Domnatng Set and Network Codng-based Routng n Wreless Mesh Networks Jng Chen, Kun He, Ruyng Du, Mnghu Zheng, Yang Xang, Senor Member, IEEE, Quan Yuan Abstract Wreless mesh networks are wdely appled n many felds such as ndustral controllng, envronmental montorng and mltar y operatons. Network codng s promsng technology that can mprove the performance of wreless mesh networks. In partcular, network codng s sutable for wreless mesh networks as the fxed backbone of wreless mesh s usually unlmted energy. However, codng collson s a severe problem affectng network performance. To avod ths, routng should be effectvely desgned wth an optmum combnaton of codng opportunty and codng valdty. In ths paper, we propose a Connected Domnatng Set (CDS)-based and Flow-orented Codng-aware Routng (CFCR) mechansm to actvely ncrease potental codng opportuntes. Our work provdes two maor contrbutons. Frst, t effectvely deals wth the codng collson problem of flows by ntroducng the nformaton conformaton process, whch effectvely decreases the falure rate of decodng. Secondly, our routng process consders the beneft of CDS and flow codng smultaneously. Through formalzed analyss of the routng parameters, CFCR can choose optmzed routng wth relable transmsson and small cost. Our evaluaton shows CFCR has a lower packet loss rato and hgher throughput than exstng methods, such as Adaptve Control of Packet Overhead n XOR Network Codng (ACPO), or Dstrbuted Codng-Aware Routng (DCAR). Index Terms Network codng, domnatng Set, WMNs 1. INTRODUCTION N etwork codng has ganed sgnfcant momentum after t was frst proposed by Ahlswede et al [8]. Many researchers consder t effcent technology for wred and wreless networks to mprove network performance [1]. Network codng can remarkably ncrease network throughput dependng on certan factors [2], such as convergence of data flows or codng opportunty. Some exstng schemes passvely wat for codng opportuntes and do not suffcently consder the nfluence of routng. Recently t was dscovered network performance can be further optmzed f the routng s desgned n consderaton of codng opportuntes. Ths s called codng-aware routng [3]. Most self-organzed networks have the characterstcs of energy lmtaton and node moblty. As a result, desgners are nclned to dstrbute the flow of data to dfferent routng to make sure energy consumpton s balanced [4]. However, n wreless mesh networks, partcularly wth fxed backbone, the locatons of nodes are statc and energy s unlmted. The more the data flow converges to a node, the greater the codng beneft. Snce a Connected Domnatng Set (CDS) can effcently cover the network topology [5], domnatng J.Chen, K. He, R.Y.Du are wth the Computer School, Wuhan Unversty, Chna. E-mal: chenng@whu.edu.cn. M.Z heng s wth the Department of Computer Scence, Hube Unversty for Natonaltes, Chna Y.X ang s wth the School of Informaton Technology, Deakn Unversty, Burwood, VIC 3125, Australa. Q. Yuan s wth the Department of Math and Computer Scence, Unversty of Texas-Perman Basn, TX, USA Manuscrpt receved on the date of submsson. nodes are a good choce to converge data flows [6]. In addton, t has been noted that codng collson caused by mult-hop transmsson of data flows [7] can have a sgnfcant mpact on effcent codng. In ths paper, we propose a CDS-based and Flow-orented Codng-aware Routng (CFCR) mechansm to mprove the throughput of wreless mesh networks. The maor contrbutons of ths paper nclude two components. Frst, accordng to features of the fxed backbone and unlmted energy, CFCR constructs the approxmate Mnmum Connected Domnatng Set (MCDS), and can choose domnatng nodes to effectvely ncrease codng opportuntes. Unlke exstng routngs based on CDS, we defne CDS routng as the routng whch ncludes Domnatng des (DNs). We consder that f all nodes n routng are selected from CDS, t wll possbly nduce the problem of codng collson. As a result, CFCR takes DNs nto account frst, and then consders normal nodes as canddates for DNs f a codng collson s lkely. Hence, n CFCR, the best stuaton s f all nodes n routng are DNs and the worst stuaton s f all nodes n routng are normal nodes. Compared wth exstng algorthms based on CDS, CFCR s more flexble and practcal. Secondly, consderng the requrement of mult-hop codng-aware, we desgn an algorthm to confrm potental codng opportuntes n routng, thus guaranteeng the avalablty of network codng and mprovng codng effcency and relablty. Most researchers want to fnd optmal schemes to maxmze codng opportuntes. However, n practce, more codng opportuntes does not mean better performance. If flows
