Coalitional Game Theoretic Approach for Cooperative Transmission in Vehicular Networks
aa r X i v : . [ c s . G T ] F e b Coalitional Game Theoretic Approach forCooperative Transmission in Vehicular Networks
Tian Zhang †∗ , Wei Chen † , Zhu Han ‡ , and Zhigang Cao †† State Key Laboratory on Microwave and Digital Communications,Tsinghua National Laboratory for Information Science and Technology (TNList)Department of Electronic Engineering, Tsinghua University, Beijing 100084, China ∗ School of Information Science and Engineering, Shandong University, Jinan 250100, China ‡ Department of Electrical and Computer Engineering, University of Houston, Houston, TX 77004Email: [email protected], { wchen, czgdee } @tsinghua.edu.cn, [email protected] Abstract —Cooperative transmission in vehicular networks isstudied by using coalitional game and pricing in this paper.There are several vehicles and roadside units (RSUs) in thenetworks. Each vehicle has a desire to transmit with a certainprobability, which represents its data burtiness. The RSUs canenhance the vehicles’ transmissions by cooperatively relayingthe vehicles’ data. We consider two kinds of cooperations:cooperation among the vehicles and cooperation between thevehicle and RSU. First, vehicles cooperate to avoid interferingtransmissions by scheduling the transmissions of the vehiclesin each coalition. Second, a RSU can join some coalition tocooperate the transmissions of the vehicles in that coalition.Moreover, due to the mobility of the vehicles, we introduce thenotion of encounter between the vehicle and RSU to indicatethe availability of the relay in space. To stimulate the RSU’scooperative relaying for the vehicles, the pricing mechanism isapplied. A non-transferable utility (NTU) game is developed toanalyze the behaviors of the vehicles and RSUs. The stability ofthe formulated game is studied. Finally, we present and discussthe numerical results for the 2-vehicle and 2-RSU scenario, andthe numerical results verify the theoretical analysis.
I. I
NTRODUCTION
Vehicular networks, from which drivers can obtain usefulmessages such as traffic conditions and real-time informationon road to increase traffic safety and efficiency, has gainedmuch attention [1]. Meanwhile, vehicular networks can alsoprovide entertainment content for passengers and collect datafor road and traffic managers. In vehicular networks, vehi-cles and roadside units (RSUs) can communicate with eachother through vehicle-to-vehicle (V2V), roadside-to-vehicle(R2V), vehicle-to-roadside (V2R) and roadside-to-roadside(R2R) communications.As an important modus operandi of substantially improvingcoverage and communication efficiency in wireless networks,cooperative transmission has gained considerable attentionrecently. In cooperative communications, some neighboringnodes can be used to relay the source signal to the des-tination, hence forming a virtual antenna array to obtainspatial diversity. Decode-and-forward (DF) is a commonly-used cooperative protocol [2]. In DF relaying, the relay nodefirst decodes the received signal from the source, re-encodesit, and then forwards it to the destination. For the purposeof improving the system spectral efficiency, the cooperative relaying with relay selection [3], [4] has been introduced onone hand. On the other hand, the non-orthogonal relayingprotocols have been investigated [5].Since the coalitional game theory provides analytical toolsto model the behaviors of rational players when they cooper-ate, it is a powerful tool for designing robust, practical, effi-cient, and fair cooperation strategies and has been extensivelyapplied in communication and wireless networks, which in-cludes the vehicular networks [6]. In [7], the coalitional gametheory was utilized to investigate the cooperation betweenrational wireless users, and the stability of the coalition wasanalyzed. Cooperative transmission between boundary nodesand backbone nodes was studied based on coalition games in[8]. In [9], bandwidth sharing was studied by using coalitionformation games in V2R communications. In [10], the coali-tion formation games for distributed cooperation among RSUsin vehicular networks were studied. In [11], the coalitionalgame theory was applied in studying how to stimulate messageforwarding in vehicular networks. The coalition formationproblem for rational nodes in a cooperative DF network wasformulated in [12]. The coalitional game theoretic approachfor secondary spectrum access in cooperative cognitive radionetworks was studied in [13]. The stability of cooperationin multi-access systems was analyzed in [14]. In [15], thecoalitional game was utilized to study the cooperative packetdelivery in hybrid wireless networks. In cooperative relaynetworks, there are costs (e.g., energy consumption, opera-tional cost, bandwidth) at the relays for forwarding the