GAME THEORETICAL ANALYSIS OF WIRELESS MULTIVIEW VIDEO MULTICAST USING COOPERATIVE PEER-TO-PEER REPAIR. Vicky Zhao o, Gene Cheung #

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1 GAME THEORETICAL ANALYSIS OF WIRELESS MULTIVIEW VIDEO MULTICAST USING COOPERATIVE PEER-TO-PEER REPAIR Vicky Zao o, Gene Ceung # o University of Alberta, # National Institute of Informatics ABSTRACT Receivers of wireless video broadcast can suffer catastropic decoding errors wen experiencing eavy packet losses due to transmission cannel fades. Cooperative repair scemes, exploiting te uncorrelatedness in wireless cannels of peers pysically located more tan one transmission wavelengt apart, call for neigboring peers listening to te same video stream to locally sare received packets via a secondary network. Since te likeliood of te entire peer group suffering fades in statistically independent cannels at te same time is very small, cooperative peers can collectively recover lost packets via local packet saring wit ig probability. For interactive multiview video streaming (IMVS), were a client receives and watces only one periodically selected view out of N available, te packet recovery problem is more callenging, since te likeliood of a neigboring cooperative peer watcing te same view as a cannel-corrupted peer is now /N. To enable cooperative recovery even wen neigboring peers are watcing different but correlated video views, cleverly designed redundantly coded information (RCI) suc as Distributed Source Coded (DSC) frames are inserted into streams of different views. On one and, RCI in te video streams promotes cooperative repair among peers watcing different views; on te oter, it leaves fewer available bits for cannel coding, given a fixed transmission budget, to combat cannel noise. In tis paper, using game teoretical analysis, we searc for te optimal amount of RCI in te video streams to foster te rigt balance between cooperation among peers and leftover bits for cannel coding to maximize decoding success. Experimental results sow tat expected video decoding probability can be increased noticeably compared to non-optimized resource allocation scemes. Index Terms Wireless video streaming, cooperative communication, multiview video, game teory. INTRODUCTION Wireless video streaming is known to be difficult because of stringent packet playback deadlines and unavoidable packet losses due to transmission cannel fades. It is particularly callenging in te broadcast/multicast scenario, were server cannot perform packet retransmission on a per-packet, per-client basis due to te well-known NAK implosion problem []. One solution is to employ strong forward error correction codes (FEC), so tat source packets are well protected even in te face of deep fades [2]. However, tis leaves preciously little leftover bit budget for source coding, resulting in large quantization errors and poor visual quality for te viewer. One promising alternative is cooperative peer-to-peer repair (CPR) [3], were neigboring peers listening to te same video broadcast in te primary network (suc as Wireless Wide Area Network (WWAN)) sare received video packets locally via an ortogonal secondary network (suc as ad oc Wireless Local Area Network (WLAN)). Because peers pysically located more tan one transmission wavelengt apart experience (more or less) uncorrelated cannels to te broadcasting server [4], te likeliood of an entire cooperative peer group suffering cannel fades at te same time is very small. Tat means for a sufficiently large peer group, te probability of eac packet being correctly received by at least one peer is very ig, and CPR can ten ensure te received packet is sared among all cooperative peers for perfect recovery. scene of interest server M capturing cameras WWAN multicast cannels client client client displayed views ad oc WLAN Fig.. Overview of wireless multiview video streaming system wit cooperative peer-to-peer repair. In an ortogonal development, te decreasing cost of consumerlevel cameras means video of a scene of interest can now be sot by multiple closely spaced cameras from different viewpoints. In an interactive multiview video streaming (IMVS) scenario [5], a client periodically requests one of N available views from te server as te video is played back in time uninterrupted. Wile te viewswitcing capability offers clients a new media interaction, wireless video streaming is now more difficult, since te likeliood of a neigbor watcing te same view as a cannel-corrupted peer (and ence can participate in CPR for packet recovery) is now /N. To enable cooperative packet recovery even wen neigboring peers are viewing different but correlated video views, cleverly designed redundantly coded information (RCI) suc as