ASYMPTOTIC ENTROPY-CONSTRAINED PERFORMANCE OF TESSELLATING AND UNIVERSAL RANDOMIZED LATTICE QUANTIZATION

Two results are given. First, using a result of Csiszar, the asymptoti c (i.e., high-resolution/low distortion) performance for entropy-const rained tessellating vector quantization, heuristically derived by Gers ho, is proven for all sources with finite differential entropy. This i mplies, using Gersho's conjecture and Zador's formula, that tessellati ng vector quantizers are asymptotically optimal for this broad class o f sources, and generalizes a rigorous result of Gish and Pierce from t he scalar to the vector case. Second, the asymptotic performance is es tablished for Zamir and Feder's randomized lattice quantization. With the only assumption that the source has finite differential entropy, i t is proven that the low-distortion performance of the Zamir-Feder uni versal vector quantizer is asympotically the same as that of the deter ministic lattice quantizer.