excessvely converge n some specfc routes or nodes, the codng collson wll be marked and the performance wll be degraded, such as throughput and packet loss rato. In ths paper, CFCR fnds a balance between codng opportuntes and collsons by the confrmaton process of network codng. CFCR ntally detects alternatve routngs as classcal on-demand routng. Then, t excludes routngs wth codng collson usng the confrmaton process. Fnally, the routng wth the most metrc beneft s selected. Because estmatons of the domnatng node and codng opportunty are mportant factors n routng selecton, we analyze these two problems before descrbng our routng protocol. The rest of ths paper s organzed as follows. The second secton presents related work about network codng and codng awareness routng of wreless networks. The soluton method of CDS, and the defnton of CDS routng are ntroduced n Secton 3. Secton 4 analyzes the condton of codng awareness. CDS-based and flow-orented codng aware routng s proposed n Secton 5. Secton 6 presents the smulaton results and analyzes the performance of codng opportunty, packet loss rato and throughput. A summary of ths paper and future work are descrbed n Secton 7. 2. RELATED WORK Network codng was frst proposed by Ahlswede et al. [8]. Ths research hghlghted a novel drecton for mprovng network throughput, and as a result, t has attracted sgnfcant attenton. In 23, L et al. successfully proved lnear codng could acheve maxmum capacty n multcastng [9]. Koetter and Medard proposed the polynomal tme algorthm of encodng and decodng [1], and T. Ho et al. extended ths algorthm to nclude random codng [11]. Due to open wreless channels, many researchers found network codng more sutable to wreless networks, and therefore proposed a number of schemes [12,13]. S. Katt desgned an orgnal wreless network forwardng framework called COPE [14], whch combned network codng theory and practcal requrements. COPE can be ntegrated nto an exstng network protocol stack, and can work together wth TCP and UDP [15]. Besdes COPE, there are stll many creatve XOR-based schemes. Tebatso Nage proposed a new adaptve scheme called ACPO [15] whose obectve s to adaptvely control the watng tme for montorng packets stored n a buffer. The am of ths scheme s to acheve a tradeoff between throughput and overhead. The work n [24] consdered an algorthm wth a lower complexty than COPE, and desgned ts optmal scheduler consderng Phy and MAC constrants. [25] consdered parwse Inter-sesson Network Codng (IRNC) whch allows codng over multhops, however t only lmts codng between two orgnal packets. It s desgned to correspond wth the optmal scheduler and rate controller. The work n [27] exploted the use of drectonal antennas to network codng-based broadcastng to further reduce energy consumpton. The XOR-based and Reed-Solomon based codng algorthms were desgned by determnstc broadcast approaches to reduce the number of transmssons n the network n [28]. Abdallah Khreshah et al consdered energy effcency n lossy wreless networks wth XOR-based IRNC, and provded a heurstc to solve the IRNC problem [26]. Further more, they proposed a dfferent approach by lookng at flows or batches nstead of ndvdual packets n [29]. All of these works have made an mportant contrbuton to mprovng the XOR-based network codng algorthm. However, ther man focus s to decompose the network nto a superposton of small two-hop networks for network codng. Even though a two-hop network s more convenent for XOR-based network codng, t remans an open problem to dscover an algorthm that wll fnd an optmal superposton. If the routng protocol was aware of codng opportuntes, ths could lead to mprovng the performance of wreless networks. Based on the COPE approach, the problem of codng-aware routng and schedulng was studed by [23]. Sudpta Sengupta e propose XOR-based codng-aware routng called CA-PATH-CODE, whch s the shortest path routng wth network codng. However, the formulaton n [23] nvolves lnear programmng computed centrally. J. Le et al. proposed Dstrbuted Codng-Aware Routng (DCAR) whch can fnd avalable routng and potental codng opportuntes [16]. They defned generalzed codng condtons (GCCs) that made the network codng scheme more practcal. Utlzng the GCCs, the algorthm was proposed to detect codng opportuntes out of the two-hop range. In addton, they also dscussed the Codng-aware Routng Metrc (CRM) that can help estmate the performance of routng. B.Guo et al. formally establshed codng condtons for a general scenaro [17]. They systematcally analyzed possble codng scenaros, and developed generalzed codng condtons to ensure decodng ablty at the destnatons. These two papers pcked smlar routes that satsfed the codng condton. However, they pad lttle attenton to selectng sutable nodes to ncrease codng opportuntes and avod codng collson. S. Wang et al. desgned a scheme that consdered the connected domnatng node along wth network codng n an ad hoc network when routes were chosen [18]. Though t does have some advantages, they do not consder that multple codng nodes mght exst along a path, and that multple flows mght ntersect at one node nducng a codng collson. Furthermore, compared wth the moblty of ad hoc networks, a wreless mesh network wth fxed backbone s more sutable for utlzng the connected domnatng node to ncrease codng opportuntes [19]. In our opnon, practcal effcent routng should explot codng opportuntes wth domnatng nodes, as well as avodng a codng collson. If the domnatng nodes n the backbone were selected as the codng nodes wthout nterference, t s possble to obtan better performance.
