T. Linder et K. Zeger, ASYMPTOTIC ENTROPY-CONSTRAINED PERFORMANCE OF TESSELLATING AND UNIVERSAL RANDOMIZED LATTICE QUANTIZATION, IEEE transactions on information theory, 40(2), 1994, pp. 575-579
Citations number
15
Categorie Soggetti
Information Science & Library Science","Engineering, Eletrical & Electronic
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.