Cooperative Network Coding-Aware Routing for Multi-Rate Wireless Networks

Transcription

1 Ts full text paper was peer revewed at te drecton of IEEE Communcatons Socety subject matter experts for publcaton n te IEEE INFOCOM 009 proceedngs. Cooperatve Network Codng-Aware Routng for Mult-Rate Wreless Networks Jn Zang Qan Zang Department of Computer Scence and Engneerng ong ong Unversty of Scence and Tecnology Emal: {zjzj, qanz}@ust.k Abstract Recent researc as proven tat network codng as great potental to mprove network trougput n wreless networks. To fully explot te performance gan brougt by network codng, codng-aware routng as been studed to proactvely cange route of flows for creatng more codng opportuntes. owever, n today s mult-rate wreless networks, codng may not be a wse decson as te lowest rate as to be used for coded nformaton broadcastng, wc causes sgnfcant resource waste for te g-rate lnks. In ts paper, we propose te dea of cooperatve network codng (CNC) to explot spatal dversty for mprovng codng opportunty. We provde a teoretcal formulaton for calculatng te maxmal trougput of uncast traffc tat can be aceved wt CNC n mult-rate wreless networks. CNCaware routng under bot Alce-ob and X-structure are dscussed n ts paper. Te performance evaluaton demonstrates tat a CNC-aware route selecton sceme tat leverages cooperatve communcaton to mprove codng opportunty leads to ger end-to-end trougput comparng wt te codng-oblvous and tradtonal codng-aware scemes. eywords Network Codng, Cooperatve Communcaton, Codng-aware Routng, Mult-Rate Wreless Networks I. INTRODUCTION Network codng s an nnovatve tecnque for mprovng potental network trougput and robustness []. Tere s an ncreasng nterest n understandng te potental performance gans accrung from te use of network codng n wreless networks. Te performance gan aceved by network codng for bot uncast and multcast traffc ave been nvestgated n te past several years [, 3, 4]. Fundamentally, adoptng network codng n wreless networks s tryng to explore te wreless broadcast advantage so as to reduce te number of needed transmssons and te fracton of cannel tme tat s requred by a sngle transmsson, and tereby ncrease te overall network trougput. Te basc dea of ow network codng can mprove te network performance n wreless networks can be llustrated n te typcal Alce-ob structure and X-structure. For Alce-ob structure case (sown n Fg. ), Alce wants to send packet A to ob, wle ob wants to send packet to Alce. Due to transmsson range lmtatons, bot of te packets ave Te researc was supported n part by grants from RGC under te contracts CERG 6407, 6508 and N UST609/07, by grant from UST under te contract RPC06/07.EG05 and MRA05/06.EG03, by grant from Natonal asc Researc Program of Cna (973 Program) under te contract No. 006C30300, te NSFC oversea Young Investgator grant under Grant No , Natonal 863 Program of Cna under Grant No. 006AA0Z8 (a) Transmssons w/o network codng. (b) Transmssons w/ network codng. Fg. Illustraton of Alce-ob structure. to be relayed va te router R. Usng standard tecnques of packet forwardng, four wreless transmssons are needed to complete te end-to-end packet transfers, wc can be llustrated n Fg. (a). In comparson, usng a smple form of network codng (trougout ts paper, we use XOR), tree wreless transmssons nstead of four are needed (sown n Fg. (b)). Smlar codng gan can be aceved n Xstructure wt opportunstc lstenng (sown n Fg. ), were node X as a packet A for node Y and node M as a packet for node N. ere, by opportunstc lstenng, t means tat eac node can turn nto a promscuous mode to snoop on all packets communcated by ts negbors []. In Fg., by codng, suc a message excange can be done wt only tree transmssons nstead of four, as follows. After X transmts A and M transmts, te router R broadcasts coded packet A. Assume tat N can overear A opportunstcally wen t s transmtted by X, and Y can overear opportunstcally wen t s transmtted by M. Ten, upon recevng te coded packet A, bot Y and N can successfully decode te proper A and packets, respectvely. From te above fgures we can see tat, network codng can elp to sgnfcantly mprove te overall system capacty. owever, we can also see tat, te codng opportuntes depend on te occurrences of Alce-ob and X-structures formed n te transmsson pats. Tus, performance gan can be obtaned wen takng codng opportuntes nto account wle selectng te transmsson route. Ts s te fundamental dea tat drves codng-aware routng [5-8]. Take te followng example sown n Fg. 3(a). Tere already exts one flow from node A to node E wt te route A D E. A new flow from node F to node requests to access te network. Wt tradtonal lnk-qualty (or nterference aware) routng strategy [9, 0], te optmal route sould be F E C. Now suppose tat network codng s allowed, t turns out tat te route F E D provdes better performance, as codng opportunty n node D can be fully leveraged /09/$ IEEE 8 Autorzed lcensed use lmted to: Memoral Unversty. Downloaded on November, 009 at 08:53 from IEEE Xplore. Restrctons apply.

