The Capacity and Ambiguity of a Transducer

Abstract

A particular noiseless, discrete channel with memory (called a transducer) is made to correspond to a function in the unit square by associating the infinite sequences of symbols of the transducer with the expansions of points in the unit interval. It is shown that the Hausdorff dimension of the set of points received over the transducer is equal to the transducer capacity. A definition of ambiguity is given which has a geometric interpretation in the square, and it is shown that the transducer has a homogeneity property by proving that the ambiguity is almost everywhere the same.