3. THE CONNECTED DOMINATING SET ROUTING To descrbe CFCR step by step, we ntroduce the algorthm to select CDS, and provde the defnton for CDS routng n ths secton. The wreless mesh network s treated as a graph G ( V, E),whereV s the vertex set, and E s the edge set. A Connected Domnatng Set (CDS) of a graph G s a set D of vertces wth two propertes: (1) Any node n D can reach any other node n D by a path that stays entrely wthn D. That s, D nduces a connected subgraph of G. (2) Every vertex n G ether belongs to D or s adacent to a vertex n D. That s, D s a domnatng set of G. Each node n graph G ( V, E) wll be marked as mv (). Where v V.If v s a domnatng node, mv () T,otherwse mv () F. Intally, all nodes are set as F. V ' denotes the marked domnatng node set whle V' { uu Vmu, () T} G' GV ( ') ndcates the connected graph consstng of the domnatng nodes. Nv ( ) denotes the sngle-hop neghbors of node v whle Nv () { (, u vu) E}. Nv [] presents the set of node v, and ts sngle hop neghbors, whch s Nv [] Nv () {} v. Please refer to the supplement fle n Appendx A for markng steps and rules. In a strct sense, CDS routng s routng where all nodes n the path are domnatng nodes except the source and destnaton node. For example, 3, 6, 7, 9, 12 are domnatng nodes n Fgure 1. If a source node s 15 and a destnaton node s 8, the routng 15->12->9->7->8 s CDS routng, and the routng 15->12->11->8 s not because node 11 s not a domnatng node. However, CFCR focuses on ncreasng codng opportuntes nduced by domnatng nodes. To gan more codng opportuntes as well as avod codng collson, t s not practcal that all nodes along the route are domnatng nodes. Hence, n ths paper, we defne CDS routng as routng that ncludes domnatng nodes. As a result, the routng 15->12->11->8 s CDS routng because t ncludes the domnatng node 12 even though t does not satsfy the strct defnton. 4. THE CONDITION OF CODING AWARENESS Accordng to dfferent standards, network codng can be dvded nto dfferent types, such as node orented or flow orented, nter-flow or ntra-flow, and XOR-based or non XOR-based network codng [17, 2]. COPE and ACPO are typcal node orented nter-flow XOR-based schemes. However, they have two lmtatons. Frst of all, nodes can only wat for a codng opportunty and cannot proactvely fnd t durng routng. Besdes, the network codng condton states the range must be less than two hops. However nter-flow network codng s more suted for a wreless mesh network wth multple flows. In ths paper, n order to mprove practcablty, our network codng algorthm s a flow orented, nter-flow, XOR-based type. As a scheme for flow codng, we analyze the codng condton n a mult-hop scenaro. Before analyzng the network codng condton, let us defne symbols. f ndcates a data flow. a f denotes node a belongs to the routng of data flow f whle the source node s s and the destnaton node s d. Na ( ) means the sngle-hop neghbor set of node a. For(, a f ) ndcates the forwardng nodes set of nodea n the routng of data flow f. Bac (, a f ) ndcates the backward nodes set of node a n the routng of data flow f. For example, n Fgure 2, For(3, f1) {1,2}, Bac (3, f 1) {4}, For (3, f 2) {5}, Bac(3, f2) {6,7}. Generally, f two flows ntersect n a node and satsfy the network codng condtons, the packets of flow can then be encoded, and transmtted by the crossng node. Fg. 2. Mult-hop codng awareness Codng condton: For the flow f 1 and f 2 whch ntersect at node c, f the followng condtons are satsfed, network codng s feasble [17]. (1) Exstng node d1 Baccf (, 1) whle d1ns () 2 s2forcf (, 2) or d1 Forcf (, 2) (2) Exstng node d2bacc (, f2) dns () sforcf (, ) or d2forcf (, 1) 2 1 1 1 whle Fg. 1. The connected domnatng set and domnate routng 5. THE CDS-BASED AND FLOW-ORIENTED CODING-AWARE ROUTING (CFCR) IN A WIRELESS MESH NETWORK Generally, n a wreless mesh network, backbone nodes are statc wth unlmted energy. Hence, we can focus on mprovng performance.
