FIXED-RATE UNIVERSAL LOSSY SOURCE-CODING AND RATES OF CONVERGENCE FORMEMORYLESS SOURCES

A fixed-rate universal lossy coding scheme is introduced for independe nt and identically distributed (i.i.d.) sources, It is shown for finit e alphabet sources and arbitrary single letter distortion measures tha t as the sample size n grows the expected distortion obtained using th is universal scheme converges to Shannon's distortion rate function D( R) at a rate O (log n/n). The scheme can be extended to universal quan tization of real i.i.d sources subject to a squared error criterion, I t is shown in this case that the per-letter distortion converges to D( R) at a rate O(root log n/n) both in expectation and almost surely for any real-valued bounded i.i.d. source.