PDF-IEEETRANSACTIONSONINFORMATIONTHEORY,VOL.46,NO.7,NOVEMBER2000TheAnalysi
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oneoffsetfromtheotherbyhalfastepsizeThefirstquantizerindexissentonthefirstchannelandthesecondquantizerindexissentonthesecondchannelIfbothchannelsworkthedecoder whereasifonlyasinglechannelworksthe
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IEEETRANSACTIONSONINFORMATIONTHEORY,VOL.46,NO.7,NOVEMBER2000TheAnalysi: Transcript
oneoffsetfromtheotherbyhalfastepsizeThefirstquantizerindexissentonthefirstchannelandthesecondquantizerindexissentonthesecondchannelIfbothchannelsworkthedecoder whereasifonlyasinglechannelworksthe. withthefollowingstructuralproperties:1)eachrowconsistsof ones;2)eachcolumnconsistsof ones;3)thenumberofonesincommonbetweenanytwocolumns, ,isnogreaterthan ;4)both an loglog log(5)istheshiftoperator,(,foreach.Theactionofonthefunctionisgivenby):=denotesshift-invariantprobabilitymeasures.Forwede (thetotalnumberofusers)andlength .Wepresentbinaryfingerprintingcodessecureagainstsize- tionswhichenablethedistributor(decoder)torecoveratleastoneoftheusersfromthecoalitionwithprobabilityoferrorexp( fo ontheminimumdistance.Forthesecodes,asoft-decision,reliability-based,linear-timedecodingalgorithmisintroduced,thatcorrectsanyfractionoferrorsuptoalmost .Forthebinary-symmetricchannel,thisalgorithm VOL. XXXIVNO. 2 2013 VOL. XXXIVNO. 2 2013 VOL. XXXIVNO. 2 2013 VOL. XXXIVNO. 2 2013 LETTERS CONSCIENCE VOL. XXXIVNO. 2 2013 LETTERS CONSCIENCE VOL. XXXIVNO. 2 -regularLDPCcode,forexample,thecomplexityofencodingisessentiallyquadraticintheblocklength.However,we 100000isstillquitepractical.Moreimportantly,wewillshowthatoptimizedcodesactuallyadmitli TROPPetal.:DESIGNINGSTRUCTUREDTIGHTFRAMESVIAANALTERNATINGPROJECTIONMETHOD189Notethatthereisamajorconceptualdifferencebetweentheuseofnitemodelsinthenumericalcalculationofinmensionalframesandthedesignof Fig.1.Two-userGaussianinterferencechannel.basicinformationtheorymodeltostudythisquestionisthetwo-userGaussianinterferencechannel,wheretwopoint-to-point Authorized licensed use limited to: Hewlett-Pack X Thisinformationstructureissaidtobe[14],[15]and(asexplainedin[13])appearstobetheonlyinformationstructurethatleadstoatractabledetectionproblem.However,itispossibletofindaminimaxsolutionunderrestrictio (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 InterestsIambroadlyinterestedinTheoreticalComputerScienceandspeci28callyinCodingTheoryPseudo-randomnessComplexityTheoryandAdditiveCombinatoricsWork2018-2020PostdoctoralResearcherTheorygroupMicrosoftRe
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