VIDEO streaming over multihop wireless networks has

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1 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 6, NO. 12, DECEMBER Dstorton-Drven Vdeo Streamng over Multhop Wreless Networks wth Path Dversty Xaoln Tong, Yanns Andreopoulos, Member, IEEE, and Mhaela van der Schaar, Senor Member, IEEE Abstract Multhop networks provde a flexble nfrastructure that s based on a mxture of exstng access ponts and statons nterconnected va wreless lnks. These networks present some unque challenges for vdeo streamng applcatons due to the nherent nfrastructure unrelablty. In ths paper, we address the problem of robust vdeo streamng n multhop networks by relyng on delayconstraned and dstorton-aware schedulng, path dversty, and retransmsson of mportant vdeo packets over multple lnks to maxmze the receved vdeo qualty at the destnaton node. To provde an analytcal study of ths streamng problem, we focus on an elementary multhop network topology that enables path dversty, whch we term elementary cell. Our analyss s consderng several cross-layer parameters at the physcal and medum access control (MAC) layers, as well as applcaton-layer parameters such as the expected dstorton reducton of each vdeo packet and the packet schedulng va an overlay network nfrastructure. In addton, we study the optmal deployment of path dversty n order to cope wth lnk falures. The analyss s valdated n each case by smulaton results wth the elementary cell topology, as well as wth a larger multhop network topology. Based on the derved results, we are able to establsh the benefts of usng path dversty n vdeo streamng over multhop networks, as well as to dentfy the cases where path dversty does not lead to performance mprovements. Index Terms Wreless systems, multmeda nformaton systems, vdeo, multhop networks, dstorton-aware path dversty, cross-layer desgn. Ç 1 INTRODUCTION VIDEO streamng over multhop wreless networks has recently attracted sgnfcant attenton [1], [2]. Ths s due to the fact that the nterconnecton of exstng hghspeed IEEE wreless LANs n resdental or offce envronments nto one multhop topology [3] and recent qualty-of-servce (QoS)-enabled Medum Access Control (MAC) protocols [4] provdes new opportuntes for such delay-constraned hgh-bandwdth applcatons [5]. However, for the foreseeable future, commercal wreless multhop networks wll be bult upon unrelable nodes (wreless access ponts or statons) that are connected by wreless lnks wth hghly varyng channel condtons [3]. Therefore, even under QoS guarantees for the MAC layer, robust vdeo streamng applcatons must stll be able to tolerate lnk falures or deep lnk fadng, whch may occasonally occur due to node moblty or the unwllngness of the user to share node resources n the multhop topology [3]. Thus, a varety of protecton schemes deployed n the dfferent layers of the protocol stack should be explored and evaluated under dfferent scenaros.. X. Tong s wth the Corp R&D Department, Qualcomm Inc., 5775 Morehouse Drve, San Dego, CA E-mal: xltong@ee.ucla.edu.. Y. Andreopoulos s wth the Department of Electronc Engneerng, Queen Mary Unversty of London, Mle End Road, London, E1 4NS, UK. E-mal: yanns.a@elec.qmul.ac.uk.. M. van der Schaar s wth the Department of Electrcal Engneerng, Unversty of Calforna Los Angeles, E Engneerng IV Buldng, 420 Westwood Plaza, Los Angeles, CA, E-mal: mhaela@ee.ucla.edu. Manuscrpt receved 31 Mar. 2006; revsed 3 Mar. 2007; accepted 21 Mar. 2007; publshed onlne 2 Apr For nformaton on obtanng reprnts of ths artcle, please send e-mal to: tmc@computer.org, and reference IEEECS Log Number TMC Dgtal Object Identfer no /TMC Related Work From the applcaton-layer perspectve, path dversty emerged as an effcent mechansm for provdng robustness n vdeo communcatons [2], [6], [7], [8], especally when node or path falures occur [9]. Path dversty nvolves the adaptve selecton of two or more network paths for the transmsson of each vdeo packet usng an overlay network nfrastructure [14] at the applcaton layer. Although prevous work apples path dversty wth nonscalable multple-descrpton