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I proposed rate tolerance and discussed its relation to rate distortion in mybook "A Generalized Information Theory" published in 1993. Recently, I examinedthe structure function and the complexity distortion based on Kolmogorov'scomplexity theory. It is my understanding now that complexity-distortion isonly a special case of rate tolerance while constraint sets change from fuzzysets into clear sets that look like balls with the same radius. It is not truethat the complexity distortion is generally equivalent to rate distortion asclaimed by the researchers of complexity theory. I conclude that a ratedistortion function can only be equivalent to a rate tolerance function andboth of them can be described by a generalized mutual information formula whereP(Y|X) is equal to P(Y|Tolerance). The paper uses GPS as an example to derivegeneralized information formulae and proves the above conclusions usingmathematical analyses and a coding example. The similarity between the formulafor measuring GPS information and the formula for rate distortion function candeepen our understanding the generalized information measure.

GPS Information and Rate Tolerance - Clarifying Relationship between Rate Distortion and Complexity Distortion