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

MultipleDescriptionVectorQuantizationwithLattice

Codebooks:DesignandAnalysis

VinayA.Vaishampayan,N.J.A.Sloane

AT&TShannonLaboratoryFlorhamPark,NJ07932

and

SergioD.Servetto

EcolePolytechniqueF´ed´eraledeLausanne,CH-1015Lausanne,Switzerland

Jan.25,2000;revisedOct.7,2000

Abstract

TheproblemofdesigningamultipledescriptionvectorquantizerwithlatticecodebookΛ

isconsidered.Ageneralsolutionisgiventoalabelingproblemwhichplaysacrucialroleinthedesignofsuchquantizers.NumericalperformanceresultsareobtainedforquantizersbasedonthelatticesA2andi,i=1,2,4,8,thatmakeuseofthislabelingalgorithm.

Thehigh-ratesquared-errordistortionsforthisfamilyofL-dimensionalvectorquantizersarethenanalyzedforamemorylesssourcewithprobabilitydensityfunctionpanddi erentialentropyh(p)<∞.Foranya∈(0,1)andratepair(R,R),itisshownthatthetwo-channel

¯0andthechannel1(orchannel2)distortiond¯ssatisfydistortiond

R→∞

¯022R(1+a)=1limd