2 Ts full text paper was peer revewed at te drecton of IEEE Communcatons Socety subject matter experts for publcaton n te IEEE INFOCOM 009 proceedngs. (a) Transmssons w/o network codng. (b) Transmssons w/ opportunstc lstenng and codng. Fg. Illustraton of X-structure. owever, n all te exstng codng-aware routng desgn, tere s no dscusson related to te mult-rate wreless envronment, wc s te major focus of our paper. Most of te commodty wreless cards ave te capablty of conductng adaptve modulaton to adjust te lnk rate n response to te cannel condton. Ts mult-rate capablty as been defned n many standards suc as IEEE 80., perlan, etc. Wen takng mult-rate nto consderaton, more codng opportuntes are not necessarly mean ger trougput. Look at te same topology wt dfferent lnk rates as sown n Fg. 3(b). Te numbers on eac edge denote te maxmum transmsson rate and te avalable bandwdt of te correspondng lnk, respectvely. In ts example, wtout network codng, te optmal route sould be F E C, under wc te total trougput of te two flows are.5mbps consderng lnk contenton. Now suppose network codng s allowed, we wll ceck weter we sould proactvely adjust te route for more codng opportuntes. If te route F E D s selected, we can see tere s codng opportunty n node D. owever, ere D can only code te two flows togeter and broadcast usng te mnmal rate of te two outgong lnks, wc s. Ten, te total trougput s.5mbps, wc s equal to te non-network codng result. Tus, n ts example, codng aware routng provdes no endto-end trougput gan compared wt tradtonal routng. Te key reason s tat te g-rate lnks cannot be fully utlzed as te lowest-rate lnk became te bottleneck for broadcastng transmsson rate selecton. To solve ts capacty waste problem and really explore te performance gan by network codng, n ts paper, we consder usng cooperatve communcaton to enance te codng opportuntes. Cooperatve communcaton s a pyscal layer tecnque wc explots spatal dversty to ncrease transmsson relablty [, ]. Te core dea of cooperatve communcaton s tat wen te cannel qualty between te source and te destnaton s not good enoug (lke E to D n Fg.3(b)), use anoter relay node (C n Fg.3(b)) wc as a better cannel condton to te destnaton to cooperatvely transmt data wt te source node. In suc a vrtual multple antenna system, te capacty of te cooperatve lnk s muc larger tan tat of te orgnal lnk from sender to recever, tus, te overall system capacty can be dramatcally mproved by explotng spatal and user dversty. Partcularly, suppose A A 6,6 6, C 6,6 C D D 6,6 6,6 E, E 6,6 F F (a) Sngle-rate topology. (b) Mult-rate topology. Fg. 3. Te llustraton about codng-aware routng. smple repeated codng tecnque s used n node C, C cannot receve and transmt smultaneously, tus te effectve data rate of te cooperatve lnk sould be 3Mbps. Ten, under te route F E D, te total trougput of te two flows s Mbps, wc aceves 33.3% trougput gan. If more advanced cooperaton tecnque (suc as space-tme codng) s supported, ger performance gan can be aceved. Explotng te dea of cooperatve communcaton, for a router tat as unbalanced outgong lnks n terms of lnk qualty, a cooperatve relay node can be selected to form a cooperatve lnk wt wc te coded packet can be transmtted wt a ger rate. As low-rate lnk s te bottleneck for te broadcastng, te broadcastng transmsson rate can be mproved and terefore te overall network trougput can be enanced due to cooperatve network codng (CNC). In ts paper, we focus on applyng CNC to a wreless network were mult-rate s supported. We wll answer te queston: wat s te maxmal trougput tat can be obtaned for a uncast sesson and gve te teoretcal analyss for tat. Pror work as sown tat f te wreless routng protocols can take te codng opportuntes nto consderaton [6-8], better performance can be aceved compared wt te ones [9, 0] tat only aware of nterference (and lnk-qualty). owever, as we demonstrated n ts paper, n mult-rate network, due to te exstence of unbalanced outgong lnks n a broadcast, te route provdng more network codng opportunty s not necessarly wt better performance. Wt te ntroducton of cooperatve network codng, te data rate of te low-rate lnk can be ncreased wt te elp of relay node, wc n turn elmnate te bottleneck lnk wtn broadcastng. Snce te cooperatve network codng provdes more opportunty for te wole network, te routng sceme under suc a CNC-aware network sould be revsted to explot te beneft of spatal dversty, opportunstc lstenng, codng and cooperaton. Ts s te core focus of ts paper. Te man contrbuton of ts paper ncludes te followng aspects. Frst, n ts paper, we are te frst to propose te dea of explotng cooperatve network codng for route selecton to enance te overall network performance. A detaled analyss for acevng maxmal trougput by leveragng CNC-aware routng s presented. Second, a jont cooperatve codng-aware and nterference-aware routng algortm under mult-rate wreless networks s proposed. Two dfferent codng structures (Alce-ob structure and X-structure) are consdered. Trd, accordng to te smulaton results, some nspraton s 8 Autorzed lcensed use lmted to: Memoral Unversty. Downloaded on November, 009 at 08:53 from IEEE Xplore. Restrctons apply.

