Adaptive Network Coding for Wireless Access Networks

Adptive Network Coding for Wireless Access Networks Tun Trn School of Electricl Engineering nd Computer Science Oregon Stte University, Corvllis, Oregon 9733 Emil: trntu@eecs.orst.edu Thinh Nguyen School of Electricl Engineering nd Computer Science Oregon Stte University, Corvllis, Oregon 9733 Emil: thinhq@eecs.orst.edu Abstrct We propose frmework for optimizing the qulity of service of multiple simultneous flows in wireless ccess networks vi network coding. Specificlly, we consider the typicl scenrio in which multiple flows originte from multiple sources in the Internet nd terminte t multiple users in wireless network. In the current infrstructure, the wireless bse sttion is responsible for relying the pckets from the Internet to the wireless users without ny modifiction to the pcket content. On the other hnd, in the proposed pproch, the wireless bse sttion is llowed to perform network coding by pproprite liner mixing nd chnnel coding of pckets from different incoming flows before brodcsting single flow of mixed or coded pckets to ll wireless users. Ech user then uses n pproprite decoding method to recover its own pckets from the set of coded pckets tht it receives. We show tht in principle, for the given chnnel conditions nd QoS requirements, pproprite mixing nd chnnel coding of pckets cross different flows cn led to substntil qulity improvement for both rel-time nd non-rel time flows. On the other hnd, blind mixing cn be detrimentl. We formulte this mixing problem s combintoril optimiztion problem, nd propose heuristic lgorithm bsed on simulted-nneling method to pproximte the optiml solution. Simultion results verify the performnce improvement resulting from the proposed pproch over the non-network coding nd the stte-of-the-rt network coding pproches. I. INTRODUCTION In tody communiction networks such s the Internet nd wireless d hoc networks, dt delivery is performed vi the store-nd-forwrd routing, using which, the intermedite routers do not lter the contents of pckets s they trverse hopby-hop from source to destintion. In contrst, Network coding (NC), new routing pproch pioneered by Ahlswede et l. [], llows intermedite routers to generte dt on its output link by mixing dt from multiple of its input links. In this wy, it is theoreticlly possible to chieve the throughput cpcity of multicst/brodcst session, while this is not possible with the store-nd-forwrd routing scheme. Recently, NC technique hs lso been pplied successfully to increse throughput in wireless networks [2] [4]. Hving sid tht, supporting sophisticted functionlities t intermedite routers goes ginst the end-to-end design principle [5] which rgues for simple routers to increse performnce nd sclbility. This principle hs been cited in prt for the huge success of the Internet. In this pper we propose using NC t wireless bse sttion to improve Qulity of Service for ll-type pplictions. Specificlly, we consider the typicl scenrio in which, multiple flows originte from the Internet, trverse wireless bse sttion, nd terminte t multiple users in wireless ccess network. As such, the wireless bse sttion is llowed to perform network coding by pproprite liner mixing nd chnnel coding of pckets from different incoming flows before brodcsting single flow of mixed or coded pckets to ll wireless users. Ech user then uses n pproprite decoding method to recover its own pckets from the set of coded pckets tht it receives. Studying NC in this setup is not entirely new. NC hs been suggested in the context of Wi-Fi nd WiMx networks. Indeed, Nguyen et l. [6] proposed some XOR bsed network coding schemes together with scheduler t Wi-Fi Access Point (AP) to improve throughput where feedbck is redily vilble. Nguyen et l. further extended this work to reduce dely for video trnsmission in [7]. Eryilmz et l. [8] lso proposed to use NC technique tht employs lrge finite field, rther thn XOR-bsed NC techniques, to improve throughput t the BS. In ddition, Trn et l. [9] lso showed tht employing NC jointly with chnnel coding cross the multiple wireless unicst sessions cn