otherusers’ signals. Hence, a proper compensation mechanism isindispensable to provide the relays with incentives to forwardthe signals. Pricing mechanism was studied accordingly [16].In this paper, we investigate the cooperative transmissionin vehicular networks under the framework of the coalitionalgame theory and pricing mechanism. On one hand, the vehi-cles can form coalitions to cooperatively schedule their trans-missions. On the other hand, the RSUs can join the coalitionsto cooperate the transmission of the vehicles. In the consideredscenario, as the vehicles are dynamic with respect to theRSUs, the vehicles and RSUs may be very far away. In thiscase, the cooperative transmission may be unprofitable if notimpossible. Accordingly, we propose the notion of encounter oPRSU 2 RSU 1RSU 3 (cid:57)(cid:72)(cid:75)(cid:76)(cid:70)(cid:79)(cid:72)(cid:3)(cid:20) (cid:57)(cid:72)(cid:75)(cid:76)(cid:70)(cid:79)(cid:72)(cid:3)(cid:21) (cid:57)(cid:72)(cid:75)(cid:76)(cid:70)(cid:79)(cid:72)(cid:3)(cid:22)
Fig. 1. Cooperative transmission with coalitions in vehicular networks between the vehicles and RSUs. Two conditions should besatisfied before a RSU cooperates a vehicle’s transmission: 1)the RSU and vehicle are in the same coalition; 2) the RSU andvehicle encounter each other. When the two conditions hold,the RSU can use cooperative transmission to help the vehicle.In return, the vehicle should pay for the RSU. We considerthe problem as a non-transferable utility (NTU) game. Thestability of the existing coalition is studied. Numerical resultsdemonstrate the efficiency of the proposed game.The reminder of the paper is structured as follows. SectionII presents the system model. Next, the coalitional gameapproach for the considered problem is proposed in SectionIII. We first formulate a NTU game to model the cooperativetransmission in the considered vehicular network, and thenthe analysis of the proposed coalitional game is carried out.In Section IV, the numerical results are discussed. Finally, weconclude the paper in Section V.II. S
YSTEM MODEL
Consider a wireless network in Fig. 1, which consists ofa network operator (NoP), K vehicles, and M RSUs. Thevehicles and RSUs can form coalitions and the RSUs can co-operate the transmissions of the vehicles when they are in thesame coalition. Let denote the NoP, and V = { , , · · · , K } and R = { K + 1 , , · · · , K + M } represent the set of thevehicles and RSUs, respectively.We consider the uplink communications from the vehicleto the NoP. Each i ∈ V has its transmission range d i . WhenRSU i ∈ R is in the transmission range of vehicles j ∈ V , wecall i encounters j . Vehicle i ∈ V is active in each time-slotwith probability p i , independently of other vehicles. Whentwo or more vehicles transmit simultaneously, it is called acollision, and we suppose that the transmissions will fail whena collision occurs. The cooperative protocol utilized in thispaper is the non-orthogonal decode-and-forward (NDF) [5].In the first half of the time-slot, the source transmit to the The concept of relay node has been introduced in IEEE 802.16j forWiMAX networks. It is assumed that within the transmission range, the correct decoding atthe receiver can be guaranteed. relay and destination; In the second half, the relay decodes andforwards the source message. Meanwhile, the source transmitsa new message to the destination.We assume that vehicles in the same coalition can cooperateto schedule the transmissions, and only one vehicle transmitsat a time to avoid interference. In each coalition, a schedulerdetermines the active user that can transmit while other activeusers remain silent. When vehicle j is scheduled to transmit ata time-slot, it selects one RSU from the feasible RSU set (i.e.,the set of RSUs that are in the same coalition with vehicle j and encounter vehicle j ) as relay to assist its transmission. Then one vehicle only employs at most one RSU as relay foreach transmission. Furthermore, as no more than one vehicleis scheduled to transmit at a given time-slot, one RSU assiststhe most one vehicles at a given time-slot. When the vehicle j utilizes RSU i as relay for its transmission, RSU i chargesvehicle j with price ξ ij per transmission.When some vehicles and RSUs form a coalition, the ve-hicles would share the channel with each other in TDMAmode, and they need to pay for the RSU’s relaying. However,the vehicles can avoid collision and gain diversity as well asrate increase. On the other hand, although there are costs inreceiving and forwarding the vehicles’ signals [17], the RSUscould achieve revenues by charging the vehicles. In a word,both vehicles and RSUs have incentives to form coalitions.III. C OALITIONAL GAME APPROACH
In this section, we first formulate the coalitional game inSection III-A, and then we analyze the formulated game inSection III-B.