5.1 The procedure of routng To assst understandng, we llumnate the routng procedure of CFCR n Fgure 3. To begn wth a node estmates whether t s the destnaton. Second, the destnaton node feeds back the RREP (Routng REPly) packet to the source node. Thrd, relay nodes udge whether they are domnatng nodes usng the algorthm n Secton 3 and whether they have codng opportunty usng the scheme n Secton 4. Fourth, routng wth the smallest value of CFCR s selected by the algorthm n Secton 5.4. The source node broadcasts RREQ The relay node udges whether t s a destnaton? Has the node receved the RREQ? Update the routng nformaton and broadcast the RREQ Yes The destnaton node sends RREP back accordng to RREQ Yes Drop RREQ The relay node udges whether t has potental codng opportunty The source node acheves the routng length and codng nformaton of each alternatve routng by RREP Does the alternatve routng nclude the potental codng node? Choose the shortest path The source node computes the CFCR value of each routng consderng CDS preference Send data va the routng wth smallest CFCR value Yes Yes Fg. 3. The procedure of CFCR Mark routng as alternatve routng The source node sends the confrmaton packet The relay nodes and destnaton node confrm the codng opportunty by flow state and routng nformaton The destnaton node udges whether the codng collson exsts 5.2 The confrm process of network codng Due to the possblty that dfferent flows may nterfere wth each other, the problem of codng collson does affect the performance of routng. Codng collson: When a flow ons the network, t selects the routng wth more codng opportunty whch satsfes the codng condton. However, due to excessve codng, the packets may not be decoded. Update routng nformaton and send t to the source node Yes Delete the potental codng node wth problem of alternatve routng Fg. 4. Multple potental codng nodes exst n the same routng As we know, the routng selecton process s launched va a source node n on-demand routng whch CFCR belongs to. When routng nformaton s sent backward from the destnaton node to the source node, the relay nodes can udge whether they are potental codng nodes [16]. For example, f flow f 1 and f 2 exst n fgure 4(a), R 1 s the potental codng node, and R 2 s not the potental codng node n the routng of flow f 3. Accordngly, f the stuaton occurs n Fgure 4(b), both R 1 and R 2 can potental codng nodes. As prevous analyss demonstrates, udgment of codng opportunty needs nformaton from relay nodes. However, f nformaton s added to the header of the RREQ (Routng REQuest) packet, the network load s observably ncreased by broadcastng. In order to satsfy the network codng condton wth mnmum network overload, we desgn a lghtweght confrmaton process explotng uncast to estmate whether the relay node s a potental codng node. As n Fgure 4(a), for example, there are two flows, f 1 and f 2. At some tme, flow f 3 ons the network. Accordng to the defnton n Secton 3, flow f 1 and f 3 satsfy the network codng condton n vew of node R1, and flow f 2 and f 3 satsfy the network codng condton n vew of node R 2. However, after node R 1 codes P 1 P 3, and broadcasts t, node R 2 receves P1 P, whch s not 3 the expected packet P 3. As a result, node R 2 XORs P 1 P 3 and P 2, and broadcasts P1P2 P3. In ths case, node D 2 cannot decode the packet and acheve P 2, due to excessve codng. In other words, flow f 3 nduces the codng collson problem. Fg. 5. The four steps n the confrm process Fgure 5 descrbes the nteractons between the source and destnaton node. In a sense, t s a smplfed verson of Fgure 3. There are four steps n Fgure 5
whch are RREQ, RREP, RC (Routng Confrmaton) and RC ACK (RC ACKnowlegement). In the RREQ and RREP process, the source node detects alternatve routes to the destnaton node wth potental codng nodes. Then, the source node sends uncast to the destnaton node by each alternatve routng n the RC process. In ths process, potental codng nodes n each route check whether there exsts any codng collson. After RC, ACKs provde feedback about the stuatons to the source node, and the source node then marks potental codng nodes as normal nodes f these nodes have the potental to cause a codng collson. From Fgure 5, we fnd the frst two steps are necessary n on-demand routng. The other two steps are dfferent wth exstng protocols such as DSR [21] and DCAR. It s worth notng that only RREQ needs broadcastng, and the other three steps rely on uncastng. In addton, the last two steps are only executed n alternatve routng. These two steps am to verfy whether the potental codng node nduces codng collson at low cost. As a result, t can effectvely decrease the packet loss rato by reducng the possblty of decodng falure. If routng does not contan potental codng nodes, the last two steps are unnecessary and routng becomes normal on-demand routng. Flow Lstenng Codng opportunty de Flow Lstenng Codng opportunty de f 1 f 1 +f 3 f 1 +f 3 f 3 f 1, f 2 Wth f 1 R 1 R 2 D 3 (a) f 3 f 1 +f 3 f 3 f 2 +f 3 f 1 f 1 Wth f 1 Wth f 2 R 1 k R 2 (b) Fg. 6. Routng nformaton of the confrmaton process