3 Ts full text paper was peer revewed at te drecton of IEEE Communcatons Socety subject matter experts for publcaton n te IEEE INFOCOM 009 proceedngs. aceved regardng to te tradeoff of spatal dversty, codng opportunty and nterference avodance. Note tat n ts paper we do not target at proposng a concrete codng or routng sceme, nstead we manly focus on teoretcal analyss to quantfy te potental performance gan brougt by explotng cooperatve network codng n route selecton. We beleve our work provdes nterestng nsgts to desgn concrete routng protocols for future work. Te rest of te paper s organzed as follows. Te problem formulaton s presented n Secton II. In te followng two sectons, te cooperatve network codng aware routng under Alce-ob and X structures are dscussed, respectvely. Numercal result s gven n Secton V. In Secton VI, some related work s ntroduced and fnally te paper s concluded n Secton VII. II. PROLEM FORMULATION As mentoned n Introducton Secton, we can clearly see tat under mult-rate wreless networks, transmsson route sould be re-selected so as to explot te beneft of cooperatve network codng. In ts paper, we would lke to provde a teoretcal formulaton for maxmzng te transmsson trougput. To aceve ts target, n ts secton, we wll defne te notatons needed for problem formulaton. To support cooperatve communcaton, generalzed network topology grap s constructed wc conssts tradtonal lnks and cooperatve lnks, and cooperatve transmsson rate s calculated for eac cooperatve lnk. Under generalzed network topology grap, cooperatve pat s defned and network flow model s constructed to descrbe a potental pat n te grap. For a router conductng cooperatve network codng, te cooperatve broadcast rate s calculated and fnally generalzed conflct grap s constructed to descrbe te contenton relatonsp between cooperatve lnks. A. Generalzed Network Topology Grap In tradtonal wreless networks, te network topology, gven by te nodes and te lnks correspondng to pars of nodes wtn transmsson range, s modeled as a grap G = (N, E) wt node set N and edge set E. Eac edge e E as a gest transmsson rate R(e) wc denotes te gest rate at wc packets can be transmtted on te correspondng lnk under certan packet error probablty. Wen cooperatve communcaton s leveraged, te edges denotng cooperatve transmssons sould be created and te network topology grap sould be reconstructed. In ts work, t s assumed tat at most one cooperatve relay node s used for eac source-destnaton par. For eac drected lnk e = (, j), f node r s te best relay for t, we defne cooperatve lnk as e = (, r, j). In suc a cooperatve transmsson, node j combnes te transmsson of node and node r togeter usng Maxmum Rato Combnng before decodng, under wc te sgnal to nose rato (SNR) of te combned sgnal equals to te sum of te two separated sgnals SNR(, r, j ) = SNR(, j) SNR( r, j). Tus, te rate of te cooperatve lnk e can be calculated as R( r,, j) = g ( grj ( (, )) grr ( (, j))), were g s te correspondence functon between te transmsson rate of a lnk and ts SNR requrement, wc s related to specfc modulaton sceme. Te factor / denotes tat te transmsson of te source and relay node are tme-dvded, wt te frst alf tme used for source transmsson and te second for relay transmsson. Note tat ts equaton s under te assumpton tat smple repeated codng s used n cooperaton. We wll see later troug smulaton tat wen syncronzed cooperaton (suc as space-tme codng) s supported wt opportunstc lstenng, better performance can be aceved. If R(, r, j) > R(, j), lnk (, r, j) s added to te orgnal network topology grap G = (N, E) as an edge from node to node j wt te correspondng rate beng R(, r, j). Te same procedure s done for eac edge n tradtonal network topology and fnally a new grap G = (N, E ) s constructed, n wc N s te orgnal node set wt V = N number of nodes, E s te unon set of all tradtonal lnks and cooperatve lnks, wt L = E number of lnks totally. As te new topology grap G ncludes bot tradtonal and cooperatve lnks, t s called generalzed network topology grap. To keep te lnk notaton consstent, we use (, 0, j) to denote te tradtonal drect lnk, were 0 means tat tere s no cooperatve relay for ts transmsson.. Pat notaton and network flow model We use network flow model to defne a feasble pat under V L a network topology. A node-lnk ncdence matrx A R s ntroduced to represent te network topology, were te value of element n row, column j, a j ( V, j L, N, ej E ' ) denotes dfferent relatonsp of node and lnk e j f ej E ( ) aj = f ej E ( ). 0 else In wc, E - () and E () denote respectvely te sets of ncomng and outgong edges at node. A pat consstng contnuous lnks e, e,, e n s defned P = ee e, and x(p) s defned to be a vector of lengt L as n L ( xp ( ) R ) wt te t element to be, f e P x ( P) =, L. 0, else For te k t traffc flow, gven te source and te destnaton node s k and d k, ten te flow can be denoted by a vector V uk R, wt te tem correspondng to te source to be, and te tem correspondng to te destnaton to be -, wle all te oter tems to be 0. Ten, te pat P k for flow k sould satsfy te followng k constrant Ax(P k ) = u k. We defne R to be te set contanng all te possble solutons of pats P k for flow k. C. Cooperatve roadcast Rates In ts subsecton, we wll calculate te broadcast rate and cooperatve broadcast rate of a network coded broadcast 83 Autorzed lcensed use lmted to: Memoral Unversty. Downloaded on November, 009 at 08:53 from IEEE Xplore. Restrctons apply.

