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

4PRELIMINARIES

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Figure3:This gureshowsaportionoftheA2lattice(thepointsonthegridlineinter-sections),partofageometricallysimilarsublatticeofindex31,adiscreteVoronoisetforasublatticepoint(thelatticepointsinthehexagon)andtheVoronoisetofasublatticepoint(allthepointsinthehexagon).

equivalently,thedirectededgeis(λ′a,λ′b).Thetwodirectedversionsofan(undirected)edge

→ .ewillbedenoted eand←eForagivenlabelingfunctionα,anassociatedundirectededgelabelingfunctionαuis

→de nedasfollows:ifα(λ)= e,thenαu(λ)=e,i.e.,αumapsλtoitsundirectedlabel.

→ ,thenα(λ)=α(λ)=e,i.e.,αisnotone-to-one.Notethatifα(λ)= eandα(λ)=←e

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Adirectededgeisuniquelyassociatedwithalatticepointwhereasanundirectededgewillingeneralbeassociatedwithtwolatticepoints,oneforeachorientationoftheedge.The