PDF-IEEETRANSACTIONSONINFORMATIONTHEORY,VOL.52,NO.6,JUNE2006RandomizedGoss

Author : conchita-marotz | Published Date : 2016-04-20

Fig1SensornodesdeployedtomeasureambienttemperaturesensornetworksthecomputationalpowerandenergyresourcesmaybeverylimitedTheseconstraintsmotivatethedesignofsimpledecentralizedalgorithmsforcomputati

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IEEETRANSACTIONSONINFORMATIONTHEORY,VOL.52,NO.6,JUNE2006RandomizedGoss: Transcript

Fig1SensornodesdeployedtomeasureambienttemperaturesensornetworksthecomputationalpowerandenergyresourcesmaybeverylimitedTheseconstraintsmotivatethedesignofsimpledecentralizedalgorithmsforcomputati. withthefollowingstructuralproperties:1)eachrowconsistsof “ones”;2)eachcolumnconsistsof “ones”;3)thenumberof“ones”incommonbetweenanytwocolumns, ,isnogreaterthan ;4)both an loglog log(5)istheshiftoperator,(,foreach.Theactionofonthefunctionisgivenby):=denotesshift-invariantprobabilitymeasures.Forwede (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 repeat Fig.1.Sensornodesdeployedtomeasureambienttemperature.sensornetworks,thecomputationalpowerandenergyresourcesmaybeverylimited.Theseconstraintsmotivatethedesignofsimpledecentralizedalgorithmsforcomputati 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 andanygivenrealnumber afamilyoflinearcodesofrate whichcanbeencodedintimeproportionalto timestheirblocklength .Furthermore,acodewordcanberecoveredwithhighprobabilityfromaportionofitsentriesoflength(1+ oftherandom matrix .Theprobabilityofarandomrotation(andscaling) of beingcollinearwith iszero.Usingasimilarargument,wecanshowthatmatrices and haveafullrankof almostsurelyandthereforereceivers2and3cande

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