4 Ts full text paper was peer revewed at te drecton of IEEE Communcatons Socety subject matter experts for publcaton n te IEEE INFOCOM 009 proceedngs. transmsson. Wen network codng s ntroduced nto te network, to save transmsson tme, te router broadcasts te coded packets nstead of multple uncast transmssons, and te broadcast rate s bottlenecked by te low-rate transmsson. Wen cooperatve communcaton s exploted to enance te broadcast rate of te coded packets, te cooperatve broadcast rate needs to be renvestgated. It s assumed tat for eac wreless lnk e (ncludng bot tradtonal lnk and cooperatve one), we are gven te rate of transmsson R e. Let be a subset of outgong lnks at a node. Te transmsson rate of broadcastng on can be calculated as follows. If = {e} conssts of a sngle lnk, ts effectve transmsson rate s R() = R e. If = {e, e } conssts of multple tradtonal lnks, te broadcast transmsson rate of s te mnmum rate of ts component lnks, wc equals R() = mn{r e, R e }. If conssts some cooperatve lnks, as tere s only one node actng as te cooperatve node for broadcast transmsson, some equvalent or dervatve broadcast subset sould be ntroduced as follows. o If = {e, e } conssts one tradtonal lnk e = (v, 0, v ) and one cooperatve lnk e = (v, v 3, v 4 ), ten, te effectve broadcast rate of s equal to tat of an equvalent broadcast ', R( ) = R( '), n wc ' = { e', e} and e ' = (v, v 3, v ). R( ') = mnr e. e ' o If = {e, e } conssts of two cooperatve lnks, n wc e = (v, v, v 3 ) and e = (v, v 4, v 5 ), ten, te effectve broadcast rate of s equal to maxmal of two dervatve broadcast R( ) = max( R( '), R( '')), n wc ' = {(v, v, v 3 ), (v, v, v 5 )}, '' = {(v, v 4, v 3 ), (v, v 4, v 5 )}, and R( ') = mnr e, R( '') = mnr e. e ' e '' D. Generalzed conflct grap In wreless networks, wen a new flow s ntroduced, some lnks n ts flow may contend wt eac oter, wc s called ntra-flow contenton. Meanwle, tey may also contend wt oter lnks served for exstng flows, wc s called nter-flow contenton. A better route selecton sceme sould try to mnmze te performance degradaton caused by lnk contenton. To descrbe te contenton relatonsp among multple lnks, conflct grap s usually constructed. Especally, n ts subsecton, cooperatve broadcast based conflct grap s constructed to support cooperatve network codng. A cooperatve broadcast transmsson at node on a subset of ts outgong lnks s represented as (, ) and te assocated broadcast traffc on t s denoted as y. Note tat t ncludes uncast as a specal case wen te set conssts of only one lnk. It also ncludes tradtonal broadcast transmsson as a specal case wen te set as no cooperatve lnks. We defne te cooperatve broadcast conflct grap F as a natural extenson of te conflct grap for uncast transmssons. Eac node n ts grap represents a cooperatve broadcast transmsson (, ). Let d() denotes te set of destnaton nodes for te lnks n broadcast set and r() denotes te cooperatve relay node n broadcast set. Two broadcasts (, ) and (, ) are defned to nterfere wt eac oter, and ence ave an edge between tem n te cooperatve broadcast conflct grap, f at least one of te followng cases appens: Some node j d( ) s wtn te nterference range of ; Some node j d( ) s wtn te nterference range of ; Some node j d( ) s wtn te nterference range of r( ); Some node j d( ) s wtn te nterference range of r( ). In one word, two cooperatve broadcast transmssons nterfere wt eac oter wen eter one of te transmttng nodes or one of te cooperatve relay nodes nterfere wt te destnaton nodes n te oter broadcast set. Gven te cooperatve broadcast conflct grap, we now use constrants correspondng to clques n te conflct grap to formulate te contenton relatonsp. Consder a clque n te broadcast conflct grap. Let C be te set of broadcast nodes (, ) tat correspond to nodes of ts clque. Te fracton of tme tat broadcast (, ) s actve can be represented as y /R(). Snce te broadcasts n C mutually conflct wt eac oter, at most one of tem can be actve at any gven tme. Ts can be modeled by te constrant y clques C n F. (, ) CR ( ) After all tese preparaton works are fnsed, te route selecton problem can be formulated nto an optmzaton problem as sown n next two sectons. III. CNC-AWARE ROUTING UNDER ALICE-O STRUCTURE Frst, we consder a smplest scenaro were only Alce- ob structure s allowed wen applyng network codng, wc means tat te router can only XOR two packets from two flows wc enter and leave te router usng te same lnks but n te opposte drectons. We assume tat n a wreless network, tere already exst several flows, say totally flows. For eac flow k, k, te routng pat s P k,te traffc for ts flow s f(p k ). Now new flows are njected nto te network, for eac flow,, te traffc s from source node s() to destnaton node d() wt te gven traffc demand t(). Te possble pat set R can be calculated ac- cordng to Secton II.. Assume for eac pat P R, f t s selected, ten f (P) =, else f (P) = 0. Let y denote te traffc tat s broadcasted at node on lnk set E (). ecause we are dscussng network codng under Alce-ob structure, tere are at most two nodes n set.. We need to decde ts (a) transmsson route; (b) network codng rate; (c) cooperatve node to explot te beneft of cooperatve network codng, eventually maxmze te trougput of all te new flows under te contenton constrants and packet decodng constrants. Wt te above target and constrants, te problem can be formulated as te followng optmzaton problem (n next page). ere ( tλ ) denotes te trougput for routng te flow 84 Autorzed lcensed use lmted to: Memoral Unversty. Downloaded on November, 009 at 08:53 from IEEE Xplore. Restrctons apply.