For example, from Fgure 4(a), there are two potental codng nodes (R 1 and R 2 ) n the alternatve routng of flow f 3 after RREP and RREQ. In step three, when RC reaches node R 1, we fnd the flow satsfes the network codng condton. However, when the RC arrves at node R 2, a codng collson occurs f the packet P 1 P 3 s encoded wth P 2. Hence, R 2 cannot be a potental codng node. As a result, the potental codng node n the alternatve routng of flow f 3 s R 1 after four steps, whle step three confrms the codng condton, and step four turns back acknowledgement. Fgure 6 presents the routng nformaton stored n a source node after the confrmaton process whch manly corresponds to step three and four. Fgure 6(a) and 6(b) demonstrate the stuaton n the examples of Fgure 4(a) and 4(b) respectvely. From Fgure 6, the source node can realze the stuaton of the flow, plus the lstenng and f 1, f 2 D 3 f 3 codng opportunty n relay nodes and the destnaton node. The lstenng nodes ndcate the nodes belongng to the lstenng range of the source node. Ths nformaton s very useful to help the source node select routes. To help destnaton and source nodes estmate, each node n routng should mantan some routng nformaton. Table 1 presents the routng nformaton of flow f 3 n Fgure 4(a). The ffth row n Table 1 ndcates whether t s CDS routng. The udgment method s descrbed n Secton 3. Furthermore, nodes must store a dfferent routng table for each flow that passes through them. In ths table, we also provde the recommended sze for each part. Hence, the storage overhead of each flow s approxmately 122 bts. TABLE 1 THE DATA STRUCTURE OF ROUTING INFORMATION Flow (8b) f 3 des n routng (48b) S 3 R 1 R 2 D 3 Flow state (48b) f 3 f 1 +f 3 f 1 +f 3 f 3 Lstenng nodes (16b) D 1 D 2 CDS routng (2b) True 5.3 The routng metrc of CFCR The obectve of our algorthm s to mprove mesh network performance, whch s measured by the length of path, the flow codng beneft, and the flow codng opportunty n routng. For example, n Fgure 1, routng 15->12->11->8 has three hops and the routng 15->12->9->7->8 has four hops. If the metrc s only related to the shortest path, the former s better. However, the domnatng node has more opportunty for codng. If certan flows, such as 17->9->1 and 13->12->16 on the network, the domnatng node wll save two transmssons. As a result, the throughput of routng 15->12->9->7->8 s hgher. As the backbone of a wreless mesh network s statc and energy s unlmted, the domnatng nodes are feasble for codng to optmze performance. We ntend to desgn the routng metrc that can present these factors unformly. 1. The flow codng beneft There are two factors that nfluence the codng beneft. One s the routng length, and the number of codng nodes n the routng. The other s the matchng degree of nteractve flows. (a) The routng codng beneft In order to descrbe ths more accurately and concsely, we frst defne some symbols. F { F,1 k} denotes the alternatve routes set of the new flow, whle k presents the number of alternatve routngs. For route F, ( F ) ndcates the codng beneft of the route. dnum( F ) denotes the decreased number of transmsson n routng
F. H( F) presents the hop number of route F between the source and destnaton node. Hmn mn H( F) 1 k ndcates the hop number of the shortest route. Regardless of data matchng, the queston remans as to how much beneft the codng node can produce. As we know, network codng s technology transmttng multple packets usng broadcastng to mprove performance. For example, one transmsson can be saved f two packets are coded. If we use ths analogy, n-1 transmssons can be saved f n packets are coded n a node. For the sake of smplfcaton, we consder the decreased transmsson number as the decreased hop number. For routng F, the number of flows through the codng node a s denoted by na ( ), whch can be computed from the flow state of routng nformaton. The total number of decreased hops s cnum( F ) n( a ), 1m whle m presents the number of codng nodes n routng F. As a result, f there are codng nodes n routng, the routng codng beneft s defned as follows: cnum( F ) (( a) n( a)). Ths means the routng 1 m codng beneft s presented as follows. ( F) ( ( a ) n( a )) ( H( F) H ) 1 m It should be noted the data quantty of the flow s not easy to compute. In ths paper, we adapt an approxmate method by the length of the buffer queue to estmate the matchng factor. In practce, CFCR only needs to compute the rato between the length of the codng node output queue Qa ( ), and the length of the source node packet queue Qs (). 