Distributed Source Coded (DSC) [6] frames were inserted periodically to video stream of eac view to promote cooperative repair among peers of different views [7]. On one and, added RCI in te video streams of different views promotes cooperative repair among peers watcing different views; on te oter, it leaves fewer available bits for cannel coding, given a fixed transmission budget, to combat cannel noise. In tis paper, using game teoretical analysis, we searc for te optimal amount of RCI in video streams to foster te rigt balance between cooperation among peers and leftover bits for cannel coding to maximize decoding success. Experimental results sow tat expected video decoding probability can be increased noticeably compared to non-optimized resource allocation scemes. Te outline of te paper is as follows. We first briefly discuss related work in Section 2. We ten describe our system model, including an overview of DSC and its role as RCI in cooperative recovery, in Section 3. We formalize our game teory analysis of wireless multiview video streaming using CPR in Section 4. Results and con //$ IEEE

2 Table. Definitions for Game Teoretical Analysis M number of available video views N number of local peers in cooperative repair a = N/M number of peers in eac view (integer) H v view set a peer of view v can elp or receive elp α d probability a peer cannot decode a coding unit α r probability a peer fail to receive a coding unit via WWAN multicast γ raw WWAN packet transmission loss probability R WWAN transmission budget in one video epoc g gain to stop error propagation p price for eac seller to sare a decoded frame c cost for seller to sare a decoded frame n =[n,...,n M ] n v a is number of undecodable peers in view v wo cannot decode previous unit ñ =[ñ,...,ñ M ] ñ v n v is number of potential buyers wo are undecodable peers but received current unit b =[b,...,b M ] b i ñ v is number of willing buyers wo pay for cooperative repair service l v number of successful users wo can elp buyer(s) watcing view v clusions are presented in Section 5 and 6, respectively. 2. RELATED WORK Te selected IMVS application [5] we study in tis paper is an example of ig-dimensional media data navigation [8], were only a small subset of te large original dataset is accessed along a client s own uniquely cosen trajectory. Te common tread for different applications in tis class is te callenge in acieving bot compression efficiency of media data and navigation flexibility witin te data. To be discussed in Section 3 in details for IMVS, flexible media data navigation is acieved troug insertion of cleverly designed RCI suc as DSC [6] into te coded dataset, at a modest cost in coding efficiency. Besides navigation flexibility, RCI can also promote cooperation among peers in different viewing trajectories in collaborative tasks suc as content saring and loss recovery. It is ence foreseeable tat our developed game teory analysis for IMVS ere can be extended to oter applications in tis class of ig-dimensional media data navigation, for example, interactive ligt field streaming wit cooperative cace [9]. Wile we discuss IMVS in te wireless multicast scenario, our analysis also applies to cooperative loss recovery in te unicast case, wit te stipulation tat te unicasted video contents of different views to different local clients must be syncronized in time, so tat cooperative recovery of frames in different views but same time instants can take place. Incentive mecanisms ave been well studied for peer-to-peer video streaming over Internet [0,, 2, 3], wile little as been done to stimulate user cooperation in wireless multicast applications. In [4, 5], payment based incentive mecanisms were proposed for ad oc networks were some receivers do not ave direct connection wit te source node. Tere, eac node in te network claims te cost to relay a packet, based on wic te source calculates an optimal multicast tree tat spans all receivers wit te lowest cost. Te work in [6] considered single-view 2-op multicast wit direct link between te source and all receivers, and proposed a multi-seller multi-buyer price based sceme, were users pay to receive relay service and get paid if tey forward packets to oters. 