5 Ts full text paper was peer revewed at te drecton of IEEE Communcatons Socety subject matter experts for publcaton n te IEEE INFOCOM 009 proceedngs. maxmze tλ ( ) = subject to f( P) =,, f( P) = 0, () P R { e, e} ( k) ( ) ( ) λ, ( ), () k= ee Pk = P R, ee P y f P f P t e e E N { e, e} ( k) ( ) ( ) λ, ( ), (3) k= ee Pk = P R, ee P y f P f P t e e E N {} e λ k k =,, ( ) k s( k), e P P R e P s = = = k e E ( ) k= ee P y = f ( P) t( ) f( P ) [ f( P ) (, ) C, = P R, ee P n te network, λ s a fractonal varable. For a lnk e = (, j, k), e denotes ts reverse lnk e = ( k, j, ). Te target of te above optmzaton problem s to maxmze te possble trougput of all te ncomng flows under te gven flow conservaton constrant, network codng traffc relatonsp, and te contenton constrant. More specfcally, Constrants () denote te routng selecton constrants. Constrants () and (3) denote te maxmum encoded traffc can be transmtted n te broadcastng lnk at node after network codng. Constrants (4) sow te remanng traffc n te orgnal uncast lnks. Constrants (5) are te contenton relatonsp due to te maxmum clque constrants. f P t y e E N {, ee} ( ) ( ) λ ] ( ), y clques C n F (5) R ( ) (a) Mult-rate reduces potental codng gan. (4) IV. CNC-AWARE ROUTING UNDER X-STRUCTURE Due to broadcast property of wreless meda, transmttng packets can be opportunstcally overeard by some negborng nodes besdes te potental destnaton. Terefore, network codng can be used for te networks wt X-structure as we dscussed n te Introducton Secton. Let us revst te example sown n Fg. (b). For ts case, as node N and Y can opportunstcally overear te transmssons from X and M respectvely, te message excange can be done wt only 3 transmssons nstead of 4. Tus, at least 5% performance gan can be aceved. owever, ts s under te assumpton tat sngle data rate s supported n te system. Suppose multrate s exploted n te network (as n Fg. 4(a)), after recevng packets from X and M, R can only broadcast te coded packet at te low rate. Tus, te g capacty of lnk (R, N) wll be wasted. If tere s one negborng node,, wc as g-rate connectons to R, Y, and N, ten we can leverage node by cooperatve network codng dea (see n Fg. 4(b)). For a CNC-aware network, te correspondng codng structure can be represented as: e = (X, 0, R), e = (M, 0, R), e 3 = (R,, Y), e 4 = (R,, N), n wc e 3 and e 4 are cooperatve lnks. Wle node R transmts te coded packet, te cooperatve node (b) Cooperaton to elmnate te bottleneck lnk. Fg. 4 X-structure for cooperatve network codng. wll elp t as a cooperatve relay. In te frst alf of te slot, node R broadcasts te coded packets, and ten n te second alf, node transmts te packet t overeard before. Fnally, node N and node Y combne te two transmssons and decode te coded packets. In suc crcumstance, te network codng structure can be denoted by S = {e e 3, e e 4 }. It s noted tat Alce-ob structure s a specal case of te X-structure wen applyng network codng. We need to pay specal attenton to te transmtted packets from M or X n Fg. 4(a), nstead of sendng packet to R, f M sent a coded packet C n te transmsson, ten, altoug Y can overear te coded packet, t cannot know exactly ow packet s lke, tus, tere wll be no codng opportunty n tat case. ere te tng tat s also very mportant s tat weter te prevous node transmtted a natve packet or a coded packet. To descrbe ts property, one element s added n set S, and fnally t becomes {(e e 4, n), ( e e 3, n)}, n wc, 85 Autorzed lcensed use lmted to: Memoral Unversty. Downloaded on November, 009 at 08:53 from IEEE Xplore. Restrctons apply.