significntly increse the overll wireless throughput. Wht new in this pper, however, is frmework for pplying NC coding t the BS, tht optimizes for the qulity of service of both rel-time nd non-rel time trffic. We show tht in principle, for the given chnnel conditions nd QoS requirements, pproprite mixing nd chnnel coding of pckets cross different flows cn led to substntil qulity improvement for both rel-time nd non-rel time pplictions, e.g. video streming nd FTP. On the other hnd, blind mixing of flows my ctully degrde their qulities. Quntifying the performnce of flow mixing, nd finding the optiml mixing with respect to some metric, re the min objectives of this pper. We formulte this mixing problem s combintoril optimiztion problem, nd propose heuristic lgorithm bsed on simulted-nneling method, to pproximte the optiml solution. Simultions confirm the performnce improvement resulting from the proposed controlled mixing pproch over the non-network coding nd the stte-of-the-rt network coding pproches. We first introduce the bckground nd relted work. II. BACKGROUND AND RELATED WORK The notion of NC, i.e., mixing of dt t intermedite nodes to increse the overll multicst cpcity of network, ws first proposed in the seminl pper by Ahlswede et l. []. Ahlswede provided n existence proof of some network codes (method of mixing dt t intermedite nodes) tht chieve multicst cpcity. In recent yers, NC hs been lso pplied successfully to wireless d hoc networks [2],[]. A clssicl exmple first proposed by Wu et l. [] for efficient informtion exchnge in wireless d hoc network is shown in Fig.. Two nodes U nd U 2 wnt to exchnge their pckets through U 3. Pcket sent by U to U 2 is relyed through U 3, nd pcket b sent by U 2 to U is relyed through U 3. As result, U 3 hs both nd b. In n existing wireless d hoc network, U 3 hs to perform two trnsmissions, one trnsmission for sending to U 2, nd nother one for sending b to U. Now using NC, upon 978--4244-76-4//$26. 2 IEEE

b= ( b) b b b 4 3 U U 3 U 2 2 () 3 b b b U U b 3 U 2 2 b =b ( b) (b) Fig.. () Informtion exchnge using () the store-nd-forwrd scheme using 4 trnsmissions nd (b) the NC scheme using only 3 trnsmissions. S S 2 Flow 2 Fig. 3. pckets..9.7.5.4.3.2 Rel time. Time dptive 5 5 2 25 3 Number of pckets Stisfction functions of different pplictions versus the number of Flow WLAN AP/WiMAX BS () (b) Fig. 2. () A trnsmission scenrio of unicst flows in WLAN/WiMAX network. (b) Lost pcket ptterns t the receivers; in ech time slot, the first nd second pckets correspond to trnsmitted pckets of the trditionl nd NC techniques. X, O nd - denote lost, successful nd don t cre pckets, respectively. receiving nd b, U 3 brodcsts ( b) to U nd U 2. Since U hs, it cn recover b s b = ( b). Similrly, U 2 cn recover s = b ( b). Following this work, Ktti et l. [2] proposed n opportunistic XOR-bsed scheme for wireless mesh networks nd showed substntil bndwidth improvement over the current store-nd-forwrd pproch. In similr spirit, NC hs been proposed to improve throughput in wireless ccess networks by Nguyen et l. [6] nd Eryilmz et l. [8]. Fig. 2() shows simple exmple of how performing NC t wireless bse sttion cn increse the throughput. Assuming tht, there re two concurrent flows f : S D nd f 2 : S 2 D 2, both shre the sme wireless chnnel from the BS to the receivers. With the existing infrstructure, upon receiving pckets nd b, the BS uses the first nd second time slots to deliver nd b to D nd D 2, respectively. The receivers use ACK or NAK messge, respectively, to signl the BS whether they receive pcket correctly or not. Assuming tht, fter the first two time slots, the BS hs pcket loss pttern s shown in Fig. 2.