3. SYSTEM MODEL We first overview te wireless multiview video streaming system wit cooperative repair in Section 3.. We ten describe te use of DSC in te video coding structure and its role in cooperative recovery in Section System Overview Te WWAN multiview video multicast system under investigation is sown in Fig.. M cameras in a one-dimensional array captured a scene of interest from different viewing angles. A server compresses video of eac view into cunks of coding units of e frames eac (to be discussed). Server transmits different video views, syncronized in time, in different WWAN multicast cannels suc as Multimedia Broadcast/Multicast Service (MBMS) in 3GPP [7]. A peer interested in a particular view will subscribe to te corresponding multicast cannel and can switc to a neigboring view interactively by switcing multicast cannels every e frames (of epoc duration in time). Te WWAN server first multicasts an epoc wort of video to peers. Ten during WWAN transmission of te second epoc, cooperative peers, locally connected via ad oc WLAN, will excange received packets / decoded frames in te first video epoc. Wen te server multicasts te tird epoc, peers repair te second epoc, and video frames in te first epoc are played back and displayed. View-switcing delay is ence two epocs, or 2e frames Distributed Source Coding in IMVS view, 2, 3, 4, 5, 6, view 2 view 3, 2 2, 2 3, 2 4, 2 5, 2 6, 2, 3 2, 3 3, 3 4, 3 5, 3 6, 3 e = 3 e = 3 Fig. 2. Example of frame structure for M =3views and coding unit of size e =3. Circles, squares and diamonds are I-, P- and DSC frames, respectively. Eac frame F t,v is labeled by its time index t and view v. [7] proposed to encode captured multiview video frames as follows: for eac view v, encode a starting intra-coded I-frame F,v wit e trailing P-frames, eac differentially coded from previous frame, followed by one DSC frame F e+,v and e trailing P-frames, following by anoter DSC frame F 2e+,v and e trailing P-frames, etc. A frame group composed of a DSC frame and e trailing P-frames is termed a coding unit, wic is transmitted by te WWAN server in epoc time duration as described earlier. See Fig. 2 for an illustration of two coding units for tree views. [7] encodes eac DSC frame F ie+,v, i I, using (at most) 2 +decoded P-frames F ie,max(,v ),...,F ie,min(m,v+) of time instant ie in te previous coding unit as predictors. In oter words, te set of predictors views for DSC frame of view v is H v = {max(,v ),...,min(m,v + )}. By DSC s construction [6], as long as one of te predictor frames is correctly decoded and available at te client s buffer as side information, DSC frame F ie+,v can be correctly decoded. Size of a DSC frame increases wit ; typically, DSC frame size falls between a P-frame and an I-frame. Using te proposed structure wit DSC frames ( ) inserted, a client can switc from view v to a neigboring view v ± at te

3 DSC frame boundary (by subscribing to a different WWAN multicast cannel). An alternative coding structure tat uses I-frames instead can also facilitate view-switcing, but requires significantly more transmission bandwidt due to te large size of I-frames. DSC frame is ence an example of smartly designed RCI tat offers some data navigation flexibility (view-switcing in tis IMVS application) wile incurring a modest cost in coding efficiency Game Model for Cooperative Repair In tis work, we use view-switc-enabling DSC frames to also facilitate cooperative repair among peers watcing different views. We assume N local peers participate in cooperative repair. For simplicity, we assume eac view as a = N/M viewers (a is an integer). For eac given coding unit, n v a undecodable peers of view v did not decode it correctly, due to WWAN transmission losses in tat coding unit, or error propagation from previous coding unit. a n v peers of view v are potential sellers of CPR recovery service: peers wo ave correctly decoded teir coding units can elp undecodable peers by locally forwarding correctly decoded frames. Among n v undecodable peers, ñ v n v are potential buyers wo receive te next coding unit correctly, and ence ave motivation to buy cooperative repair service to ensure correct decoding of te next unit. Among ñ v potential buyers, b v ñ v coose to purcase te service to become willing buyers. See Table for a list of definitions. During cooperative repair, a potential seller of view v can sare er decoded P-frame F ie,v wit a willing buyer of view v, were v H v, so tat buyer of view v can correctly decode te next coding unit using decoded F ie,v as predictor for DSC frame F ie+,v. If a willing buyer in b v can identify suc a potential seller in a n v peers of view v, ten te buyer becomes a paying buyer and te seller a paid seller. Paying buyers collectively need to pay eac seller a price p, wic can be sared if a seller s forwarded frame can elp multiple buyers. 