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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orylessGaussiansourcewithasquared-errordistortionmeasure.Theproblemofmultipledescriptionquantizerdesign,includingaformulationandsolutionoftheunderlyinglabelingprobleminonedimension,waspresentedin[26].Anasymptoticperformanceanalysisofthisquantizerwaspresentedin[4].Apreliminaryversionoftheworkpresentedherewas rstpresentedin[25].

Latticequantizers(forthesingledescriptionproblem)havebeenextensivelystudied.In[31]arandomquantizationargumentisusedtogiveupperandlowerboundsontheperformanceofquantizersfora xeddimension.DetaileddescriptionsoftheVoronoiregionsofspeci clatticesaregivenin[9]andtheirsecondmomentsareevaluated.Fastquantizingalgorithmsforlatticequantizersaregivenin[10],[1],[14],[30].In[15]itisconjecturedthatforrthpowerdi erencedistortionmeasures,anyoptimalquantizer,inanydimension,hasVoronoiregionsthatarecongruenttosomepolytope.

Approachestomultipledescriptioncodingbasedontrelliscodedquantizationarepre-sentedin[28,20],thosebasedonvectorquantizationarepresentedin[13]andapproachesusingforwarderrorcorrectionarepresentedin[22].

Therearealsoapproachestomultipledescriptioncodingbasedonsubspacemethods.Oneapproachistodesignapredictororatransformsoastoachieveacorrelationstructurethatallowsonehalfofthepredictionerrorsamplesortransformcoe cientstobepredictedfromtheotherhalf.Examplesofthisapproacharepresentedin[19,23,29].

Anotherapproachtomultipledescriptioncodingisbasedonusingovercompleteexpan-sions.Heretheideaistoconstructaredundantsignalrepresentation,inawaythatallowsthesignaltobeestimatedwithacontrolledamountoferrorwhentherepresentationisincompletelyreceived[3,7,17].