A generalization of the Pursley-Davisson- Mackenthun universal variable-rate coding theorem

Suppose nature selects a source from among a class of sources according to some prior probability distribution. With respect to a given fidelity criterion and a given distortion level, it is shown that there exists a variable-rate code such that the following is true. It is highly likely that nature will choose a source whose average distortion with respect to the given code achieves the given distortion level and whose average rate is approximately the optimum rate theoretically attainable. Only a very weak assumption has to be made. The assumption is satisfied, for example, for separable metric space alphabets and a distortion measure which is a nondecreasing continuous function of the metric. This generalizes work of Pursley, Davisson, and Mackenthun and settles a conjecture of Pursley and Davisson.