6 Ts full text paper was peer revewed at te drecton of IEEE Communcatons Socety subject matter experts for publcaton n te IEEE INFOCOM 009 proceedngs. maxmze t ( ) λ = subject to f ( P) =,, f ( P) = 0, (6) P R t( e) k t( e) ( ee, n) S k= ee P k = P R, ee P u ( S) z ( P ) z ( P) e E ( ), e E ( ), N (7) u ( S) [ f( P ) z ( P )] λ t e k t( e ) k ( ee, c) S k= ee Pk = P R, ee P [ f ( P) t( ) z ( P)] k λ = k t( e ) k= ee Pk =, P R ee P k= ee Pk = P R, ee P u( S) u( S), e ( ee, n) S ( ee, c) S ( ) e E (), e E (), N (8) f( P ) f ( P) t( ) z ( P ) z ( P) {} e = k k= e P k = P R, e P S Γ, b( S) = y E ( ), e E ( ), N (9) zs( k) ( Pk) = f( Pk) zs( ) ( P) = f( P) t( ) λ k (0) () z ( Pk) f( Pk) N { s( k), d( k)}, k () z ( P) f ( P) t( ) λ N { s( ), d( )}, (3) y z ( P ) z ( P) e E (), N (4) y u ( S) N, (5) (, ) CR ( ) clques C n F (6) n denotes natve packets. Anoter type of packets s coded Constrants (9) are balance constrants for te total traffc packets wc are denoted by c. For example, {( ee 4, n ), njected troug lnk e and extng troug lnk e at node. Te LS s te traffc along te lnk e ( ee 4, c)} s anoter feasble codng structure n node R. For a e of exstng flows and ncomng flows. Te frst and second terms on codng structure S, we defne te broadcast lnk of S b(s) = (e 4, RS, s te amount of traffc tat goes out as natve (.e., e 3 ). For eac node, we can calculate all te codng structures does not partcpate n any codng). Te trd porton s Γ on t. te amount of traffc tat partcpates n codng as natve y ntroducng codng structure S, te traffc under more receved flows. Te fort porton s te amount of traffc generalzed cooperatve network codng can be calculated and tat partcpates n codng as coded receved flows. te route selecton problem can be formulated to be a new Constrants (0)-(3) are te boundary condtons for te optmzaton problem as above. In wc, u (S) denotes te z (P k ) varables. Constrants (0) and () state tat te traffc assocated wt codng structure S at node ts s te source node of every pat transmts te entre traffc on traffc amount assocated wt eac e e lnk-par partcpatng tat pat as natve, snce no codng opportuntes are n te structure. z (P k ) denotes te porton of te traffc on pat avalable for orgnatng traffc at te source node. Constrants P k for exstng flow k tat s transmtted as natve from node. () and (3) state tat for a gven pat, te z (P) denotes te porton of te traffc on pat P R for amount of traffc transmtted as natve at eac node s at new flow tat s transmtted as natve from node. most te total traffc on tat pat. Constrants (4) express te uncast traffc varable as te Constrants (6) are te routng selecton constrants. total amount of traffc tat s transmtted as natve on lnk Constrants (7) are te porton of traffc tat partcpates n e at node. codng from te ncomng lnk e to te outgong lnk e as Constrants (5) express te broadcast traffc varable y natve-receved flows at node. It sould be smaller or as te total amount of traffc tat s transmtted as coded equal to te amount tat was receved by t(e ). on lnk set at node. Ts corresponds to te sum of Constrants (8) are te porton of traffc tat partcpates n traffc over all codng structures wt b(s) =. codng from te ncomng lnk e to te outgong lnk e as Fnally, as before, constrants (6) are te broadcast coded-receved flows at node. It sould be smaller or transmsson scedulng constrants correspondng to clques n te broadcast conflct grap. equal to te amount tat was njected n mnus te amount sent as natve packets. Autorzed lcensed use lmted to: Memoral Unversty. Downloaded on November, 009 at 08:53 from IEEE Xplore. Restrctons apply. 86

7 Ts full text paper was peer revewed at te drecton of IEEE Communcatons Socety subject matter experts for publcaton n te IEEE INFOCOM 009 proceedngs. TALE. DISTANCE TRESOLD FOR DIFFERENT TRANSMISSION RATES Data Rate(Mbps) Receved power(dm) Dstance(m) Trougput Gan SPR-CODE CAR-A CNCR-A CAR-X CNCR-X CNCR-syn V. SIMULATION RESULTS We evaluate te performance of te followng scemes on a varety of network routng scemes: () sortest pat routng (SPR); () sortest pat routng wt network codng (SPR- CODE); (3) codng aware routng (CAR) (te same as CA- MPAT-CODE n [7]), wc conssts two scemes: CAR-A, wc s under Alce-ob structure (correspondng to CA- MPAT-CODE wtout opportunstc lstenng n [7] ), and CAR-X, wc s under X-structure (correspondng to CA- MPAT-CODE wt opportunstc lstenng n [7]); (4) cooperatve network codng aware routng (CNCR), wc also conssts CNCR-A and CNCR-X, respectvely, correspondng to two dfferent codng structure. Moreover, we use CNCRsyn to ndcate te protocol tat advanced cooperaton tecnque (suc as space-tme codng) s adopted nstead of smple repeated codng. We take te trougput of SPR as te baselne and compare te trougput gan of all te oter scemes. We solve all lnear programs usng CPLEX [4]. We do smulaton under two dfferent types of topologes, frst s an llustratve topology, and te second s random topology. A. Illustratve Topology Frst, we evaluate te performance of dfferent routng scemes on llustratve topology sown n Fg. 3(b). Assume tat te transmsson range s 00 unts and nterference range s 00 unts. Te data rate s 6,, 8, 4, 36, 48, 54Mbps, accordng to IEEE80.a standard. Tere are 0 exstng flows from node A to E along te route A D E. Anoter 0 flows from F to are requred to access. Te traffc demand for eac flow s unt. Te smulaton sows tat te trougput gan of CAR-A and CAR-X over SPR-CODE s 0, wle tat of CNCR-A and CNCR-X s 35.4%, and tat of CNCR-syn s 6.7%, wc s n accordance wt te analyss n Secton II.. Random Topology In ts secton, we run varous routng scemes on randomly generated network topology. Te postons of te nodes were cosen randomly n a square of sde 400 unts. Te communcaton range of eac node s set to 00 unts and nterference range s set to 00 unts. Te transmsson rate can be cosen from 6,, 8, 4, 36, 48, 54Mbps, accordng to IEEE80.a standard. Te receved power tresold and correspondng maxmal dstance for eac rate n ts smulaton s sown n Table. We coose 00unts to be 6 Mbps transmsson range. 