Practical Network Coding

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1、ra ti aletworkCodingyhilipA.Chou,YunnanWu,andamalaini rosoftCorporation,nei rosoftWay,Redmond,WA98052-6399USAyDept.ofEle tri alEngineering,rin etonUniversity,rin eton,08544USApa houmi rosoft. om,yunnanwuee.prin eton.edu,kamaljmi rosoft. omAbstra tWeproposeadistributeds hemeforp

2、ra ti alnetwork odingthatobviatestheneedfor entralizedknowledgeofthegraphtopology,theen odingfun tions,andthede odingfun tions,andfurthermoreobviatestheneedforinformationtobe ommuni atedsyn hronouslythroughthenetwork.Theresultisapra ti alsystemfornetwork odingthatisrobusttorandompa ketlossanddel

3、ayaswellasrobusttoanyhangesinthenetworktopologyor apa ityduetojoins,leaves,nodeorlinkfailures, ongestion,andsoon.Wesimulatesu hapra ti alnetwork odingsystemusingthenetworktopologiesofseveral ommer ial
nternetServi eroviders,anddemonstratethatit ana hieve losetothetheoreti allyoptimalperforman e

4、.1
ntrodu tion
ntheirpioneeringtheoreti alworkonnetwork oding,inwhi hthenetworkismodeledbyadire tedgraph(V;E)withedge apa ities,Alswedeetal.[1℄showedthatasenders2V an ommuni ate ommoninformationtoasetofre eiversTVataratea hievingthebroad ast apa ityh(thevalueoftheminimum utbetweensandanyt2T)pro

5、videdoneallowsnetwork oding,i.e.,en odingattheinteriornodesofthenetwork.Conversely,itisgenerallynotpossibletoa hievethis ommuni ationrateifoneallowsonlyroutingor opyingmessagesattheinteriornodesofthenetwork.Shortlyafterwards,i,Yeung,andCai[2℄showedthatitissuÆ ientfortheen odingfun tionsattheint

6、eriornodestobelinear.oetterandedard[3℄showedhowtondthe oeÆ ientsofthelinearen odingandde odingfun tionsbyndingvaluesfortheindeterminatesofapolynomialforwhi hthepolynomialisnon-zero.Theyalsoshowedthatsu hvalues analwaysbefoundinaeldofsizehjTj,wherejTjisthenumberofre eivers.aggi,Sanders,eta

7、l.[4,5,6℄showedfora y li networkshowtondtheen odingandde oding oeÆ ientsinpolynomialtime,andshowed(asdid[7℄)thateldsizejTjsuÆ es.Theyalsoshowedthatthelinearen odingfun tions anbedesignedrandomly,andthatiftheeldsizeisatlea