PDF-IEEETRANSACTIONSONINFORMATIONTHEORY,VOL.49,NO.7,JULY2003OntheAchievabl

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singleantennareceiversand antennasatthetransmitterisconsideredBothtransmitterandreceivershaveperfectknowledgeofthechannelDespiteitsapparentsimplicitythismodelisingeneralanondegradedbroadcastcha

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IEEETRANSACTIONSONINFORMATIONTHEORY,VOL.49,NO.7,JULY2003OntheAchievabl: Transcript

singleantennareceiversand antennasatthetransmitterisconsideredBothtransmitterandreceivershaveperfectknowledgeofthechannelDespiteitsapparentsimplicitythismodelisingeneralanondegradedbroadcastcha. Fig.1.Sensornodesdeployedtomeasureambienttemperature.sensornetworks,thecomputationalpowerandenergyresourcesmaybeverylimited.Theseconstraintsmotivatethedesignofsimpledecentralizedalgorithmsforcomputati loglog log(5)istheshiftoperator,(,foreach.Theactionofonthefunctionisgivenby):=denotesshift-invariantprobabilitymeasures.Forwede -qubitquantumstatecouldbecommunicatedtoareceiverbyphysicallytransmittingonly + ( qubitsinadditiontoconsuming ebitsofentanglementandsomesharedrandomness.Whenthestatestobepreparedareentangled,we ,oneoffsetfromtheotherbyhalfastepsize.Thefirstquantizerindexissentonthefirstchannelandthesecondquantizerindexissentonthesecondchannel.Ifbothchannelswork,thedecoder whereasifonlyasinglechannelworks,the concatenatedzigzagcodewithfourconstituentencoderswithinterleaverlength65536,yieldsabiterrorrate(BER)of at0.9dBand1.4dBawayfromtheShannonlimitbyoptimal(APP)andlow-costsuboptimal(MLA)decoders,respective repeat 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 (1)where isaknownmatrixwithunit-normcolumns, asparsecoef ,atail-bitingtrellisthatminimizestheofstate-spacesizesamongallpos-siblelineartail-bitingtrellises.Wealsoprovethateverylineartail-bitingtrellisfor arisesfromacertain character-isticmatrix,andshowhowtoc 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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