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

3ORGANIZATIONOFTHEPAPER7

3OrganizationofthePaper

Themultipledescriptionvectorquantizerisdescribed,notationisestablished,certainreg-ularityassumptionsforthelabelingfunctionarestatedandpreliminaryexpressionsarederivedforratesanddistortionsinSection4.Adetailedexamplewiththetwo-dimensionalhexagonallatticeA2ispresentedalongwithsomegeneraltheoryinSection5.ThenecessarytheoryforgenerallatticesispresentedinSection6.Anasymptoticanalysisfora xedvectordimensionispresentedinSection7.ThepaperissummarizedalongwithconclusionsanddirectionsforfutureworkinSection8.

4Preliminaries

Ablockdiagramofamultipledescriptionvectorquantizer(MDVQ)withalatticecodebookisshowninFig.2.

Channel1Decoder

λ′1

Source

Q

λ′1

λ

α

α

λ′2

λ

Decoder

Channel2

Decoder

λ′2

Figure2:Blockdiagramforamultipledescriptionvectorquantizer.

Asourceofinformationgeneratesasequenceofindependent,identicallydistributedrandomvariableswithprobabilitydensityfunction(pdf)p.Thissourceisblockedo intoL-dimensionalvectorsx=(x1,x2,...,xL).TheL-foldpdfisdenotedbypL,wherepL(x)= L

RL.Wedenotei=1p(xi).ThevectorxisquantizedtothenearestvectorλinalatticeΛ I