1 Qa ( ) Qs ( ) Qa ( ) Qa ( ) Qs ( ) Qs () 2. The codng-aware routng metrc Based on prevous analyss, we fnd the more domnate nodes n routng, the more benefts receved. Accordng to our metrc, f there are two routes wth the same beneft, CFCR wll select the one wth more domnate nodes. The reason s these domnatng nodes may provde future codng opportuntes. Accordng to equaton (4) and (5), we can obtan mn (4) (5) CFCR( F) ( ) ( ( )) ( F) cuum( F) ( H( F) Hmn ) n( a) ( H( F) Hmn) H F a n a (1) 1 (b) Data matchng In the transmsson process of a data flow, other flows coded wth ths one may end sooner or later. As a result, some codng opportuntes dsappear, and the codng beneft of the data flow wll be lower than when computed wth equaton (1). Hence, consderng the data flow matchng problem, f the flow codng opportunty dsappears when one half of the data n flow has been sent, the routng codng beneft wll be defned as follows. ( F) n( a)/2 ( H( F) Hmn ) (2) 1 m 1 m Accordngly, the matchng factor ( a ), whch denotes the rato between the data quantty of old flow B old, and the data quantty of new flow B new, n codng node a s contnually modfed. 1 Bold Bnew Bold B (3) old Bnew Bnew Therefore, the actual decreased hop number s ( a ) n( a ). The total decreased hop number s m CFCR( F ) denotes the length of route F after the codng beneft s transformed. To encourage t to choose domnate nodes, we defne an ncentve factor. The value of s adustable, and s determned by the CDS routng preference of CFCR. As a result, the CFCR( F ) s defned as follows. H( F) ( ( a )* n( a )) F s not n CDS routng 1m CFCR( F ) * H( F) ( ( a )* n( a )) F s n CDS routng 1m CFCR metrc presents the path length, the codng beneft and opportunty. The metrc also reflects the stuaton of network resource occupaton. A smaller CFCR value ndcates lower consumpton of network resources n routng. In addton, the CFCR metrc has certan dfferences wth the codng beneft of routng ( F ) n equaton (4). The most obvous dfference s that ( F ) may be postve or negatve, but CFCR( F ) s always postve. If ( F ) s mnus, t means routng consumes more network resources than routng wthout domnatng (6)
nodes. If ( F ) s plus, t means the codng beneft of routng decreases the network resource consumpton. However, CFCR( F ) denotes the length of routng after transformaton, and no matter whether t s CDS routng, CFCR( F ) cannot be less than zero. The other dfference s the route wth the smallest CFCR( F ) wll be selected as the transmttng route. ( F ) only llumnates the beneft of a routng. Even f ( F ) s the largest, the consumpton of network resources may not be the smallest. Compared wth other metrcs of exstng codng-aware routng, the proposed metrc of CFCR has the followng characterstcs. (1) The metrc of CFCR s sutable for both CDS, mult-hop codng-aware routng and non-cds, non-codng routng. For the latter, the metrc of CFCR degenerates nto the number of hops. (2) As the source node needs enough nformaton to estmate whether a codng collson exsts, and how much the codng beneft s, the metrc can be calculated after all confrmaton packets return from the destnaton node, unless t s overtme. (3) The metrc of CFCR has good extendblty. For example, f the phenomenon of losng packets s serous, the expected transmsson count can also be consdered n the metrc. 5.4 The algorthm of routng selecton In our algorthm, when the source node receves all confrmaton packets, t excludes all non-codng routng except the shortest. It then computes each CFCR value of the alternatve routng, and selects the best routng wth the smallest CFCR value. The pseudocode for routng selecton s as follows. Algorthm1The selecton of routng Input:F,1 kfrom the confrmaton packets Output: The optmzaton routng F* F*= ; H mn =; CFCR*=; for =1; 1k; ++ / / Computng the shortest path Computng the value of H(F ) f H(F ) H mn then H mn = H(F ) end end for =1; 1k; ++ / / Computng CFCR CFCR(F )=; f(smn(f )) then CFCR(F )= H mn ; f (scds(f ) scode(f )) then f(scode(f )) then / / udgng whether t s alternatve routng CFCR(F )=H(F )- ( a n( )); end fscds(f ) then CDS routng 1 m a / / udgng whether t s CFCR(F )= CFCR(F ); End End f CFCR(F ) CFCR*then CFCR*= CFCR(F ); F*= F ; End End Return F* 6. SIMULATION RESULTS AND ANALYSIS In order to verfy the performance of CFCR, we utlze NS2 to smulate and analyze the results. ACPO [15] s an extended scheme of COPE [14], whch s a typcal scheme n network codng. The CA-PATH-CODE [23] and DCAR [16] are codng-aware routngs. CA-PATH-CODE s a centralzed algorthm and DCAR s a dstrbuted algorthm, wth a smlar routng selecton process to CFCR. Hence, we compare these three schemes wth our algorthm. Please refer to the supplement fle n Appendx B for topology and parameters of the smulaton. 6.1 The nfluence of CDS Through prevous analyss, we know CFCR tends to select the domnatng nodes n routng dscovery. However, f all flows converge to a certan domnatng node, there wll be a bottleneck n the network. As a result, CFCR wll balance some flows to routng ncludng normal nodes when the network traffc s heavy. To estmate the nfluence of the CDS metrc, we ndvdually smulate the CFCR algorthm wth and wthout the CDS metrc. Fgure 7(a) and 7(b) show the movement of total throughput wth dfferent flow rates n grd and random topology. Obvously, n both topologes, we fnd that CFCR wth a CDS metrc has a bgger total throughput. Ths means the flow centralzaton of the CDS metrc ncreases network codng opportuntes as a whole. Total throughput(mbps) 3.5 3 2.5 2 1.5 1.5 N-CDS CDS 4 8 12 16 2 24 28 32 36 4 44 48 52 56 6 Flow rate(kbps) Fg. 7(a). Flow rate vs the total throughput n grd topology
