A rate of convergence result for a universal D-semifaithful code

The problem of optimal rate universal coding is considered in the context of rate-distortion theory. A D-semifaithful universal coding scheme for discrete memoryless sources is given. The main result is a refined covering lemma based on the random coding argument and the method of types. The average codelength of the code is shown to approach its lower bound, the rate-distortion function, at a rate O(n^-1log n), and this is conjectured to be optimal based on a result of A.J. Pilc (1968). Issues of constructiveness and universality are addressed