A fixed-rate block code is said to be strongly robust for a class of sources\Lambdaif its maximum distortion over\Lambdah is no larger than the maximum of the distortion-rate functions of the sources in the class at the rate of the code. It is shown that such codes exist at all positive rates whenever the class is compact with resect to the topology of weak convergence and satisfies certain additional, but not very strong, constraints on the alphabet and distortion measure. Examples of classes that satisfy these conditions are given. In addition, classes are exhibited for which there are no strongly robust codes. These help to demarcate the boundary between classes for which strongly robust codes do and do not exist. More specifically, they show that strongly robust codes exist more widely than strongly universal codes but !ess widely than weakly universal codes.

The following problem in universal source coding is explored. Some members of a class of sources have various constraints on the maximum rate at which they may be encoded, and thc remainder have various constraints on the maximum distortion that may result from encoding. It is desired to find a universal code that will adapt its performance so that whatever source in the class is encoded, the resulting performance meets the constraint and is optimal in the rate-distortion function sense for that particular source. It is shown that such codes exist when the class is totally bounded and the constraints are uniformly continuous in an appropriate sense. A key result shows that the value of any uniformly continuous function on a totally bounded class can be uniformly well estimated from observations of the output of any source in