3.5 3 N-CDS CDS 6 5 DCAR CFCR ACPO CA-PATH-CODE Total throughput(mbps) 2.5 2 1.5 1 Packet loss rato(%) 4 3 2.5 1 4 8 12 16 2 24 28 32 36 4 44 48 52 56 6 Flow rate(kbps) 1 2 3 4 5 6 7 8 9 1 Flow rate(kbps) Fg. 7(b). The flow rate vs total throughput n random topology On the other hand, there s an nterestng phenomena that does not always ncrease the total throughput. When the flow rate s low, the total throughput wth a dfferent metrc clmbs smoothly, and the dfference s small. When the flow rate ncreases, the total throughput grows quckly, and the dfference contnues to become larger. When the flow rate reaches a certan level, the total throughput fluctuates and decreases whle the dfference becomes smaller and smaller. The reason s the CDS metrc nduces opportuntes and nterference for network codng at the same tme. If the flow rate s too hgh, the nfluence of nterference s larger than the codng beneft. Fnally, f the flow rate s suffcently large, the new routng has to choose normal nodes. Ths means the throughput wll degrade, whch s the same as the scenaro wthout the CDS metrc. In addton to ths, because the number of selectable routes n the grd are fewer than n random topology, the dfference of total throughput s accordngly smaller, and reaches the fluctuaton and declne status qucker. 6.2 The effectve codng opportunty To present the effectve codng opportunty, we analyze the packet loss rato, encoded rato and the decoded rato respectvely. We compare the performance between DCAR, CFCR, ACPO and CA-PATH-CODE. Packet loss rato(%) 6 5 4 3 2 1 DCAR CFCR ACPO CA-PATH-CODE Fg. 8(b). The flow rate vs the packet loss rato n random topology Fgure 8(a) and 8(b) show the packet loss rato of DCAR, CFCR, ACPO and CA-PATH-CODE wth dfferent flow rates n grd and random topology. From these fgures, we see the packet loss rato s lower n the CA-PATH-CODE and CFCR than n other algorthms. When the flow rate s n low speed, the packet loss rato of CA-PATH-CODE and CFCR mantans stablty at a very low level, whle the flow rate of DCAR and ACPO contnuously ascends. There are two reasons that result n packet loss. () Network congeston nduces the buffer to overflow wth nodes. () Encoded packets can t be decoded when they reach the destnaton node. Obvously, the loss of packets s not nduced by: () a low flow rate. Ths stuaton demonstrates the CA-PATH-CODE and CFCR can more effectvely guarantee the rato of packet decodng. When the flow rate ncreases, congeston leads to a hgher packet loss rato. Even though the CA-PATH-CODE can decrease codng nterference by routng selecton, t doesn t consder the stuaton of codng collson. As a result, the packet loss rato of the CA-PATH-CODE s hgher than CFCR when the flow rate reaches a threshold. The packet loss rato of CFCR rses from 4kbps n grd topology and 5kbps n random topology. Due to more optonal routngs n random topology, the packet loss rato can mantan a stable status for a longer perod of tme. The sucessful rato of decodng 1.2 1.8.6.4 CFCR DCAR ACPO CA-PATH-CODE 1 2 3 4 5 6 7 8 9 1 Flow rate(kbps).2 Fg. 8(a). The flow rate vs the packet loss rato n grd topology Grd(5x5) 25-node random Fg. 9. The comparson of successful decodng rato
Rato of encoded packet(%).5.45.4.35.3.25.2.15.1.5 CFCR DCAR ACPO CA-PATH-CODE Grd(5x5) Fg. 1. Comparson of the encodng rato 25-node random Accordngly, Fgure 9 presents the comparson of the successful decodng rato n four algorthms. Because ACPO only deals wth two-hop codng, the successful decodng rato of ACPO s the hghest. Due to the codng confrmaton process and consderaton of codng nterference, CFCR and CA-PA-CODE has a hgher successful decodng rato than DCAR. In order to evaluate the nfluence of the codng beneft, Fgure 1 ndcates the rato of encoded packets n CFCR, DCAR, ACPO and CA-PATH-CODE. te that DCAR and CFCR have the smlar codng opportunty and ACPO has the lowest opportunty. Because the goal of the three codng-aware routng algorthms s to fnd more codng opportuntes, they have a hgher encoded packet rato. In addton, the CA-PATH-CODE adapts to a tradeoff between routng flows close to each other n order to utlze codng opportuntes and away from each other to avod wreless nterference. Hence, t has the least number of encoded packets n each of the three schemes. The CDS metrc can help CFCR fnd more codng opportuntes. However, some opportuntes are dened n the confrmaton process of CFCR. Hence, the number of encoded packets s largest n DCAR. In addton, we can refer to the supplement fle n Appendx C for some addtonal smulaton results. Fnally, we lst a comparson of the ACPO, DCAR, CA-PATH-CODE and CFCR n Table 2. In order to dstngush effectveness, we defne 1 as the worst level and 3 as the best level. TABLE 2 COMPARISON BETWEEN THE THREE SCHEMES ACPO CA-PATH-CODE DCAR CFCR Codng type de orented Flow orented Flow orented Flow orented Algorthm type Centralzed Centralzed Dstrbuted Dstrbuted Routng protocol Informaton needed by relay nodes The routng path choosng metrc Network codng range Network codng opportunty Classcal routng