Universal quantization of parametric sources has redundancy k/2 logn/n
Philip A. Chou, Michelle Effros, Robert M. Gray · 2002
Let {X/sub i/}/spl sim/P/sub /spl theta//, /spl Theta//spl isin//spl Lambda//spl sube/IR/sup k/. Rissanen has shown that there exist universal noiseless codes for {Xi} with per-letter rate redundancy as low as k/2 logn/n, where n is the blocklength and k is the number of source parameters. We derive an analogous result for universal quantization: for any given La-grange multiplier /spl lambda/>0, there exist universal fixed-rate and variable-rate quantizers with per-letter Lagrangian redundancy (i.e., distortion redundancy plus /spl lambda/ times the rate redundancy) as low as /spl lambda/k/2 logn/n.