PDF-IEEETRANSACTIONSONINFORMATIONTHEORY,VOL.47,NO.2,FEBRUARY2001ZigzagCode

Author : natalia-silvester | Published Date : 2015-12-11

concatenatedzigzagcodewithfourconstituentencoderswithinterleaverlength65536yieldsabiterrorrateBERof at09dBand14dBawayfromtheShannonlimitbyoptimalAPPandlowcostsuboptimalMLAdecodersrespective

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IEEETRANSACTIONSONINFORMATIONTHEORY,VOL.47,NO.2,FEBRUARY2001ZigzagCode: Transcript

concatenatedzigzagcodewithfourconstituentencoderswithinterleaverlength65536yieldsabiterrorrateBERof at09dBand14dBawayfromtheShannonlimitbyoptimalAPPandlowcostsuboptimalMLAdecodersrespective. loglog log(5)istheshiftoperator,(,foreach.Theactionofonthefunctionisgivenby):=denotesshift-invariantprobabilitymeasures.Forwede (thetotalnumberofusers)andlength .Wepresentbinaryfingerprintingcodessecureagainstsize- tionswhichenablethedistributor(decoder)torecoveratleastoneoftheusersfromthecoalitionwithprobabilityoferrorexp( fo single-antennareceiversand antennasatthetransmitteriscon-sidered.Bothtransmitterandreceivershaveperfectknowledgeofthechannel.Despiteitsapparentsimplicity,thismodelis,ingeneral,anondegradedbroadcastcha ontheminimumdistance.Forthesecodes,asoft-decision,reliability-based,linear-timedecodingalgorithmisintroduced,thatcorrectsanyfractionoferrorsuptoalmost .Forthebinary-symmetricchannel,thisalgorithm 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 TROPPetal.:DESIGNINGSTRUCTUREDTIGHTFRAMESVIAANALTERNATINGPROJECTIONMETHOD189Notethatthereisamajorconceptualdifferencebetweentheuseofnitemodelsinthenumericalcalculationofinmensionalframesandthedesignof X Thisinformationstructureissaidtobe[14],[15]and(asexplainedin[13])appearstobetheonlyinformationstructurethatleadstoatractabledetectionproblem.However,itispossibletofindaminimaxsolutionunderrestrictio (1)where isaknownmatrixwithunit-normcolumns, asparsecoef IEEETRANSACTIONSONINFORMATIONTHEORY,VOL.48,NO.6,JUNE2002formabasisforscheduling.Thechanneltrackingisdoneviaasinglepilotsignalwhichisrepeatedatthedifferenttransmitantennas,justlikethedata.Ifthemagnitud andanygivenrealnumber afamilyoflinearcodesofrate whichcanbeencodedintimeproportionalto timestheirblocklength .Furthermore,acodewordcanberecoveredwithhighprobabilityfromaportionofitsentriesoflength(1+ oftherandom matrix .Theprobabilityofarandomrotation(andscaling) of beingcollinearwith iszero.Usingasimilarargument,wecanshowthatmatrices and haveafullrankof almostsurelyandthereforereceivers2and3cande InterestsIambroadlyinterestedinTheoreticalComputerScienceandspeci28callyinCodingTheoryPseudo-randomnessComplexityTheoryandAdditiveCombinatoricsWork2018-2020PostdoctoralResearcherTheorygroupMicrosoftRe Vol.6(2009)1{33ISSN:1549-5787DOI: 10.1214/08-PS141 Asurveyofresultsfordeletionchannelsandrelatedsynchronizationchannels MichaelMitzenmacher y HarvardUniversity,SchoolofEngineeringandAppliedSciencese

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