PDF-IEEETRANSACTIONSONINFORMATIONTHEORY,VOL.49,NO.4,APRIL2003DigitalFinger

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thetotalnumberofusersandlength Wepresentbinaryfingerprintingcodessecureagainstsize tionswhichenablethedistributordecodertorecoveratleastoneoftheusersfromthecoalitionwithprobabilityoferrorexp fo

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IEEETRANSACTIONSONINFORMATIONTHEORY,VOL.49,NO.4,APRIL2003DigitalFinger: Transcript

thetotalnumberofusersandlength Wepresentbinaryfingerprintingcodessecureagainstsize tionswhichenablethedistributordecodertorecoveratleastoneoftheusersfromthecoalitionwithprobabilityoferrorexp fo. D.N.Ku,S.Glagov,J.E.MoorewPAbdominalAortaExperimencularSur,Vol.9,No.2,pp.309-315(1989).(1989).M.Lei,C.KleinstreuerandJ.P.Archie,\Hemo-dynamicSimulationsand,Vol.119,pp.343-348(1997).(1997).D.P.Giddens, ,oneoffsetfromtheotherbyhalfastepsize.Thefirstquantizerindexissentonthefirstchannelandthesecondquantizerindexissentonthesecondchannel.Ifbothchannelswork,thedecoder whereasifonlyasinglechannelworks,the concatenatedzigzagcodewithfourconstituentencoderswithinterleaverlength65536,yieldsabiterrorrate(BER)of at0.9dBand1.4dBawayfromtheShannonlimitbyoptimal(APP)andlow-costsuboptimal(MLA)decoders,respective single-antennareceiversand antennasatthetransmitteriscon-sidered.Bothtransmitterandreceivershaveperfectknowledgeofthechannel.Despiteitsapparentsimplicity,thismodelis,ingeneral,anondegradedbroadcastcha TROPPetal.:DESIGNINGSTRUCTUREDTIGHTFRAMESVIAANALTERNATINGPROJECTIONMETHOD189Notethatthereisamajorconceptualdifferencebetweentheuseofnitemodelsinthenumericalcalculationofinmensionalframesandthedesignof Fig.1.Two-userGaussianinterferencechannel.basicinformationtheorymodeltostudythisquestionisthetwo-userGaussianinterferencechannel,wheretwopoint-to-point Authorized licensed use limited to: Hewlett-Pack =min( transmitantennas,where isthenumberofreceiveantennasand isthelengthofthecoherenceinterval,whereasatlowSNR,themutualinformationismaximizedbyallocatingalltransmitpowertoasingleantenna.IndexTerms (1)where isaknownmatrixwithunit-normcolumns, asparsecoef ,atail-bitingtrellisthatminimizestheofstate-spacesizesamongallpos-siblelineartail-bitingtrellises.Wealsoprovethateverylineartail-bitingtrellisfor arisesfromacertain character-isticmatrix,andshowhowtoc GAFAGeometricAndFunctionalAnalysisISOPERIMETRYOFWAISTSANDCONCENTRATIONOFMAPSM.Gromov1WaistoftheSphereTheoremLetbeacontinuousmapwhereistheunit Vol()).Then( Vol.13,2003ISOPERIMETRYOFWAISTSANDCONCENTRATI ,user ndsthetwocodewordscorrespondingtocomponents andalsouniformlychoosesacodeword from .User thenaddsallthesecodewordsandtransmitstheresultingcodeword ,sothatitactuallytransmitsoneof codewords.Let No IEEETRANSACTIONSONINFORMATIONTHEORY,VOL.48,NO.6,JUNE2002formabasisforscheduling.Thechanneltrackingisdoneviaasinglepilotsignalwhichisrepeatedatthedifferenttransmitantennas,justlikethedata.Ifthemagnitud andanygivenrealnumber afamilyoflinearcodesofrate whichcanbeencodedintimeproportionalto timestheirblocklength .Furthermore,acodewordcanberecoveredwithhighprobabilityfromaportionofitsentriesoflength(1+ InterestsIambroadlyinterestedinTheoreticalComputerScienceandspeci28callyinCodingTheoryPseudo-randomnessComplexityTheoryandAdditiveCombinatoricsWork2018-2020PostdoctoralResearcherTheorygroupMicrosoftRe

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