(b), tht is, pcket is lost t D while pcket b is lost t D 2. If we ssume tht, it tkes one time slot to retrnsmit lost pcket, then the BS needs two more trnsmissions. In ll, 4 time slots re needed to deliver pckets nd b to D nd D 2, respectively. Now consider the rndomized NC (RNC) technique introduced by Koetter et l. in []. Upon receiving two pckets nd b, the BS genertes coded pckets by linerly combining nd b with rndom coefficients. For exmple, coded pcket c i is generted s c i = α i + β i b, () where α i nd β i re coefficients drwn t rndom from lrge finite field. b p 2 p D 2 D The two coded pckets re then brodcsted to both receivers. Assuming tht, fter the first two trnsmissions, the pcket loss pttern t the BS is the sme s before (the first pcket is lost t D, successful t D 2 while the second pcket is successful t D nd lost t D 2 ). In the third time slot, the BS genertes nd brodcsts nother coded pcket. Suppose t this time, both D nd D 2 receive the coded pcket correctly. Then, ech receiver hs received successfully totl of two coded pckets, nd will be ble to recover their own pckets by solving system of liner equtions. We ssume tht the coefficients re included in the pcket heder to enble the receiver to set up the eqution. With sufficiently lrge pcket size, this overhed is negligible [2]. Overll, RNC pproch needs only 3 trnsmissions to deliver two pckets to the intended receivers. However, it is not lwys beneficil to mix pckets from different flows (more results will be shown in the next Sections). In fct, blind mixing cn be detrimentl. This pper dvoctes n informed pcket mixing pproch to mximize the QoS requirements of different flows. III. SYSTEM MODEL AND TRANSMISSION TECHNIQUES To quntify nd compre the performnce of our informed pcket mixing pproch, we consider the following trnsmission techniques. A. Trnsmission Techniques We consider lst mile wireless scenrio consisting of one BS nd M receivers. In prticulr, ssume tht there re M flows from sources S i to destintions D i for i =, 2,...,M, nd these flows shre the wireless chnnel from the BS to the receivers. We ssocite ech destintion D i with demnd S i, the number of pckets tht the receiver D i wnts to receive per time unit. The ith flow hs pcket-level FEC coding scheme denoted s (n i,k i ) where code (n i,k i ) mens tht we use n i k i time slots to trnsmit k i pckets. Without loss of generlity, let us ssume tht BS hs enough memory to store dt for one trnsmission period N = M i= n i. In this pper we consider three techniques: unicst (UNI), Rndomized Network Coding (RNC), nd the proposed Adptive Rndomized Network Coding (ARNC). Before proceeding to the detils of nlysis, let us describe the protocol used in ech technique. Unicst (UNI): This is common trditionl pproch. In ech period, the BS uses pre-specified mximum n i time slots to trnsmit k i dt pckets for receiver D i.this pre-specifiction of FEC level cn be viewed s method to ccommodte vrying QoS levels s specified by different flows. If there re pcket losses, the BS uses n i k i redundnt time slots to retrnsmit the lost pckets. The BS switches to trnsmit dt pckets for the next receiver when it receives n ACK messge from the current receiving user or ll the time slots intended for the current receiver hve been used.

Rndomized Network Coding (RNC): Trnsmissions in RNC re clssified into two phses: the bsis nd the ugmenttion. In the bsic phse, ll M i= k i originl pckets will be trnsmitted first. The receivers cche ll the pckets, including ones tht re not intended for them. Next, the BS mix ll the pckets from ll users, to generte coded pckets nd brodcsts them to ll receivers. Agin, the n i nd k i re pre-specified s in the UNI technique. The receivers which hve lost some of their originl pckets now cn receive the coded pckets to decode their own dt bsed on the method described in Section II. Note tht, becuse pckets re not mixed in the bsis phse, receiver is ble to obtin frction of its pckets, even though it cnnot recover ll the mixed pckets in the ugmenttion phse. Proposed Adptive Rndomized Network Coding (ARNC): The BS now hs the bility to choose wht flows to be mixed together bsed on their chnnel conditions, types of services nd priorities. Note tht ll these prmeters (chnnel conditions, types of services, nd priorities) of different flows hve been considered in UNI nd RNC techniques through their ssigned FEC codes. Assuming tht the M incoming flows re prtitioned into G groups. Then, for ech group, the BS uses RNC to trnsmit dt to the receivers inside tht group only. Assuming n i nd k i re fixed s in the