codng (for example, see [2] and [7]), we utlze path dversty and scalable vdeo codng [16]. Our soluton has low complexty and provdes the opportunty to ntroduce redundancy postencodng at the packet level. Hence, source codng effcency s not sacrfced for the sake of robustness and redundancy can be added on the fly durng the streamng process. Moreover, f addtonal complexty s permtted, ths approach can be combned wth forward error correcton mechansms for addtonal effcency [10]. Although pror work showed the benefts of path dversty under varous transmsson scenaros, ts merts under realstc cross-layer protecton mechansms (and, n partcular, for the case of wreless multhop networks) are largely unknown. Gven the fact that crosslayer frameworks for real-tme vdeo streamng over ad hoc wreless networks also exhbt sgnfcant mprovements n robustness over sngle-layer optmzaton at the applcaton layer [1], [5], [18], we beleve that the nvestgaton of path dversty for vdeo streamng under a realstc cross-layer optmzaton framework s a sgnfcant open challenge. 1.2 Proposed Solutons for Multhop Vdeo Streamng wth Path Dversty In ths work, we address ths problem by utlzng dstorton-optmal packet prortzaton at the applcaton /07/$25.00 ß 2007 IEEE Publshed by the IEEE CS, CASS, ComSoc, IES, & SPS

2 1344 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 6, NO. 12, DECEMBER 2007 layer (derved by state-of-the-art scalable vdeo codng [16]) n order to make optmal packet orderng and optmal retransmssons at the MAC analytcally tractable [17]. In ths paper, an operatonal dstorton model for scalable coded btstreams s proposed (Secton 2.2) n order to prortze the packet transmsson of each vdeo flow accordng to the mportance n the decoded vdeo qualty. Gven ths strct prortzaton for the packets of each vdeo flow, our soluton optmally decdes among several choces for path dversty, the number of packet retransmssons at the MAC, and the optmal lnk adaptaton strategy (that s, modulaton scheme [19], [20]) at the physcal (PHY) layer. Based on the knowledge of local network condtons, we select an elementary network topology that suts our multhop network smulaton and analytcally derve the optmal streamng parameters for the varous layers of the protocol stack. The proposed approach s then generalzed across the entre multhop topology n order to obtan locally optmal streamng solutons. Based on the proposed framework, we are able to address several open questons: 1. whether the optmzed applcaton-layer path dversty provdes addtonal benefts over conventonal retransmsson schemes at the MAC and lnk adaptaton at the PHY n the scenaro that no lnk falure happens, 2. how many packets (f any) should use path dversty n the case of lnk falures, and 3. how close a cross-layer optmzed approach wth path dversty s to the performance lmt, whch assumes exact knowledge of the nstantaneous multhop network condtons and the lnk-falure occurrences and adaptvely chooses a network path based on ths knowledge. 1.3 Network Topology, Routng, and MAC-Layer Assumptons We assume that lnk falures occur due to sudden bursts of severe nterference, for example, due to node moblty. In addton, we assume that a predetermned transmsson opportunty nterval s reserved for each vdeo flow on the varous network nodes, followng the concepts of Hybrd Coordnaton Functon (HCF) Controlled Channel Access (HCCA) mechansms of IEEE e [4]. We envsage that such a reservaton mechansm can be deployed and controlled ether by a central coordnator n the multhop network [11] or by a dstrbuted soluton usng an overlay network nfrastructure [12], [13]. In ths way, the avalable resources can be determned based on the vdeo flows sharng the network and ther QoS requrements. In partcular, we assume that the mesh network topology s fxed over the duraton of the vdeo sesson (barrng falures) and that, pror to transmsson, each applcaton (vdeo flow) reserves a predetermned transmsson opportunty nterval, where contenton-free access to the medum s provded. 