PDF-IEEETRANSACTIONSONINFORMATIONTHEORY,VOL.53,NO.1,JANUARY2007LPDecodingC

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IEEETRANSACTIONSONINFORMATIONTHEORY,VOL.53,NO.1,JANUARY2007LPDecodingC: Transcript

repeat. withthefollowingstructuralproperties:1)eachrowconsistsof “ones”;2)eachcolumnconsistsof “ones”;3)thenumberof“ones”incommonbetweenanytwocolumns, ,isnogreaterthan ;4)both an 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 VOL. XXXIV—NO. 2 2013 VOL. XXXIV—NO. 2 2013 VOL. XXXIV—NO. 2 2013 VOL. XXXIV—NO. 2 2013 LETTERS CONSCIENCE VOL. XXXIV—NO. 2 2013 LETTERS CONSCIENCE VOL. XXXIV—NO. 2 ;inthissimplesetuptheTCis (1)where isthexeddistancebetweeneachtransmitterreceiverpairand isthepath-lossexponent.Notethat unitsofexpectednumberofsuccessfultransmissionsperunitRelationshiptoTransportCap Fig.1.Sensornodesdeployedtomeasureambienttemperature.sensornetworks,thecomputationalpowerandenergyresourcesmaybeverylimited.Theseconstraintsmotivatethedesignofsimpledecentralizedalgorithmsforcomputati 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.Sensornodesdeployedtomeasureambienttemperature.sensornetworks,thecomputationalpowerandenergyresourcesmaybeverylimited.Theseconstraintsmotivatethedesignofsimpledecentralizedalgorithmsforcomputati =min( transmitantennas,where isthenumberofreceiveantennasand isthelengthofthecoherenceinterval,whereasatlowSNR,themutualinformationismaximizedbyallocatingalltransmitpowertoasingleantenna.IndexTerms oftherandom matrix .Theprobabilityofarandomrotation(andscaling) of beingcollinearwith iszero.Usingasimilarargument,wecanshowthatmatrices and haveafullrankof almostsurelyandthereforereceivers2and3cande

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