[IEEE Trans. on Information Theory, March 1994, pp. 575-579]
Asymptotic Entropy Constrained Performance of
Tessellating and Universal Randomized Lattice Quantization
Tamás Linder and Kenneth Zeger
Abstract
Two results are given. First, using a result of Csiszár, the asymptotic
(i.e., high resolution/low distortion) performance for entropy constrained
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 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 low distortion performance of the Zamir-Feder
universal vector quantizer is asymptotically the same as that of the
deterministic lattice quantizer.