｉ;ｙｊ）代替经典理论中失真量ｄ（ｘｉ,ｙｊ）,从而把信息率失真论改造为保精度信息率论。文中同时提供了推导出的二元相似信源的保精度信息率函数,和上机计算出的以图像视觉为例的多元相似信源保精度信息率函数Ｒ（Ｇ）,并提供了Ｒ（

Meanings of Generalized Entropy and Generalized Mutual Information for Coding

This paper first simply introduces predictive entropy, generalized entropy, and generalized mutual information proposed by the author earlier,then discusses the coding meanings of predictive entropy, generalized entropy and generalized mutual information, defines "rate-of-limitingerrors" function R(AJ) , proves that the generalized entropy is the minimum of the Shannon mutual information under some given error-limiting, and explains the relationship between the generalized entropy, the rate-of-limiting-errors and rate-distortion. Replacing the distortion d (xi, yj)with the generalized information I(xi ;yj) ,we have the rate-of-keeping-precision theory, a revised version of the rate-distortion theory. Meanwhile, the paper provides the derived function R(G) of a binary source with a similarity relation, gives the function R(G) , which is calculated out on the computer, of a multiple source for visual information of image; and shows pictorially the relations between function R(G) , quantizing grades of a pixel, and subjective discrimination with fuzziness.The rate-of-keeping-precision theory is not only a theory for data compression, but also a theory for optimal matching between objective information and subjective understanding.