PDF-IEEETRANSACTIONSONINFORMATIONTHEORY,VOL.47,NO.7,NOVEMBER2001Substituti
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righthandsideof44 jDj p2np2 l rrArrrp r hl 1 s0rs sp1 1 jDj p2np2 l0 rrrArrrpn 1 1andtheassertionofthelemmafollows 1AAshikhminandSLitsyn147Upperboundsofthesi
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IEEETRANSACTIONSONINFORMATIONTHEORY,VOL.47,NO.7,NOVEMBER2001Substituti: Transcript
righthandsideof44 jDj p2np2 l rrArrrp r hl 1 s0rs sp1 1 jDj p2np2 l0 rrrArrrpn 1 1andtheassertionofthelemmafollows 1AAshikhminandSLitsyn147Upperboundsofthesi. Fig.1.Sensornodesdeployedtomeasureambienttemperature.sensornetworks,thecomputationalpowerandenergyresourcesmaybeverylimited.Theseconstraintsmotivatethedesignofsimpledecentralizedalgorithmsforcomputati D.N.Ku,S.Glagov,J.E.MoorewPAbdominalAortaExperimencularSur,Vol.9,No.2,pp.309-315(1989).(1989).M.Lei,C.KleinstreuerandJ.P.Archie,\Hemo-dynamicSimulationsand,Vol.119,pp.343-348(1997).(1997).D.P.Giddens, ,oneoffsetfromtheotherbyhalfastepsize.Thefirstquantizerindexissentonthefirstchannelandthesecondquantizerindexissentonthesecondchannel.Ifbothchannelswork,thedecoder whereasifonlyasinglechannelworks,the concatenatedzigzagcodewithfourconstituentencoderswithinterleaverlength65536,yieldsabiterrorrate(BER)of at0.9dBand1.4dBawayfromtheShannonlimitbyoptimal(APP)andlow-costsuboptimal(MLA)decoders,respective 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 Foranyoddprime,similarconditionssuchthat-arybentweregivenin[7],[12],andsomeresultswere 2i=1cix1+2iZ2 etal.:NEWCONSTRUCTIONSOFQUADRATICBENTFUNCTIONSINPOLYNOMIALFORM5761Further,byvirtueofthelinksbetw TROPPetal.:DESIGNINGSTRUCTUREDTIGHTFRAMESVIAANALTERNATINGPROJECTIONMETHOD189Notethatthereisamajorconceptualdifferencebetweentheuseofnitemodelsinthenumericalcalculationofinmensionalframesandthedesignof Fig.1.Sensornodesdeployedtomeasureambienttemperature.sensornetworks,thecomputationalpowerandenergyresourcesmaybeverylimited.Theseconstraintsmotivatethedesignofsimpledecentralizedalgorithmsforcomputati =min( transmitantennas,where isthenumberofreceiveantennasand isthelengthofthecoherenceinterval,whereasatlowSNR,themutualinformationismaximizedbyallocatingalltransmitpowertoasingleantenna.IndexTerms (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
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