4. PROBLEM FORMULATION In our IMVS system, tere are two sets of players wo interact wit eac oter: potential sellers wo successful decode te previous coding unit, and potential buyers wo fail to decode te previous coding unit but ave te next coding unit correctly received. In tis section, we build a game-teoretic framework to analyze teir strategies and find te stable Nas equilibrium of te game from wic no one as incentive to deviate. We first analyze te seller game and study ow potential sellers determine weter to sare a decoded frame. Let c be te cost for a seller to sare a decoded frame wit neigbors. We assume te price p paid to a seller is larger tan te cost c to motivate peers to elp. Tus, all peers wo successfully decode te previous coding unit ave sufficient incentive to sare correctly decoded frames. We next analyze te buyer game. For eac potential buyer wo cannot decode te previous coding unit but receive te next coding unit correctly, tere are two decisions to make. First, se needs to determine if se is willing to purcase te cooperative repair service and become a willing buyer. Second, given a set of potential sellers, collectively te willing buyers need to select paid sellers to satisfy as many willing buyers requests as possible at te lowest cost. In te following, we will analyze potential buyers strategies. 4.. Seller Selection Given sets of willing buyers b v s and potential sellers a n v s, paying buyers ave incentive to minimize payment wile receiving te same requested service. Towards tat goal, we construct algoritm Seller Set Minimization to select te smallest number of potential sellers wile serving as many willing buyers as possible. Seller Set Minimization : Initialize S =0and v =. 2: if b v =0or l v =0ten 3: View v requires no action, v v +. 4: else 5: S S +. 6: s(v) max{j} s.t. v H j and n j <a. 7: v s(v)+ +. 8: end if 9: Gotostep2ifv M. In words, te algoritm operates as follows. Starting wit te first view v =, we ceck if tere exists willing buyers in view v (b v > 0), and if tere exists potential sellers wo can elp willing buyers in view v (l v > 0). Potential sellers wo can elp willing buyers in view v, l v, can be derived simply: l v = (a n j) () j H v If eiter is false, ten noting sould/can be done for view v,and we move to view v+. If bot are true, ten we identify one potential seller wit te largest view index s(v) tat can elp willing buyer(s) in view v. Tis is done so tat te same seller of view s(v) can elp as many oter willing buyers of views >vas possible to minimize te size of te seller set. We ten move to view s(v) + +,te next smallest view index not already served by seller of view s(v). Te algoritm repeats until all M views are considered. We can write te algoritm in matematical form to derive minimum number of potential sellers S(n, b) as follows: S(n, b) =S, were 0 if v>m S v = S v+ else if b v =0or l v =0 +S s(v)++ o.w. were S v is te recursive term tat counts te number of potential sellers required to satisfy willing buyers in view v to M. We now analyze te number of paying buyers. We first note tat from te analysis of te seller game and te above seller selection algoritm, a willing buyer watcing view v is a paying buyer if at least one peer watcing view in H v successfully decodes te previous coding unit, tat is, l v. We can ence write te number of paying buyers given n and b as follows: B(n, b) = were I[ ] is te indicator function. (2) M I [l v] b v, (3) v= 4.2. Wen to Buy For a potential buyer wo failed to decode te previous coding unit but successfully received te current coding unit, we analyze ow se decides weter to purcase te cooperative repair service and become a willing buyer. Assume all peers ave te same probability α d to incorrectly decode te previous coding unit and te same probability α r to incorrectly receive te current coding unit via WWAN. Let g be te gain if a potential buyer can stop error propagation and correctly decode te current coding unit.

4 In te buyer game, potential buyers interact wit eac oter in teir decision making, and te number of willing buyers depends on teir collective strategies. However, due to te broadcast nature of te wireless medium, if one peer buys a cooperative repair service, oter peers can overear te packets and enjoy a free ride. Terefore, eac peer in te buyer game faces a dilemma: on one and, every peer wants to overear te cooperative repair service bougt by oter peers and pays noting; on te oter, if nobody pays, tere will be no saring and everyone will suffer from low performance. To elp peers solve tis dilemma and stimulate cooperation, we model te buyer game as an evolutionary game [8], and derive an Evolutionarily Stable Strategy (ESS) for eac player. ESS is a stable Nas equilibrium; i.e., even toug at some time instance, some players may deviate from te ESS, tey will still converge to ESS eventually, since te one wo uses ESS will receive a iger payoff. To derive te ESS, evolution game teory provides a very useful tool, called replicator dynamics. Eac peer in te buyer game as two strategies: B ( buy ) and NB ( do not buy and free ride ). Let X v be te population sare in view v tat play strategy B (or