4 We use Pr = α Pt / d as te pat loss model, ten te dstance for oter data rate can be calculated. Trougput Gan Traffc Demand Fg. 5 Performance comparson wt varyng traffc demand. SPR-CODE CAR-A CNCR-A CAR-X CNCR-X CNCR-syn Average Degree Fg.6 Performance comparson wt varyng node degree. Fg. 5 sows te trougput gan compared wt te sortest pat routng for ncreasng number of flows. Te traffc demand of eac flow s unt. Eac node n te fgure s an average of te results n 0 random generated networks. We vary te number of traffc demands from 0 to 300. Te source and te destnaton for eac flow are cosen at random. Tere are 5 nodes n total. We can see tat on average, CNCR- A can aceve 5% trougput gan compared wt SPR, wle CNCR-X and CNCR-syn can respectvely aceve 50% and 70% trougput gan. Compared wt CAR-X, CNCR-X can stll aceve 0% trougput gan on average, t s brougt by te ger transmtted rate cooperatve network codng provded. Wt te ncrease of traffc demand, at frst, te trougput gan of bot CAR and CNCR ncreases, ten to some extent, te gan of CAR-A begn to decrease as te network s saturated. owever, CNCR-A and CNCR-syn are stll keepng on ncreasng as ger data rate provded by cooperatve communcaton can provde more system capacty for te traffc demand. Fg. 6 sows te trougput gan of varous routng scemes for ncreasng average node degree n network topology. For te pont correspondng to average degree 3.3 n Fg. 6, we set te total node number to be and random generate several network topologes, coose 0 of tem wose average node degree s between 4 and 5, run eac routng scemes and 87 Autorzed lcensed use lmted to: Memoral Unversty. Downloaded on November, 009 at 08:53 from IEEE Xplore. Restrctons apply.

8 Ts full text paper was peer revewed at te drecton of IEEE Communcatons Socety subject matter experts for publcaton n te IEEE INFOCOM 009 proceedngs can furter mprove 0% gan, wc s brougt by spatal dversty, opportunstc lstenng, cooperaton and codng. Trougput Gan Fg. 7 A 5-node random topology. SPR-CODE CAR-A CNCR-A CAR-X CNCR-X CNCR-syn Traffc Demand Fg. 8 Performance comparson wt varyng traffc demand under te network n Fg. 7. calculate te average of te 0 smulaton results. Te same tng appens for oter tree node degree pont wt te total node number set to be 5, 7 and 0. We can see tat wt te ncrease of node degree, tere s no obvous dstncton for te gan of CAR-A and CNCR-A, tat s because wt Alce- ob structure, network codng doesn t requre g node densty to create codng opportunty. owever, wt larger node densty, te cance to do network codng wt X-structure ncreases, terefore te gan of CAR-X ncreases wt tat of node degree. Dramatc trougput gan s brougt by cooperatve network codng wen te node densty s g, because n tat case, te cance to fnd a sutable cooperatve node s ncreased, so, te performance of CNCR-X and CNCR-syn s really attractve under suc networks. In Fg. 7, we sow one of te random networks. Under ts network, te performance of CAR-A and CAR-X s comparable to tat of LP-CODE wtout opportunstc lstenng and wt opportunstc lstenng sown n te example n [8]. We calculate te trougput gan of varous routng scemes under ts topology and te result s sown n Fg. 8. We can see tat comparng CAR-A, CNCR-A can aceve more tan 5% performance gan. Comparng wt CAR-X, CNCR-X and CNCR-syn can aceve 0% and 0% on average. Te result sows tat, altoug, network codng aware routng as explored a lot of performance gan compared wt tradtonal network, cooperatve network codng aware routng 3 VI. RELATED WORS Te dea of network codng comes from te poneerng paper by Alswede et al. [], wc ntroduced te concept of network codng, ndcatng tat te maxmum multcast trougput can be aceved troug network codng. Ts work as started an actve researc drecton of network codng, nvolvng researc of varous areas, suc as nformaton teory, codng teory, grap teory, optmzaton algortm, and so on. In recent years, tere are sgnfcant researc nterest about ntroducng network codng to wreless applcatons [, 3, 4], were te sared nature of te wreless medum proposes a natural opportunty for network codng, not only n te multcast case but also n te uncast case. Teoretcal studes [5] ad demonstrated tat applyng network codng to wreless network can mprove te system trougput, mnmze energy and allevate te system congeston. Meanwle, att et al. [] developed a practcal network codng arctecture COPE to demonstrate te beneft of applyng network codng n wreless networks. From ter results we can see tat COPE can ncrease te system trougput by 5% - 400% n dfferent traffc envronment. To fully explot te performance gan generated by network codng, codng-aware routng concept as been proposed to proactvely cange routng of flows to create more codng opportuntes. In [6], te autors defned a new metrc ECX tat captures te expected number of coded transmssons needed for successful packets excange between two nodes va an ntermedate node. ased on ECX, tey furter formulated te optmal codng-aware routng as a lnear programmng problem gven te delvery probablty and traffc ntensty between eac node par. Sengupta et al. [7] presented an analyss of te trougput mprovements obtaned by COPE-type network codng n an optmzaton framework, meanwle tey also advocated a codng-aware routng and conducted te trougput analyss about t. Very nterestngly, tey studed te tradeoff between routng flows close to eac oter for utlzng codng opportuntes and away from eac oter for avodng wreless nterference. Te above mentoned work requres te global knowledge of network topology and traffc dstrbutons, wc s ard to mantan up to date. A protocol called END s proposed n [8], wc combned te features of network codng and opportunstc forwardng n 80.- based mes networks to create more codng opportuntes n te network. Ts protocol bends te routes locally and dynamcally to attan better codng opportuntes. All te above researc assume tat tere s only sngle rate n wreless networks, were te lnk-layer rate adaptaton feature as not been exploted. As we know, most commodty wreless cards support rate adaptaton, wc can dynamcally select a proper modulaton sceme dependng on cannel condtons. To te best of our knowledge, [6] s te only work tat nvestgated te mpact tat te use of rate-adaptaton for lnk layer broadcasts may ave on te performance of network codng. In ts paper, te autors conducted extensve smula- 88 Autorzed lcensed use lmted to: Memoral Unversty. Downloaded on November, 009 at 08:53 from IEEE Xplore. Restrctons apply.

