PDF-IEEETRANSACTIONSONINFORMATIONTHEORY,VOL.49,NO.9,SEPTEMBER2003TheStruct

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atailbitingtrellisthatminimizestheofstatespacesizesamongallpossiblelineartailbitingtrellisesWealsoprovethateverylineartailbitingtrellisfor arisesfromacertain characteristicmatrixandshowhowtoc

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IEEETRANSACTIONSONINFORMATIONTHEORY,VOL.49,NO.9,SEPTEMBER2003TheStruct: Transcript

atailbitingtrellisthatminimizestheofstatespacesizesamongallpossiblelineartailbitingtrellisesWealsoprovethateverylineartailbitingtrellisfor arisesfromacertain characteristicmatrixandshowhowtoc. withthefollowingstructuralproperties:1)eachrowconsistsof “ones”;2)eachcolumnconsistsof “ones”;3)thenumberof“ones”incommonbetweenanytwocolumns, ,isnogreaterthan ;4)both an Fig.1.Sensornodesdeployedtomeasureambienttemperature.sensornetworks,thecomputationalpowerandenergyresourcesmaybeverylimited.Theseconstraintsmotivatethedesignofsimpledecentralizedalgorithmsforcomputati loglog log(5)istheshiftoperator,(,foreach.Theactionofonthefunctionisgivenby):=denotesshift-invariantprobabilitymeasures.Forwede -qubitquantumstatecouldbecommunicatedtoareceiverbyphysicallytransmittingonly + ( qubitsinadditiontoconsuming ebitsofentanglementandsomesharedrandomness.Whenthestatestobepreparedareentangled,we (thetotalnumberofusers)andlength .Wepresentbinaryfingerprintingcodessecureagainstsize- tionswhichenablethedistributor(decoder)torecoveratleastoneoftheusersfromthecoalitionwithprobabilityoferrorexp( fo concatenatedzigzagcodewithfourconstituentencoderswithinterleaverlength65536,yieldsabiterrorrate(BER)of at0.9dBand1.4dBawayfromtheShannonlimitbyoptimal(APP)andlow-costsuboptimal(MLA)decoders,respective single-antennareceiversand antennasatthetransmitteriscon-sidered.Bothtransmitterandreceivershaveperfectknowledgeofthechannel.Despiteitsapparentsimplicity,thismodelis,ingeneral,anondegradedbroadcastcha right-handsideof(44) jDj (p2)n+p2 l rrArrr(p) r h(l) )=(+1) s=0rss(p+1) =1 jDj (p2)n+p2 l=0 rrrArrr(p)n =1 1)(andtheassertionofthelemmafollows. [1]A.AshikhminandS.Litsyn,“Upperboundsofthesi -regularLDPCcode,forexample,thecomplexityofencodingisessentiallyquadraticintheblocklength.However,we 100000isstillquitepractical.Moreimportantly,wewillshowthat“optimized”codesactuallyadmitli Fig.1.Two-userGaussianinterferencechannel.basicinformationtheorymodeltostudythisquestionisthetwo-userGaussianinterferencechannel,wheretwopoint-to-point Authorized licensed use limited to: Hewlett-Pack =min( transmitantennas,where isthenumberofreceiveantennasand isthelengthofthecoherenceinterval,whereasatlowSNR,themutualinformationismaximizedbyallocatingalltransmitpowertoasingleantenna.IndexTerms ,user ndsthetwocodewordscorrespondingtocomponents andalsouniformlychoosesacodeword from .User thenaddsallthesecodewordsandtransmitstheresultingcodeword ,sothatitactuallytransmitsoneof codewords.Let No andanygivenrealnumber afamilyoflinearcodesofrate whichcanbeencodedintimeproportionalto timestheirblocklength .Furthermore,acodewordcanberecoveredwithhighprobabilityfromaportionofitsentriesoflength(1+ Vol.6(2009)1{33ISSN:1549-5787DOI: 10.1214/08-PS141 Asurveyofresultsfordeletionchannelsandrelatedsynchronizationchannels MichaelMitzenmacher y HarvardUniversity,SchoolofEngineeringandAppliedSciencese

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