Asymptotic Performance of Multiple Description Lattice Quantizers

by

Vinay A. Vaishampayan, N. J. A. Sloane
Information Sciences Research
AT&T Shannon Lab
Florham Park, NJ 07932-0971 USA
and
Sergio D. Servetto
Ecole Polytechnique F'{e}d'{e}rale de Lausanne
CH-1015 Lausanne, Switzerland

Abstract
The high-rate squared-error distortions of a balanced multiple 
description lattice vector quantizer are analyzed for a memoryless
source with probability density function p, differential entropy
h(p) < infty, and lattice codebook Lambda. 

For any a in (0,1) and rate pair (R,R), it is shown that the
two-channel distortion d_0 and the channel 1 (or channel 2)
distortions d_s satisfy 

lim_{R -> infty} d_0 2^(2R(1+a)) = (1/4) G(Lambda) 2^{2h(p)}

and

lim_{R -> infty} d_s 2^(2R(1-a)) = G(S_L) 2^2h(p),

where G(Lambda) is the normalized second moment of a Voronoi
cell of the lattice Lambda and G(S_L) is the normalized second
moment of a sphere in L dimensions.



This paper was published (in a somewhat different form) in
Proceedings ISIT-2000 (Sorrento 2000), IEEE Information Theory Society, 2000, p. 175.


For the full version see
http://NeilSloane.com/doc/sorrento.pdf (pdf) or
http://NeilSloane.com/doc/sorrento.ps (ps)