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1、1204IEEETRANSACTIONSONINFORMATIONTHEORY,VOL.46,NO.4,JULY2000NetworkInformationFlowRudolfAhlswede,NingCai,Shuo-YenRobertLi,SeniorMember,IEEE,andRaymondW.Yeung,SeniorMember,IEEEAbstract—Weintroduceanewclassofproblemscallednetworkgatedtrafficpatternthenetworkneedstosupport.Inothersit-inf
2、ormationflowwhichisinspiredbycomputernetworkapplica-uations,thegraphmayrepresentasubnetworkinaphysicaltions.Considerapoint-to-pointcommunicationnetworkonwhichnetwork,whilethesetofmulticastrequirementsmaypertaintoanumberofinformationsourcesaretobemulitcasttocertainsetsaspecificapplicat
3、iononthissubnetwork,e.g.,avideo-confer-ofdestinations.Weassumethattheinformationsourcesaremu-tuallyindependent.Theproblemistocharacterizetheadmissibleencecall.codingrateregion.ThismodelsubsumesallpreviouslystudiedInexistingcomputernetworks,eachnodefunctionsasamodelsalongthesameline.In
4、thispaper,westudytheproblemswitchinthesensethatiteitherrelaysinformationfromanwithoneinformationsource,andwehaveobtainedasimplechar-inputlinktoanoutputlink,oritreplicatesinformationreceivedacterizationoftheadmissiblecodingrateregion.Ourresultcanbefromaninputlinkandsendsittoacertainset
5、ofoutputlinks.regardedastheMax-flowMin-cutTheoremfornetworkinforma-tionflow.Contrarytoone’sintuition,ourworkrevealsthatitisinFromtheinformation-theoreticpointofview,thereisnogeneralnotoptimaltoregardtheinformationtobemulticastasareasontorestrictthefunctionofanodetothatofaswitch.“fluid
6、”whichcansimplyberoutedorreplicated.Rather,byem-Rather,anodecanfunctionasanencoderinthesensethatployingcodingatthenodes,whichwerefertoasnetworkcoding,itreceivesinformationfromalltheinputlinks,encodes,andbandwidthcaningeneralbesaved.Thisfindingmayhavesignifi-sendsinformationtoalltheout
7、putlinks.Fromthispointofcantimpactonfuturedesignofswitchingsystems.view,aswitchisaspecialcaseofanencoder.Inthesequel,weIndexTerms—Diversitycoding,multicast,networkcoding,willrefertocodingatanodeinanetworkasnetworkcoding.switching,multiterminalsourcecoding.Letbeanonnegativerealnumberas
8、socia
