Abstract The problem of designing a multiple description vector quantizer with lattice codebook \Lambda is considered. A general solution is given to a labeling problem which plays a crucial role in the design of such quantizers. Numerical performance resu

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0d¯0(R,1)andFigure1:R→∞¯s(R,L)/d¯1(R,1)asafunctionofthelatticedimensionL.Thereductionintwo-channellimR→∞d

distortionislatticedependentandisdeterminedbythenormalizedsecondmomentofaVoronoiregionofthelattice.Thereductioninsingle-channeldistortiondependsonlyonthedimensionofthelattice.

RforanL-dimensionalquantizer.Fig.1summarizesthemainresultsofthepaper.Inthis gurewehaveplottedthelimitofthenormalizedtwo-channelandsingle-channeldis-¯0(R,L)/d¯0(R,1)andlimR→∞d¯s(R,L)/d¯s(R,1)respectively,forlatticesoftortions,limR→∞d

variousdimensions.Itisseenthatthelimitforthetwo-channeldistortionisgivenbytheratioG(Λ)/G(),whichdependsonthelattice,whereasforthesidedistortionthelimitis

G(SL)/G(S1),whichisindependentofthelattice.

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Anachievablerateregionforthemultipledescriptionproblemwas rstgivenin[12]anditwasshownin[24]thatthisregioncoincideswiththeratedistortionregionforamem-