previous two techniques, the objective of the BS is to determine the optiml prtition to mximize the verge user stisfction over ll users. Clerly, mixing pckets from ll incoming flows my result in poor performnce due to mismtch in type of services, priorities, nd chnnel conditions, while mixing pckets of flows with similr chrcteristics might be beneficil. A precise mthemticl formultion of this prtitioning problem will be given in the next section. B. Stisfction Function Before formulting the mixing problem, metric is needed in order to quntify the performnce of different trnsmission protocols. We note tht ny suitble metric cn be used with our proposed optimiztion frmework. In this pper, we simply use stisfction function which estimtes the level of stisfction with the given qulity of service (QoS). Obviously, the function depends on the number of pckets received successfully in specified period of time, nd its type of service (ToS). In our pper, we consider two types of services: time-sensitive pplictions, e.g., video streming, nd time dptive pplictions, e.g., file trnsfer nd emil. For the time-sensitive pplictions, we ssume tht the ppliction dt is seprted into lyers. For exmple, video streming is pcketized into bsic nd enhnced lyers. In order to mintin the miniml QoS, receiver needs to receive t lest N pckets of the bsic lyer per time period. If the number of received pckets is less thn N, the QoS of the receiver decreses significntly. However, if more pckets of the enhnced lyer re received, the QoS of the receiver just increses slightly. One cn think this s more detils of picture re dded into the bsic frme. We dopt the stisfction function proposed in [3]. Tht is, γ i = F(S i ) S i <γ.n γ γ Si γn ( γ )N γ N S i <N = γ +( γ ) Si (2 γ)n ( γ )N N S i < (2 γ )N S i (2 γ )N, (2) where S i denotes the number of pckets received successfully, N denotes the miniml number of pckets to mintin stisfction fctor of γ. For time-dptive pplictions, the chrcteristic of stisfction function is different. In order to obtin stisfction fctor of γ, the receiver needs to receive t lest N pckets per time period. However, when the number of received pckets is less or greter thn N, respectively, the stisfction function decreses or increses slightly. The function is given by { γ. Si N γ i = F(S i )= S i <N (3) ( γ)n S i S i N. The stisfction functions of different types of pplictions versus the number of pckets re shown in Fig. 3. Given the stisfction functions, we cll trnsmission technique is the best technique if it produces the lrgest expected stisfction over ll users. IV. PROBLEM FORMULATION OF ADAPTIVE RANDOMIZED NETWORK CODING Due to pge limit, we only provide formultion for the ARNC pproch. The problem formultion nd nlysis of the UNI nd RNC techniques cn be found in [4]. Let G denote prtition of the incoming flows nd G denote the number of groups in G. LetM i denote the number of flows in group i. Per ech group, we use RNC technique described bove, to trnsmit the dt. Consider the ith group nd let N i = Mi j= n ij nd K i = M i j= k ij denote the totl vilble time slots nd informtion pckets need to be trnsmitted for group i. Here(n ij,k ij ) denotes the FEC code pplied to the flow trnsmitting to receiver j of group i. We hve the probbility tht receiver j of group i, D ij, cn recover its ll dt is K i k ij ( ) Pij s =( p ij ) kij Ni k ij p Ni kij l ij ( p ij ) l l k ij ( kij + s= N i k ij t=k i s ) s ( Ni k ij l= p kij s ij ( p ij ) s t ) p Ni kij t ij ( p ij ) t. (4) We now clculte the probbility tht receiver D ij recovers m out of k ij originl pckets (m <k ij ). K i ( )( ) Ni k ij kij P ij (m) = p Ni l ij ( p ij ) l. (5) l m m l=m Let rndom vrible γ ij denote the stisfction of receiver D ij. Then the verge stisfction over ll users is given by G M i γ = E c ij γ ij, (6) where c ij denotes the weighted fctor (priority) for the jth flow in group i; this fctor is proportionl to the price tht the receiver D i hs to py to the service provider; thus, the higher price, the higher priority, nd E[.] denotes the expected We buse the nottion slightly since this FEC code is some originl FEC code.

