Asymptotic entropy-constrained performance of tessellating and universal randomized lattice quantization

TWO resuhs are given. First, using a result of Csiszlr, the asymptotic (i.e., high-resolution/Iow distortion) performance for entropyconstrained tessellating vector quantization, heuristically derived by Gersho, is proven for all sources with finite differential entropy. This implies, using Gersho’s conjecture and Zador’s formula, that tessellating vector quantizers are asymptotically optimal for this broad class of sources, and generalizes a rigorous result of Gish and Pierce from the scalar to the vector case. Second, the asymptotic performance is established for Zamir and Feder’s randomized lattice quantization. With the only assumption that the source has finite differential entropy, it is proven that the lowdistortion performance of the Zamir-Feder universal vector quantizer is asympotically the same as that of the deterministic lattice quantizer.