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)</spl infin/, and lattice codebook /spl Lambda/. For any a/spl isin/(0,1) and rate pair (R,R), it is shown that the two-channel distortion d~/sub 0/ and the channel 1 (or channel 2) distortion d~/sub s/ satisfy lim/sub R/spl rarr//spl infin//d~/sub 0/2/sup 2R(1+a)/=G(/spl Lambda/)2/sup 2h(p)//4 and lim/sub R/spl rarr//spl infin//d~/sub s/2/sup 2R(1-a)/=G(S/sub L/)2/sup 2h(p)/ where G(/spl Lambda/) is the normalized second moment of a Voronoi cell of the lattice /spl Lambda/ and G(S/sub L/) is the normalized second moment of a sphere in L dimensions.

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