function. Now, prtition scheme is optiml if it mximizes the verge stisfction over ll users. This optimiztion problem cn be formulted s: Mximize {γ} subject to: G M i k ij = K (7) G M i n ij = N (8) γ ij for i =, 2,..., G,j =, 2,...,M i (9) G Ω () where k ij E[γ ij ]=F(k ij )Pij s + F(m)P ij (m), m= nd Ω denotes the collection of ll the nonempty-subset prtitions of flows {f,f 2,..., f M }, N nd K respectively denote the totl number of time slots nd dt pckets in one trnsmission period. V. HEURISTIC ALGORITHM FOR OPTIMAL MIXING The combintoril optimiztion problem bove is hrd. Thus, in this section, we describe simulted-nneling heuristic lgorithm bsed on the Mrkov Chin Monte Crlo (MCMC) method to pproximte the solution [5]. Simulted-Anneling Bsed Algorithm (SAB): Inthis section, we show how to ppropritely construct trget distribution, nd use MCMC to obtin the solution. Consider scenrio with M concurrent flows trversing through the BS. Let Ω be the set of ll possible prtitions, nd let S(x) be the verge stisfction of prtition x Ω. We represent ech prtition by n M-tuple group index s x =(i,j,...,k) where i indictes tht the first flow belongs to group i, the second flow belongs to the group j, nd so on. The objective is to mximize the verge stisfction over ll users. Tht is, G M i mx S(x) = mx c x Ω x Ω ij γ ij. () We should note tht the number of possible prtitions in Ω is very lrge, tht is [6] M k ( ) k Ω = ( ) i (k i) M. (2) k! i k= i= Hence, using exhustive serch, even for resonbly smll number of flows, is infesible for time-sensitive pplictions. Moreover, every time flow joins, termintes, or its chnnel condition chnges, the AP needs to reprtition gin. Insted, by using MCMC method we will show tht the time to chieve ner optiml solution will be substntilly reduced. We first define the trget distribution to be the Boltzmnn probbility density function (pdf): f(x) =Ce S(x) T B, (3) where C is normlized fctor nd T B is temperture. As seen, if S(x) is lrge, then f(x) is lrge. Thus, with high probbility, we will drw smples corresponding to S(x) which by design, will mximize the verge user stisfction. Next, we need mechnism for moving from one stte to nother in the chin. To do so, we define neighbor of prtition in the smple spce Ω: Definition 5.: A prtition y is clled neighborhood of prtition x if nd only if x nd y differ in only one element. From the bove definition, y cn be generted from x by replcing n element of x with different one drwn t rndom from the index set, 2,..., M. For exmple, M = 5, the prtition x =(,, 3, 2, 3) hs neighbor y =(,,, 2, 3) since x nd y differ in the third element. We now propose Simulted-Anneling bsed lgorithm to generte smples ccording to the trget distribution. We propose trnsition function q(x, y) from stte x to one of its neighbors. Specificlly, n element of x is selected uniformly t rndom, nd then it is replced by one of the possible indexes uniformly. Therefore, it is cler tht q(x, y) =q(y, x) = M(M ). (4) Consequently, the cceptnce probbility, i.e., the probbility tht the chin moves from the current stte x to new stte y, is given by { } f(y)q(y, x) α(x, y) = min, f(x)q(x, y) { if S(y) S(x) = e S(y) S(x) T B if S(y) <S(x) (5) As designed, the Boltzmnn distribution becomes more nd more concentrted round the globl mximizer by grdully decresing the temperture T B. Pseudocode of the Simulted- Anneling bsed lgorithm is described in Algorithm. Algorithm : Simulted-Anneling bsed lgorithm. Input: M, c i, RS(n i,k i ). Output: Optiml Flow Prtition. : STEP : Initilize the strting stte X nd temperture T. Set n =. 2: STEP 2: Generte new stte Y from the proposl q(x n,y). 3: STEP 3: 4: if S(Y ) S(X n ) then 5: X n+ = Y 6: else 7: U U(, ) {Generte uniform rndom vrible.} S(Y ) S(Xn) Tn 8: if U<α(X n,y)=e then 9: X n+ = Y : else : X n+ = X n 2: end if 3: end if 4: STEP 4: Decrese the temperture T n+ = β.t n where β <, increse n by nd repet from STEP 2 until stopping. 5: STEP 5: Return scheme x tht produces the mximl weighted-verge stisfction. Convergence: Gurntee of convergence to the trget distribution using the SAB lgorithm is shown vi the following theorem:

Theorem 5.2: Smples drwn from the SAB lgorithm form Mrkov chin whose sttes stisfy the detiled blnce eqution: π(x)p (x, y) =π(y)p (y, x) x, y Ω, (6) where π(x), π(y) re the sttionry distributions of sttes x nd y; P (x, y) nd P (y, x) re respectively the trnsition probbilities from stte x to stte y nd vice vers. Proof: The proof is omitted due to the pge limit. VI. SIMULATIONS AND DISCUSSIONS We consider relistic wireless ccess network hving diversity in pplictions nd chnnel conditions. For exmple, scenrio where different types of users re connecting to bse sttion nd some of them re moving. It is not esy to set up network with lrge number of users stisfying those conditions. Moreover, in the exhustive serch method, we need to scn ll the possible chnnel prtitions, which increses exponentilly with the number of flows, to find the optiml prtition. Therefore, in resonble network settings, we consider single-hop wireless network consisting of 5 incoming flows. In prticulr, we ssume tht there re two types of pplictions: time-sensitive nd time-dptive. The BS decides coding scheme for flow bsed on the cost which the user hd pid to the service provider. Tht is, the higher cost, the higher priority. Note tht the type nd priority of pcket cn be esily elborted in the heder of the trnsmitted pckets. In the UNI technique, the BS uses the priorities of the incoming flows to ssign their redundncies, nd they will be used in ll techniques for fir comprison. We consider the typicl WLAN chnnel with trnsmission rte of 2 Mbps, equivlent to N = 33 time slots or 33.5Kbyte pckets. In ddition, time-dptive ppliction requires 8 dt pckets per second, corresponding to rte of 27 Kbps, while time-sensitive ppliction requires 25 nd 3 dt pckets, corresponding to rtes of 37.5 nd 45 Kbps, for medium nd high QoS, to chieve the stisfction fctor of. These numbers re equivlent with the number of frmes per second in video streming. System recoverbility TABLE I PARAMETERS OF THE TRANSMISSION FLOWS. Flow ID Rx ID (n i, k i ) p i Service type Priority f D (2, 8) Time dptive f2 D 2 (2, 8).5 Time dptive f3 D 3 (22, 8).5 Time dptive 2 f4 D 4 (3, 25).5 Rel time 3 f5 D 5 (38, 3).5 Rel time 4.75.7 5.55.5.45 p =.3 UNI RNC ARNC 5 5 2 25 3 35 4 45 5 Prtition index () System recoverbility.9.7.5.4.3.2 UNI RNC ARNC...6..6.2 Pcket loss rte p Fig. 4. () System recoverbility versus prtition schemes for the cse of 5 flows. The trnsmission prmeters of the flows re summrized in Tble I, nd p = 3%. (b) System recoverbility versus pcket loss rte p, the other prmeters re given in Tble I. (b) If the number of dt pckets received t ech receiver is less thn the required pckets, its stisfction will decrese ccording to the stisfction function s described in Section III-B. The trnsmission prmeters of the incoming flows re given in Tble I. These prmeters re set bsed on the types of pplictions, priorities of the incoming flows, nd the bndwidth vilbility. In ddition, the redundncy used for ech incoming flow depends on its priority, for exmple, in our experiments we set priorities, 2, 3 nd 4 corresponding to redundncies of 5%, 2%, 25% nd 3%. Note tht these prmeters will be pplied to ll techniques. A. System Recoverbility We first show the benefit of informed mixing nd the drwbck of blind mixing by exmining the probbility tht ll the receivers cn decode their pckets. Fig. 4() shows this probbility versus ll different prtitions, i.e., wys of mixing dt when the pcket losses of receivers from D 2 to D 5 re set to 5% while tht of receiver D is 3%. We mp ech prtition to n integer on the x-xis. The number of possible prtitions is n exponentil function of the number of the incoming flows, nd is equl to the sum of the Stirling numbers of the second kind s shown in Eq. (2). We lso plot the recoverbility probbilities for UNI nd RNC techniques on the sme grph for comprison. They re indicted