te probability tat a peer decides to purcase te service), and te rest X v population sare in view v play strategy NB (or te probability tat a peer decides not to buy). From replicator dynamics, we ave Ẋv = η[πb v (X) π v(x)]x v,wereη is a constant step size, πv B (X) is te average payoff using strategy B, and π v(x) is te average payoff of te entire population. Te intuition beind tis differential equation is tat if buying te service gives players a iger payoff tan te average payoff of te entire population, te population sare of pure strategy B sould increase. At te stable state, tis differential equation sould be equal to 0. To find te ESS, te first step is to calculate πv B (X) and π v(x). For any potential buyer watcing view v and uses strategy B, te expected benefit πv B is: π B v = n v ñ v b v [ g ] ps(n, b) Pv pb B(n, b) (n)p v B (b ñ)p v D (n, ñ), (4) were Pv pb (n) is te probability tat given n, service request of a potential buyer in view v can be satisfied; Pv B (b ñ) is te probability tat given ñ, b are willing buyers, including at least one willing buyer of view v;andpv D (n, ñ) is probability tat WWAN transmission and coding unit decoding result in n and ñ, and tere is at least one willing buyer of view v. Pv D (n, ñ) and Pv B (b ñ) can be derived as follows: ( a )( nv ) n v ñ v )( nj ñ j ) α nk d (5) ( a Pv D (n, ñ) = n j v j ( α d ) N n k ( α ñ r) k (nk ñ α k ) r, and Pv B (ñv (b ñ) = ) (X v) bv ( X b v v)ñv bv (ñj ) (X j ) b j ( X j b )ñj b j. (6) j v j For a willing buyer watcing view v,givenn v ñ v b v, te probability tat e is a paying buyer is Pv pb (n) =I [l v]. If a peer watcing view v decides to free ride, ten is/er utility is π NB v = gpv fr n v ñ v,ñ v>b v (n, b)pv NB (b ñ)pv D (n, ñ), (7) were Pv fr is te probability tat given n and b, a peer watcing view v can free ride. Pv NB (b ñ) is te probability tat given ñ, b are te willing buyers and a peer of view v decides to free ride. We can similarly derive Pv NB (b ñ) as previously done for Pv B (b ñ): P NB v (b ñ) = ( ) ñ v (X v) bv ( X b v)ñv bv v ( ) ñ j (X j) b j b ( X j b j)ñj. (8) j j v For a potential buyer of view v, se may free ride if at least one selected paid seller can elp, tat is, Pv fr (n, b) =I(P fr v, ) (9) were P fr v,i, similar to Sv in (2), is te recursive term tat cecks if peers in view v can free-ride given willing buyers from view i to M: = 0 if i>m P fr v,i+ else if b i =0or l i =0 I(v H s(i) )+P fr v,s(i)++ o.w. (0) Ten given X =[X,,X M ], te average utility for a potential buyer of view v is π v(x) =X vπv B (X)+( X v)πv NB (X), () and X satisfies Ẋ v = f v(x) =η[π B v (X) π v(x)]x v = η[π B v (X) π NB v (X)]( X v)x v (2) for v =,, M from replicator dynamics [8]. To find te equilibrium of tis buyer game, we first find te optimal strategy X tat satisfies Ẋv = fv(x) =0for v =,,M, from wic no peer will deviate. In addition, if te equilibrium of te replicator dynamics is a locally asymptotically stable point in a dynamic system, ten te optimal strategy X is an evolutionarily stable strategy (ESS). To determine if an strategy X is stable, we first calculate te Jacobian matrix of te dynamic system in (2), wic is f f X X M J = , (3) f m X f M X M and find its eigenvalues λ,,λ M. If all te eigenvalues ave negative real parts at X,tenX is an ESS Optimizing IMVS System Performance We see tat a potential seller of view v can satisfy willing buyers of views v to v +. So if is large, a given seller can satisfy more buyers, meaning te price to purcase te seller s service can be sared by a larger buyer group. Tis is not a strictly beneficial gain, owever; a large also means te DSC frame as large number of predictors, leading to a large encoded DSC frame. For a fixed WWAN transmission budget, tat means fewer bits are left over for cannel coding, and coding unit loss probability α r increases. More specifically, let R denote te WWAN transmission budget for an epoc in number of packets. Let z be te number of packets in frames oter tan te DSC frame in a coding unit, and z () be te number of packets in a DSC frame given. Assuming z ()+z< R,tereareR (z ()+z) leftover transmission budget for forward error correction (FEC) packets to combat WWAN packet losses. If

