GPS信息和限误差信息率与信息率失真及复杂性失真之间的关系

GPS Information and Rate-Tolerance and its Relationships with Rate Distortion and Complexity Distortions

在1993年发表的《广义信息论》中,提出限误差信息率(即信息率容差,rate-tolerance)并讨论了它和信息率失真之间的关系。文中用GPS作为例子推导出广义信息公式,并且通过数学分析和编码举例证明,得出结论:复杂性失真只是限误差信息率在限制集合由模糊变为清晰并呈球形时的特例;复杂性理论研究者肯定的复杂性失真和信息率失真之间的一般等价关系是不对的;一个信息率失真函数只能等价于一个特定的限误差信息率函数,两者都能用P(Y|X)=|P(Y|容许误差)时的广义互信息公式描述。度量GPS信息的公式和信息率失真函数表达式的相似性可以加深对广义信息测度的理解。

I proposed rate tolerance and- discussed its relation to rate distortion in my book ＂A Generalized Information Theory＂ published in 1993. Recently, examined the structure function and the complexity distortion based on Kol- mogorov＇s complexity theory. Now that complexity-distortion is only a special case of rate tolerance while constraint sets change from fuzzy sets into clear sets that look like balls with the same radius. It is not true that the complexity distortion is generally equivalent to rate distortion as claimed by the researchers of complexity theory. I conclude that a rate distortion function can only be equivalent to a rate tolerance function and both of them can be described by a generalized mutual information formula where P（ Y IX） is equal to P（ Y] Tolerance）. The paper uses GPS as an ex- ample to derive generalized information formulae and proves the above conclusions using mathematical analyses and a coding example. The similarity between the formula for measuring GPS information and the formula for rate distortion function can deepen our understanding the generalized information measure.