by stright lines since these techniques do not depend on the prtitions. Recll tht UNI does not mix pckets from different flows. RNC sends the originl pckets then the mixed redundnt pckets, so the mount of mixing here is rther miniml. As seen, RNC is clerly better thn UNI. It is interesting to note tht, t lest in this scenrio, blind mixing is generlly better thn UNI but worse thn ARNC (ARNC technique chooses the optiml prtition scheme to encode nd trnsmit pckets). This is indicted by the fct tht some of the prtitions lie bove RNC line. In fct, the proposed ARNC find precisely this best prtition by mixing flows f nd f 4 into one group while the other flows f 2, f 3 nd f 5 into nother. Note tht the objective of our optimiztion in this cse is not the user stisfction but the recoverbility probbility of ll users. Next, we evlute the probbility tht ll receivers cn recover the dt s function of pcket loss rtes. In this scenrio, the pcket loss rtes for receivers D i for i = {2, 3, 4, 5} re shown in Tble I while tht of receiver D is vried from % to 25%. The result is shown in Fig. 4(b). As shown, when p is smll, i.e., less thn 8%, mixing ll the incoming pckets is better thn trnsmitting them seprtely. This is indicted by the grph produced by RNC technique which is higher thn tht of the UNI technique. However, tht is not the cse when the pcket loss rte p is greter thn 9%, UNI technique outperforms RNC. Intuitively, this is becuse when mixing pckets from ll the flows, the receiver D with bd chnnel condition will not be ble to receive enough pckets to decode its own pckets. This lone cn led to substntil reduction on the overll recoverbility. In contrst, with proper mixing, ARNC outperforms ll other techniques in every scenrio. B. User Stisfction Fctor We now evlute the verge user stisfction s function of the chnnels conditions. In prticulr, we set p 3 = p 5 = 5%, while vrying p from % to 2%, p 2 = p +., nd p 4 = p +.2. These settings re pplied to mke the chnnel conditions more relistic in diversity wireless network. The other prmeters of the network re set the sme s before s

.4.4.4.2.2.2 UNI RNC SAB Exh Pcket loss rte: p =. UNI RNC SAB Exh Pcket loss rte: p =.3 Simultion D D2 D3 D4 D5 UNI RNC SAB Exh Pcket loss rte: p =.9 Fig. 5. Users stisfction fctors. given in Tble I. The stisfction of receiver is evluted bsed on the number of useful pckets received successfully nd the type of ppliction tht user uses. The bsic stisfctions, i.e., γ, of time-sensitive nd time-dptive pplictions re set t.5 nd when the number of useful received pckets is 5% of the intended pckets. This is becuse the time-sensitive pplictions re more vulnerble to pcket loss rtes. In the SAB lgorithm, we set initil temperture T =nd cooling down scle fctor β =.9. Fig. 5 represents the stisfction fctors of the users using different techniques. The left, middle nd right grphs represent the rnges of low, medium nd high pcket loss rtes, respectively. In the low loss rte, we set p =.. As seen, ll the techniques stisfy QoS of ll users. For ll techniques, the receivers with the first nd second highest priorities, i.e., D 4 nd D 5, obtin stisfctions pproximtely while the other receivers obtin stisfction fctor round.9. This is intuitively plusible since in this cse, resource is plenty, no optimiztion is needed, nd ll users get wht they wnt. In the medium loss rnge, i.e., p =.3, ll the techniques still cn mintin the users stisfction fctors t reltively high level. However, UNI technique strts reducing the QoS of the receivers hving high pcket loss rtes with low priorities, i.e., receivers D nd D 2, due to its seprte trnsmission method. Now, in the high pcket loss rnge, we set p =.9. As seen in the rightmost grph, ll the receivers with low pcket loss rtes, D 2 nd D 5, cn be kept with high QoS. However, when using the UNI nd RNC, the stisfction fctors of the other receivers with high pcket loss rtes, D 2 nd D 4,hve been reduced significntly. Notbly, for receiver with timesensitive ppliction, D 4, its