A. Coalitional game formulation
A coalitional game G is uniquely defined by the pair ( N , v ) ,where N is the set of players, any non-empty subset S ⊆ N is called a coalition, and v is the coalition value, it quantifiesthe worth of a coalition in a game.In our paper, the players are the vehicles and RSUs, i.e., N = V ∪ R . S ⊆ N is a coalition. Define S ∩ V := S u and S ∩ R := S r . Consider a time-slot, let i ↔ j denote i encounters j during the whole time-slot and P ij = Pr { i ↔ j } . The datarate increase of vehicle i with the cooperation from the RSU j is denoted as ∆ ij . Formally, the scheduler in S is a map f S : 2 S → S such that f S (Ψ) ∈ Ψ for all Ψ ⊆ S and f S (Ψ) = ∅ iff Ψ = ∅ . The average effective throughput for vehicle i can beexpressed as T i ( S ) = E Ψ (cid:8) f S (Ψ)= { i } (cid:9) (1 + ζ i ( S )) Y j ∈ V \ S u (1 − p j ) , where E Ψ (cid:8) f S (Ψ)= { i } (cid:9) denotes the ratio of time-slots thatvehicle i is chosen to transmit. For example, we can assume f S (Ψ) chooses the minimal element from the set of active We assume that the selection is performed according to a uniformprobability distribution for simplicity. Similar definitions can be found in [14]. ehicles Ψ . Let S u = (cid:8) s , · · · , s | S u | (cid:9) with s > · · · > s | S u | ,then E Ψ n f S (Ψ)= { s | Su | } o = p s | Su | (1)and E Ψ (cid:8) f S (Ψ)= { s k } (cid:9) = p s k | S u | Y i = k +1 (1 − p s i ) , k = 1 , · · · , | S u | − . (2) ζ i ( S ) is the average increase of data rate for vehicle i and itis given by ζ i ( S ) = X j ∈ S r ∆ ij P ji Y k = j ∈ S r (1 − P ki )+ X j The payoff of vehicle i is determined by u i ( S ) = α i T i ( S ) − β i P i ( S ) . For RSU j in S , the revenue charged from the vehicles canbe given by R j ( S ) = X i ∈ S u E Ψ (cid:8) f S (Ψ)= { i } (cid:9) η ij ( S ) ξ ji , (3)where η ij ( S ) is the probability that vehicle i employs RSU j as its relay for transmission, and it is given by η ij ( S ) = P ji (cid:20) Y k = j ∈ S r (1 − P ki )+ 12 X k = j ∈ S r P ki Y l = j,l = k ∈ S r (1 − P li )+ 13 X k In this section, we first present two observations. Next, weanalyze the stability of the game and propose a sufficientcondition for the existence of the core.In the beginning, we have the following observation. Observation 1. Let f ( S ) = P i ∈ S u u i ( S ) + P j ∈ S r ˜ u j ( S ) denotethe sum payoff of S . When γ j = 1 and β i = 1 , we have f ( S ) = P i ∈ S u α i T i ( S ) − P j ∈ S r µ j C j ( S ) . That is to say, thepricing has no effect on the sum payoff in this case. Proof: First we can prove that χ i = P j ∈ S r η ij ( S ) ξ ji . Then E Ψ (cid:8) f S (Ψ)= { i } (cid:9) χ i = E Ψ (cid:8) f S (Ψ)= { i } (cid:9) X j ∈ S r η ij ( S ) ξ ji ( a ) = X j ∈ S r E Ψ (cid:8) f S (Ψ)= { i } (cid:9) η ij ( S ) ξ ji . (6) a ) holds since E Ψ (cid:8) f S (Ψ)= { i } (cid:9) is irrelevant to j ∈ S r . Next,based on (6), we can derive X i ∈ S u E Ψ (cid:8) f S (Ψ)= { i } (cid:9) χ i = X i ∈ S u X j ∈ S r E Ψ (cid:8) f S (Ψ)= { i } (cid:9) η ij ( S ) ξ ji . (7)Exchanging the summation order on the right side, we get X i ∈ S u P i ( S ) = X j ∈ S r R j ( S ) . (8)When γ j = 1 and β i = 1 , f ( S ) = P i ∈ S u α i T i ( S ) − P j ∈ S r µ j C j ( S )+ P i ∈ S u P i ( S ) − P j ∈ S r R j ( S ) . Using (8), we derive f ( S ) = P i ∈ S u α i T i ( S ) − P j ∈ S r µ j C j ( S ) . Remark: Observation 1 reveals the fact that the total rev-enues obtained by the RSUs equal to the payments of all thevehicles. In addition, we obtain the second observation. Observation 2. A coalition S should have at least one vehicle.Otherwise, ˜ u i ( S ) = 0 = ˜ u i ( { i } ) and v ( S ) = P i ∈ S ˜ u i ( S ) = 0 .That is to say, when there are only the RSUs, the RSUs haveno stimuli to form coalitions and each RSU will act alone. Proof: When | S u | = 0 , we get R j ( S ) = 0 and C j ( S ) =0 according to (3) and (5), respectively. Thus, ˜ u i ( S ) = 0 .Specifically, ˜ u i ( { i } ) = 0 . As ˜ u i ( S ) = ˜ u i ( { i } ) in this case,each RSU will act alone. Remark: The function of the RSU is relaying the vehicle’ssignal. So when there is no vehicle, it is meaningless to grouponly the RSUs together. On the other hand, when there is no RSU in a coalition S , i.e., S ⊆ V , u i ( S ) = E Ψ (cid:8) f S (Ψ)= { i } (cid:9) Q j ∈ V \ S (1 − p j ) for i ∈ S and v ( S ) = P i ∈ S u i ( S ) > . Specially when S = { i } ,we derive u i ( { i } ) = p i Q j ∈ V \{ i } (1 − p j ) . Hence, when ∃ S ⊆ V & S ∋ i satisfying u i ( S ) > u i ( { i } ) , the vehicles willform coalitions to improve the utility. Specifically, let S = { s , · · · , s | S | } with s > · · · > s | S | , based on (1) and (2), wecan derive that if ≥ Q j ∈ S \{ s i } (1 − p j ) , i = | S | ; Q j ∈ S \{ si } (1 − p j ) | S | Q k = i +1 ( − p sk ) , otherwise , (9)forming coalition S is profitable. Specially, when p i = p , i.e.,all vehicles have the same active probability, we can derive that(9) holds, then forming coalitions is always profitable in thecase. Although forming S may be not optimal, it is at least better than actingalone. Next, as the core is one of the most important stabilityconcepts defined for coalitional games, we investigate the coreof our proposed coalitional game in the following.The definition for the core of our coalitional game is givenas follows. Defination 1. The core of ( V ∪ R , v ) is defined as C = (cid:8) x ∈ v ( V ∪ R ) : ∀ S, y ∈ v ( S ) , s.t. y i > x i , ∀ i ∈ S (cid:9) .The following observation gives a sufficient condition forthe existence of the core. Observation 3. The core of ( V ∪ R , v ) is nonempty once thefollowing conditions hold ( S ⊂ V ∪ R ):1) α i > , β i > , γ j > , and µ j > .2) α i T i ( S ) > β i P i ( S ) or γ j R j ( S ) > µ j C j ( S ) .3) α i T i ( V ∪ R ) − β i P i ( V ∪ R ) > α i T i ( S ) − β i P i ( S ) , and γ j R j ( V ∪ R ) − µ j C j ( V ∪ R ) > γ j R j ( S ) − µ j C j ( S ) . Proof: When 1) holds, we can find α i , β i , γ i , and µ j to satisfy 2). If 2) does not holds, we have u i ( { i } ) = Q j ∈ V / { i } (1 − p j ) ≥ ≥ u i ( S ) for i ∈ S u and ˜ u j ( S ) ≤ u j ( { j } ) for j ∈ S r . Then, each vehicle and RSU will actalone. In this case, the core is empty. When 3) holds, wecan prove that ( V ∪ R , v ) is balanced [18]. Thus, the core isnonempty according to the Bondareva-Shapley theorem [19]. Remark: The core is possibly non-empty in practice. Forexample, when the considered vehicles wait for the traffic light,the vehicles as well as the nearby RSUs are probable to formthe coalition together. IV. N UMERICAL RESULTS In this section, we demonstrate the numerical evaluationsfor the performance of the cooperative transmission schemewith coalitions. In the simulations, we assume that the nodesare uniformly located in a square area of km × km . Thenetwork topology changes at the beginning of each time-slot and remains static during the whole time-slot. That isto say, the locations of the nodes are generated accordingto the uniform distribution at the beginning of a time-slot,the locations do not change during the time-slot, and we re-generate the locations at the beginning of the next time-slot.We consider the scenario that there are 2 vehicles (vehicle 1and vehicle 2) and 2 RSUs (RSU 3 and RSU 4) in the area.Fig. 2 shows the encounter probability with different trans-mission ranges for vehicle 1 and vehicle 2. In the simulations,we set d = d = d and the probability is obtained from time-slots. We can observe that RSU 3 & vehicle 1, RSU 4& vehicle 1, RSU 3 & vehicle 2, and RSU 4 & vehicle 2have similar encounter probabilities. It is because that sinceall nodes are uniformly distributed, vehicle 1 and vehicle 2 aswell as RSU 3 and RSU 4 are exchangeable in location. Inaddition, we can see that the encounter probability increaseswith the increase of the transmission range. In the evaluations The area has been divided to × . d E n c oun t e r p r obab ili t y RSU 3 & vehicle 1RSU 4 & vehicle 1RSU 3 & vehicle 2RSU 4 & vehicle 2 Fig. 2. Encounter probability with different transmission rangesTABLE IP OSSIBLE COALITIONAL STRUCTURE C : { } C : { } , { } C : { } , { }C : { } , { } C : { } , { } C : { } , { } , { }C : { } , { } , { } C : { } , { } C : { } , { }C : { } , { } , { } , { } C : { } , { } C : { } , { } , { }C : { } , { } , { } C : { } , { } , { } C : { } , { } , { } d U t ili t y vehicle 1vehicle 2RSU 3RSU 4 Fig. 3. Utility performance in C of utility performance, we set ∆ ij = 0 . , p i = 0 . , ξ ij = 1 . , c fji = 0 . , c rji = 0 . , α i = 10 , β i = 1 , and γ j = µ j = 1 . Thereare totally 15 coalitional structures for 2 vehicles and 2 RSUsas illustrated in Table I. Using Observation 2, we need notconsidering C and C . Meanwhile, as vehicle 1 and vehicle2 as well as RSU 3 and RSU 4 are exchangeable, we onlyneed to consider C - C . Fig. 3 plots the utility performance for 4 nodes whenthey form the coalition together( C ). The utility performanceincreases when we increase the transmission range. Thereason is that the encounter probability will increase whenthe transmission range increases (see Fig. 2). Consequently, vehicle 1 and vehicle 2 are not exchangeable because of the schedulingwhen they are in the same coalition. However, as exchanging elements in thesame coalition is meaningless, it does not affect the analysis here. C is similar as C ; C is similar as C ; C , C and C are similar as C ; and C is similar as C . d U t ili t y vehicle 1vehicle 2RSU 3RSU 4 (a) C d U t ili t y vehicle 1vehicle 2RSU 3RSU 4 (b) C Fig. 4. Utility performance in C and C d U t ili t y vehicle 1vehicle 2RSU 3RSU 4 (a) C d U t ili t y vehicle 1vehicle 2RSU 3RSU 4 (b) C Fig. 5. Utility performance in C and C the probability of cooperative transmission will increase. Ascooperative transmission could benefit both the vehicle andRSU, the utility performance increases. Another observationis that the utility performance for vehicle 1 is better than thatof vehicle 2, and the utility performance for RSU 3 and RSU4 is similar. This can be explained as follows: when vehicle1 and vehicle 2 are in the same coalition and both of themare active, the scheduler selects vehicle 1 to transmit, i.e.,the vehicle 1 has higher transmission priory than vehicle 2.Consequently, the utility performance for vehicle 1 is better.In contrast, RSU 3 and RSU 4 have same priority in the relayselection of vehicle and they have same encounter probabilitywith vehicle 1 (or vehicle 2), the same relaying price, and thesame cost for receiving and forwarding, so they have similarutility performance.Fig. 4(a) - Fig. 6(a) illustrate the utility performance for C - C , respectively. As compared with Fig. 3, the utilityperformance of vehicle 1 evidently decreases, and the util-ity performance of vehicle 2, RSU 3, and RSU 4 slightlydecreases in Fig. 4(a). Based on the scheduling