High-resolution source coding for non-difference distortion measures: the rate distortion function

The problem of asymptotic (i.e., low-distortion) behavior of the rate-distortion function of a random vector is investigated for a class of non-difference distortion measures. The main result is an asymptotically tight expression which parallels the Shannon lower bound for difference distortion measures. Applications include remote source coding and high resolution quantization theory for non-difference distortion measures.