stisfction fctor is decresed substntilly when mixing its pckets with ll other flows in the RNC technique. Obviously, ARNC with exhustive serch lwys chieves the best performnce. However, n interesting observtion is tht SAB lgorithm cn pproximte the optiml solution very well with only itertions. In prticulr, the stisfction fctor of receiver D 4 is round.78 nd bout % less thn tht of the exhustive serch, but 3% higher thn tht of UNI, the second best technique. VII. CONCLUSIONS AND FUTURE WORK We hve investigted the problem of how to mix flows or perform network coding t BS in wireless ccess network, in order to improve the QoS of the wireless pplictions. We hve shown tht blind mixing, in the sense tht ll incoming flows re mixed together, then brodcst to the receivers, my ctully reduce the qulity of wireless pplictions. We hve proposed n optimiztion frmework in which we consider the types of pplictions, service priorities nd chnnels conditions to control the mount of flow mixing, in order to mximize the verge qulity over ll flows. A heuristic lgorithm clled SAB is proposed to pproximte optiml solution efficiently. As our future work, there re mny interesting directions tht we wnt to extend from this pper. Mthemticlly finding n upper bound on the runtime of the SAB lgorithm is still theoreticl open question. Other directions included design nd nlysis of more sophisticted Mrkov chin tht llows fster convergence speed re lso worthwhile to pursue. REFERENCES [] R. Ahlswede, N. Ci, R. Li, nd R. W. Yeung, Network informtion flow, IEEE Trns. Inform. Theory, vol. 46, pp. 24 26, July 2. [2] S Ktti, D Ktbi, W Hu, H Rhul, nd M. Medrd, The importnce of being opportunistic: Prcticl network coding for wireless environments, in Proc. 43rd Annul Allerton Conference on Communiction, 25. [3] Schin Ktti, Hrihrn Rhul, Wenjun Hu, Din Ktbi, Muriel Medrd, nd Jon Crowcroft, Xors in the ir: Prcticl wireless network coding, in ACM SIGCOMM, Sept. 26. [4] T. Trn, T. Nguyen, B. Bose, nd V. Gopl, A hybrid network coding technique for single-hop wireless networks, IEEE Journl of Selected Topics in Advnced Communiction (JSAC) - Specil Issue on Network Coding for Wireless Communiction, Jun. 29. [5] J. Sltzer, D. Reed, nd D. Clrk, End-to-end rguments in system design, ACM Trnsction on Computer System, vol. 2, no. 4, pp. 277 288, November 984. [6] D. Nguyen, T. Trn, T. Nguyen, nd B. Bose, Wireless brodcst using network coding, IEEE Trnsctions on Vehiculr Technology, Feb. 29. [7] D. Nguyen, T. Nguyen, nd X. Yng, Wireless multimedi trnsmission with network coding, in IEEE Pcket Video Workshop 27, November 27. [8] A. Eryilmz, A. Ozdglr, nd M. Medrd, On dely performnce gins from network coding, in CISS, mrch 26. [9] T. Trn, T. Nguyen, nd B. Bose, A joint network-chnnel coding technique for single-hop wireless networks, in Fourth Workshop on Network Coding, Theory, nd Applictions, Jn. 28. [] Y. Wu, P. A. Chou, nd S.-Y. Kung, Informtion exchnge in wireless networks with network coding nd physicl-lyer brodcst, in Technicl Report MSR-TR-24-78, Microsoft Reserch, Aug. 24. [] R. Koetter nd M. Medrd, Beyond routing: An lgebric pproch to network coding, in Proceedings of the 22 IEEE Infocom, 22. [2] P. A. Chou, Y. Wu, nd K. Jin, Prcticl network coding, in Proc. 4st Allerton Conf. Communiction, Control nd Computing Monticello, 23. [3] Guowng Mio nd Zhisheng Niu, Bndwidth mngement for mixed unicst nd multicst multimedi flows with perception bsed qos differentition, in ICC 26, pp. 687-692, 26. [4] T. Trn, Throughput Optimiztion for Single-Hop Wireless Networks Using Network Coding, Ph.D. thesis, Oregon Stte University, 2. [5] Mrk Jerrum nd Alistir Sinclir, The mrkov chin monte crlo method: n pproch to pproximte counting nd integrtion, in Approximtion Algorithms for NP-hrd Problems, D.S.Hochbum ed., PWS Publishing, Boston, 996. [6] M. Abrmowitz nd I. A. (Eds.) Stegun, Hndbook of mthemticl functions with formuls, grphs, nd mthemticl tbles, in 9th printing. New York: Dover, pp. 824-825, 972.