scheme, thesuccessful transmission probability of RSU 1 is p = 0 . in C . In contrast, it is p × (1 − p ) = 0 . in C . That is to say,the successful transmission probability obviously decreases.Thus, the utility decreases evidently. With respect to vehicle2, the successful transmission probabilities are the same in C and C (i.e., (1 − p ) × p = 0 . ). However, there are noRSUs that are in the same coalition with vehicle 2 in C . Thenno cooperative transmission can be implemented for vehicle Under the simulation settings, cooperative transmission is preferable forboth vehicle and RSU. d U t ili t y vehicle 1vehicle 2RSU 3RSU 4 (a) C d U t ili t y vehicle 1vehicle 2RSU 3RSU 4 (b) C Fig. 6. Utility performance in C and C 2, and the utility performance decreases accordingly. In C ,both vehicle 1 and vehicle 2 may utilize RSU 3 (or RSU 4)for cooperative transmission. In contrast, only vehicle 1 mayutilize RSU 3 (or RSU 4) in C , i.e., the probability of beingutilized as a relay will decrease in C . As being utilized as arelay is profitable in our settings, the utility performance ofRSU 3 (RSU 4) decreases.Comparing Fig. 4(b) with Fig. 5(a), it can be observed thatthe utility performance of vehicle 1 is much better in Fig. 4(b),and the utility performances of the other three nodes (vehicle2, RSU 3, and RSU 4) are the same. It can be explained byusing (9). Firstly, S = { , } with s = 2 and s = 1 . Thenwe have Q j ∈ S \{ s i } (1 − p j ) = 1 − p = 0 . < , i = 2; Q j ∈ S \{ s i } (1 − p j ) " | S | Q k = i +1 (1 − p s k ) − = (1 − p )[1 − p ] − = 1 , i = 1 . (10)That is to say, the utility of RSU s = 1 will increase and theutility of RSU s = 2 will remain the same when they formthe coalition { , } .Finally, we can see that the utility performance in C is better than other coalitional structures and the utility ispositive in all coalitional structures. Meanwhile, α i = 10 > , β i = 1 > , and γ j = µ j = 1 > . Thus, the conditions inObservation 3 hold. Applying Observation 3, we claim that thecore of the coalitional game is nonempty under the simulationsettings. Furthermore, ( u ( C ) , u ( C ) , u ( C ) , u ( C )) is inthe core. V. C ONCLUSION Cooperation among vehicles and cooperation between ve-hicle and RSU in vehicular networks have been studied. Wepropose the notion of encounter to characterize the relativelocation between the vehicle and RSU when the vehicle islocomotive. Utilizing the coalitional game theory and pricingmechanism, we have formulated a NTU coalitional game toanalyze the behaviors of the vehicles and RSUs. Moreover, thestability of the proposed game is studied. A sufficient conditionfor the non-empty of the core is obtained. Numerical resultsfor the 2-vehicle and 2-RSU scenario verify the theoreticalanalysis. A CKNOWLEDGMENT This work is partially supported by the National BasicResearch Program of China (973 Program) under Grants2013CB336600 and 2012CB316001, the National Nature Sci-ence Foundation (NSF) of China under Grants 60832008,60902001, and 61021001, US NSF CNS-1117560, CNS-0953377, ECCS-1028782, CNS-0905556, CNS-1265268, andQatar National Research Fund.R EFERENCES[1] G. Karagiannis, O. Altintas, E. Ekici, G. J. Heijenk, B. Jarupan, K. Lin,and T. Weil, “Vehicular networking: a survey and tutorial on requirements,architectures, challenges, standards and solutions,” IEEE Commun. Surv.Tut. , vol. 13, no. 4, pp. 584-616, 2011.[2] J. N. Laneman, D. N. C. Tse, and G. W. Wornell, “Cooperative diversity inwireless networks: efficient protocols and outage behavior,” IEEE Trans.Inf. 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