5 Table 2. System parameters for IMVS simulations. parameter M N γ R z p z o g p value we now assume WWAN is an independent and identically distributed (iid) cannel wit raw packet loss rate γ, te probability α r() tat a coding unit is incorrectly received is: α r() = z ()+z i=0 ( R i ) ( γ) i γ R i (4) were (4) assumes FEC used is a perfect code. For z (), weassume ere te simple model were te size of a DSC frame is approximately linear wit respect to ; i.e., z () =z p + z o, were z (0) = z p, te size of a P-frame. We can derive te optimal tat leads to te largest expected utility π v(x) for an undecodable peer as follows. For given, we calculate te corresponding coding unit loss probability α r() for a fixed WWAN transmission budget R. We ten perform te previous analysis to find probabilities X v s potential buyers of views v s will purcase cooperative repair service. Te expected utility π v(x) is ten computed using (). Te process is repeated for different values of to find optimal. 5. EXPERIMENTATION 5.. Experimental Setup In our simulations, we consider an IMVS system wit M =3views and N =6peers. Tat means eac view as a = N/M =2users. For simplicity, we assume tat users do not switc views for te duration of te experiment. We assume initially raw WWAN packet loss rate γ =0.5, and a WWAN transmission budget of R = 0 packets per video epoc. Te size of a P-frame is z p =3packets, and assuming z 0 =, te sizes of a DSC frame for =and 2 are 4 and 5 packets, respectively. We assume tere are 29 P-frames following a DSC frame in a coding unit. We assume user utility gain to stop error propagation is g =.0, and te price to pay eac seller is p =0.8. We consider te simplified scenario were α d = α r, tat is, te probability to incorrectly decode te previous coding unit and tat to incorrectly receive te current coding unit are te same. Table 2 sows te system parameter values used for our experiment Experimental Results Fig. 3 plots X v and te fraction of users wo successfully decode te current coding unit after cooperative repair (including tose wo succeed in WWAN broadcast) for different DSC span. First, we observe tat for =0, i.e., wen DSC frame is actually a P-frame, te probability of peers in any view buying te cooperative repair service is. Tis is because wen DSC frame is not used, peers of one view cannot free-ride on repair service of a different view, and given a =2, not purcasing te service will necessarily mean not being able to decode te current coding unit. We next observe tat for, undecodable users of view 2 ave te smallest probability to buy, wile undecodable users of view always become buyers. Tis is because wit our system setup, undecodable users of view 2 can free ride as long as tere is a paying buyer of any view; wile users of view ave te smallest probability to free ride since our seller selection algoritm in Section 4. always look for a potential seller wit te largest view s(v) tat can Table 3. Fraction of successful viewers for different γ s. γ =0.5 γ =0.7 γ =0.20 = = = elp buyer(s) in view v. In addition, from Fig. 3, wen =2,te probability of undecodable users of view 2 and 3 buying te service is zero, since bot groups can free-ride from buyer(s) of view. We also study te impact of raw WWAN packet loss probability γ on te system. Table 3 sows te fraction of successful users (of any view) for different γ. We observe tat toug te resulting fraction of successful users vary quite dramatically, te optimal DSC span tat maximizes user decoding success is for tis range of γ. Tis sows tat toug a larger creates a larger incentive for peers to sare te cost of a seller s frame forwarding service, te resulting larger unsuccessful coding unit transmission probability α r creates a more serious problem and drags down te system-wide performance. Using our derived game teoretical analysis, we are able to find tis optimal DSC span to optimize system-wide performance. 6. CONCLUSION In tis paper, we study system optimization of a wireless multiview multicast system using game analysis. An interactive multiview video streaming (IMVS) system allows a client to switc to neigboring video views as te video is played back uninterrupted by periodically re-subscribing to different WWAN multicast cannels. Distributed source coding (DSC) frames are periodically inserted into te video streams of different views to facilitate viewswitcing witout resorting to bandwidt-expensive intra-coded I- frames. DSC frames are also used to promote peer cooperation, so tat clients, locally connected via ad oc WLAN, wo are watcing different video views can neverteless sare decoded frames to alleviate error propagation. Due to te wireless broadcast property, a sared decoded frame can be overeard by multiple receiving peers, meaning a paid cooperative repair service by a single seller can be overeard by multiple willing buyers, but also free-riders. We derive Nas-equilibrium-stable solutions were te optimal proportion of peers suffering decoding losses in eac view will opt to purcase te cooperative repair service from potential sellers. We ten find te optimal set of predictors for DSC frames tat maximizes user utility, balancing te overead in encoding DSC frames and its ability to promote cooperation among peers. 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