such as DSR or AODV Sngle hop neghbor node lst; packets n the cache of sngle hop neghbors Routng length Codng aware routng Codng aware routng Codng aware and confrm routng wth CDS consdered Neghbor nodes lst and the data queues n ther cache; the data flows through tself Routng length, network codng beneft Neghbor nodes lst and the data queues n ther cache; the data flow s through tself Routng length, network codng beneft Neghbor nodes lst and the data queues n ther cache; the data flow s through tself Routng length, network codng beneft, CDS routng Tw o-hop Mult-hop Mult-hop Mult-hop rmal Many(1) Many(3) Many(2) Packet loss rato Low (1) Low (2) Hgh Low (3) Decodng rato Medum(3) Medum(2) Medum(1) Hgh Intalzaton Smp le Smp le Complex Complex Routng overhead Lght Medum(3) Medum(2) Medum(1) Network throughput rmal Hgh(2) Hgh(1) Hgh(3) 7. CONCLUSIONS AND FUTURE WORK In ths paper, we proposed a novel CDS-based and Flow-orented Codng-aware Routng (CFCR), whch focused on utlzng the characterstcs of the wreless mesh network to enhance performance. Our scheme selected the approprate codng node from the connected domnatng set. In order to solve the codng collson problem and decrease the packet loss rato, we desgned a method to confrm potental codng opportuntes n the process of route selecton. In partcular, we desgned the routng metrc to unformly present many factors such as length of routng, the beneft of network codng and codng opportuntes. Consderng the requrement n practce, our scheme was nclned to select domnatng
nodes but not ust ones lmted to connected domnatng sets. To optmze the beneft of CDS routng and flow codng, CFCR analyzes the routng metrcs usng a formalzed method, and verfes them by smulaton. The future work of CFCR s as follow s: (1) We wll research a more precse computng method to solve the problem of data flow matchng when computng the flow codng beneft. (2) We wll compare the advantage and dsadvantage of the flow-orented and node-orented methods. We beleve the hybrd method wll perform better because the node-orented codng method deals wth a small amount of data, and the flow-orented method deals wth a large amount of data. ACKNOWLEDGEMENTS Ths work was partally supported by the Natonal Natural Scence Foundaton of Chna under Grant. 61272451, 612322, 6133219, 61173175, and the Maor State Basc Research Development Program of Chna under Grant. 214CB346. REFERENCE [1] A. Khreshah, I. M. Khall and J. 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Jng Chen receved the BS degree n computer scence n 23 from Wuhan Unversty of Technology. He also receved hs Ph.D degree n computer scence n 28 from Huazhong Unversty of Scence and Technology, Wuhan, Chna. He s an assocate professor at the Computer School, Wuhan Unversty. Hs research nterests nclude network securty, wreless networks, and moble computng. Kun He receved the MS degree n computer scence n 211 from Wuhan Unversty, Wuhan, Chna. He s a Ph.D student of Wuhan Unversty. Hs research nterests nclude network securty, and moble computng. Ruyng Du receved the BS, MS, and Ph.D degrees n computer scence n 1987, 1994 and 28, from Wuhan Unversty, Wuhan, Chna. She s a professor at the Computer School, Wuhan Unversty. Her research nterests nclude network securty, wreless network, and moble computng. Mnghu Zheng receved the BS degree n Appled Mathematcs from Hube nsttute for Natonaltes n 1995, and receved hs MS and Ph.D degree n Informaton Securty from Huazhong Unversty of Scence & Technology, Chna, n 24 and 28 respectvely. He s a professor at Hube Insttute for Natonaltes. Hs research nterests nclude cryptography, securty protocols, and network securty. Yang Xang s a full professor at the School of Informaton Technology, Deakn Unversty. He s the Drector of the Network Securty and Computng Lab (NSCLab). Hs research nterests nclude network and system securty, dstrbuted systems, and networkng. He s the Chef Investgator of several proects n network and system securty, funded by the Australan Research Councl (ARC). He has publshed more than 13 research papers n many nternatonal ournals and conferences, such as IEEE Transactons on Computers, IEEE Transactons on Parallel and Dstrbuted Systems, IEEE Transactons on Informaton Securty and Forenscs, and IEEE Journal on Selected Areas n Communcatons. Two of hs papers were selected as the featured artcles n the Aprl 29 and the July 213 ssues of IEEE Transactons on Parallel and Dstrbuted Systems. He has served as the Program/General Char for many nternatonal conferences such as ICA3PP 12/11, IEEE/IFIP EUC 11, IEEE TrustCom 13/11, IEEE HPCC 1/9, IEEE ICPADS 8, and NSS 11/1/9/8/7. He serves as the Assocate Edtor of IEEE Transactons on Computers, Securty and Communcaton Networks (Wley), and s the Edtor of the Journal of Network and Computer Applcatons. Quan Yuan s an Assstant Professor at the Department of Math and Computer Scence, Unversty of Texas-Perman Basn, TX, USA. Hs research nterests nclude moble computng, routng protocols, peer-to-peer computng, parallel and dstrbuted systems, and computer networks.