[IEEE Trans. on Information Theory, March 1999, pp. 548-561]
High-Resolution Source Coding for Non-Difference Distortion
Measures: Multidimensional Companding
Tamás Linder, Ram Zamir, and Kenneth Zeger
Abstract
Entropy coded vector quantization is studied using high resolution
multidimensional companding over a class of non-difference distortion
measures. For distortion measures which are ``locally quadratic'' a
rigorous derivation of the asymptotic distortion and entropy coded rate of
multidimensional companders is given along with conditions for the
optimal choice of the compressor function. Examples are shown for the
existence of optimal compressors. The rate distortion performance of
the companding scheme is studied using a recently obtained asymptotic
expression for the rate distortion function which parallels the
Shannon lower bound for difference distortion measures. It is proved
that the high resolution performance of the scheme is arbitrarily
close to the rate distortion limit for large quantizer dimensions if
the compressor function and the lattice quantizer used in the
companding scheme are optimal, extending an analogous statement for
entropy coded lattice quantization and MSE distortion. The companding
approach is applied to obtain a high resolution
quantizing scheme for noisy sources.