PDF-IEEETRANSACTIONSONINFORMATIONTHEORY,VOL.47,NO.7,NOVEMBER2001Low-Densit

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withthefollowingstructuralproperties1eachrowconsistsof 147ones1482eachcolumnconsistsof 147ones1483thenumberof147ones148incommonbetweenanytwocolumns isnogreaterthan 4both an

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IEEETRANSACTIONSONINFORMATIONTHEORY,VOL.47,NO.7,NOVEMBER2001Low-Densit: Transcript

withthefollowingstructuralproperties1eachrowconsistsof 147ones1482eachcolumnconsistsof 147ones1483thenumberof147ones148incommonbetweenanytwocolumns isnogreaterthan 4both an. If drops quic kly with then pro cess hanges quic kly with time its time samples ecome uncorrelated er short erio of time Con ersely when drops slo wly with samples are highly correlated er long time Th us is measure of the rate of hange of with time Fig.1.Sensornodesdeployedtomeasureambienttemperature.sensornetworks,thecomputationalpowerandenergyresourcesmaybeverylimited.Theseconstraintsmotivatethedesignofsimpledecentralizedalgorithmsforcomputati (thetotalnumberofusers)andlength .Wepresentbinaryfingerprintingcodessecureagainstsize- tionswhichenablethedistributor(decoder)torecoveratleastoneoftheusersfromthecoalitionwithprobabilityoferrorexp( fo ;inthissimplesetuptheTCis (1)where isthexeddistancebetweeneachtransmitterreceiverpairand isthepath-lossexponent.Notethat unitsofexpectednumberofsuccessfultransmissionsperunitRelationshiptoTransportCap 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 Foranyoddprime,similarconditionssuchthat-arybentweregivenin[7],[12],andsomeresultswere 2i=1cix1+2iZ2 etal.:NEWCONSTRUCTIONSOFQUADRATICBENTFUNCTIONSINPOLYNOMIALFORM5761Further,byvirtueofthelinksbetw AAPPMA de Tarare. 15 janvier 2012. Fédération du Rhône pour la Pêche et la Protection du Milieu Aquatique. Pierre GACON – Chargé d’études. Quelques informations sur l’opération de « . re. -regularLDPCcode,forexample,thecomplexityofencodingisessentiallyquadraticintheblocklength.However,we 100000isstillquitepractical.Moreimportantly,wewillshowthat“optimized”codesactuallyadmitli TROPPetal.:DESIGNINGSTRUCTUREDTIGHTFRAMESVIAANALTERNATINGPROJECTIONMETHOD189Notethatthereisamajorconceptualdifferencebetweentheuseofnitemodelsinthenumericalcalculationofinmensionalframesandthedesignof Fig.1.Sensornodesdeployedtomeasureambienttemperature.sensornetworks,thecomputationalpowerandenergyresourcesmaybeverylimited.Theseconstraintsmotivatethedesignofsimpledecentralizedalgorithmsforcomputati (1)where isaknownmatrixwithunit-normcolumns, asparsecoef ,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+

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