9 Ts full text paper was peer revewed at te drecton of IEEE Communcatons Socety subject matter experts for publcaton n te IEEE INFOCOM 009 proceedngs. ton to evaluate te relatve performance of network codng algortms vs. pure routng-based broadcastng strateges n mult-rate wreless networks. As we also sown n te motvated example (Secton I), wt mult-rate wreless network, codng may not always be a wse decson as te lowest rate among all te negbors as to be selected for coded packet broadcastng. Wt anoter completely ortogonal drecton, cooperatve communcaton s a powerful tecnology combatng sgnal fadng due to mult-pat propagaton n wreless medum [, ]. Recently, tere are some studes ncorporatng network codng n cooperatve communcaton to form network coded cooperaton (NCC) scemes. ao et al. [7] proposed a cooperaton sceme termed adaptve network coded cooperaton, te dea of wc s to matc network-on-grap wt te codes-on-grap to construct effcent lnear network codes accountng for te cangng and lossy nature of wreless networks. In [8] te autors nvestgated te dversty gan offered at g sgnal-to-nose rato by applyng network codng to a wreless network, wc contans dstrbuted antenna system as well as one tat supports user cooperaton between users. In [9], a network-coded cooperaton sceme wt dynamc codng mecansm (DC-NCC) was proposed. In DC-NCC, te relay dynamcally adapts formng te network-coded data based on te observed nstantaneous source-to-relay cannel qualty, and ten forwards te network-coded data towards correspondng destnatons. Dfferent from all te exstng works, our paper s te frst to nvestgate te performance of codng-aware routng for uncast traffc n mult-rate wreless envronment. Observng tat te lowest-rate lnk becomes te bottleneck for te performance of coded packet broadcastng, n ts paper, we explore te cooperatve network codng to mprove codng opportuntes for uncast transmssons. VII. CONCLUSIONS In ts paper, we dscuss ow to explot cooperatve network codng for route selecton n mult-rate wreless networks. Recent researc studes ave proven tat network codng s a promsng tecnque to mprove network trougput n wreless networks. Tus, codng-aware routng, wc decdes transmsson route by takng te network codng opportuntes nto consderaton can aceve better performance under sngle rate envronment. Wen consderng te mult-rate feature tat as been defned n many wreless standards, more packets coded togeter and broadcast to more negbors may not be a wse decson as te lowest rate among all te negbors as to be used for coded packet broadcastng and become te bottleneck for te overall system performance. We adopt cooperatve communcaton tecnque n ts paper to explot spatal dversty so as to mprove codng opportunty n mult-rate wreless envronment. Teoretcal formulaton as been provded to calculate te maxmal trougput of uncast traffc tat can be aceved wt cooperatve network codng n a mult-rate wreless networks. CNC-aware routng under bot Alce-ob and X-structures are dscussed n ts paper. Te performance evaluaton demonstrated tat a route selecton sceme tat leveragng cooperatve communcaton to mprove codng opportunty leads to ger end-toend trougput. REFERENCES []. R. Alswede, N. Ca, S.-Y. L, and R. Yeung, Network nformaton flow, IEEE Transactons on Informaton Teory, vol. 46, pp. 04 6, July 000. []. S. att,. Raul, W. u, D. atab, M. Medard, and J. Crowcroft. Xors n te ar: practcal wreless network codng, ACM Sgcomm 006, Sept. 006 [3]. Y. Wu, P.A. Cou, Q. Zang,. Jan, W. Zu, and S.-Y. ung. Network plannng n wreless ad oc networks: a cross-layer approac. 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L, Wreless dversty troug network codng, IEEE Wreless Communcatons and Networkng Conference (WCNC) 006, vol. 3, Campagn, IL USA, Apr. 006, pp [9]. C. Peng, Q. Zang, M. Zao, and Y. Yao, On te performance analyss of network-coded cooperaton n wreless networks, IEEE Transactons on Wreless Communcatons, Vol. 5, No., August Autorzed lcensed use lmted to: Memoral Unversty. Downloaded on November, 009 at 08:53 from IEEE Xplore. Restrctons apply.