1 Ths reservaton can be determned based on the number of flows sharng the network. Although the desgn of such a coordnaton and reservaton system s an 1. Exstng IEEE standards [4] already support such QoS mechansms, whch, barrng nterference and envronment nose, provde guaranteed transmsson tme for each admtted applcaton (vdeo flow). mportant problem and t affects our results, recent work [11], [12], [13] showed that the schedulng of multple flows n the context of a mesh topology can be done such that the average rate for every flow s satsfed and the nterference to neghborng nodes s mnmzed [11]. In our paper, we adopt a smlar overlay network soluton that operates at the applcaton layer, spannng the varous IEEE e wreless cells. Once the avalable network nfrastructure to the vdeo streamng sesson has been establshed, we assume that an overlay network topology can convey (n frequent ntervals) nformaton about the expected bt error rate (BER), the queung delay for each lnk, and the guaranteed bandwdth under the dynamcally changng modulaton at the PHY. Ths overlay nfrastructure can also mnmze the probablty of addtonal delays and lnk falures by adaptvely routng the vdeo packets. Several examples of such applcaton-layer overlay networks have been proposed n the lterature [12], [14]. Fnally, we assume that the applcaton layer of every node n the multhop network reles on an overlay nfrastructure [14] that can 1. route vdeo packets va selected lnks to the destnaton node and 2. convey nformaton about the expected BER, the queung delay for each lnk, and the guaranteed bandwdth under lnk adaptaton from the neghborng nodes n the network topology [5]. 1.4 Paper Organzaton The paper s organzed as follows: Secton 2 defnes the scenaros examned n ths work and provdes the necessary defntons and formulatons for the expected bandwdth, transmsson error rate, and the expected delay for streamng under varous network paths. Secton 3 presents the cross-layer optmzaton problem for the dfferent cases that potentally nvolve path dversty and lnk falures and analyzes the performance of the proposed scheme under each scenaro. Secton 4 presents smulaton results and valdaton for the theoretcal study. Our conclusons are presented n Secton 5. 2 PROBLEM FORMULATION 2.1 Topology Specfcaton and Parameter Defntons The wreless multhop network topology between the vdeo server (sender) and the clent (recever) can be expressed by a connectvty structure P wth M paths, that s, P¼fp 1 ;...; p M g. Each path p ð1 MÞ conssts of w total lnks, that s, p ¼½l ;1 l ;2 l ;w totalš, wth l ;j beng the jth lnk of path p. An example s gven n Fg. 1, where two possble paths from sender n0 to recever n6 are hghlghted. We assume that all utlzed paths from sender to recever are determned beforehand, for example, durng the vdeo-sesson confguraton setup, followng conventonal route dscovery algorthms. Assumng that a tmereservaton mechansm followng the IEEE e prncples s deployed at the MAC layer, the transmsson opportunty duraton s preestablshed for each lnk l ;j (1 M, 1 j w total ) based on a negotaton scheme,

3 TONG ET AL.: DISTORTION-DRIVEN VIDEO STREAMING OVER MULTIHOP WIRELESS NETWORKS WITH PATH DIVERSITY 1345 be shown n Secton 2.3. Fnally, the dstorton reducton s a utlty metrc that enforces approprate prortzaton strateges for each vdeo packet for MAC-layer schedulng and retransmsson. Followng recent state-of-the-art scalable vdeo codng schemes [16], an addtve dstorton model can be used to assocate dstorton reductons to the vdeo packets belongng to a Group of Pctures () wth the same deadlne. 2 Packets n each are ordered by ther dstorton reducton v, v ¼ 1;...;N G, that s, 1 > 2 >...> NG, where N G s the total number of packets n G. In ths paper, we model the dstorton reducton of a packet v n each by Fg. 1. A topology example llustratng two examples of paths between the sender and recever nodes, as well as the lnk state vectors cðl ;1 Þ, ¼f1;...; 3g. Network nformaton before the ndcated horzon s actvely montored (measured) by the sender node, whereas nformaton at the horzon and beyond s estmated. for example, va node resource exchange strateges moderated by a central coordnator. Thereafter, the guaranteed bandwdth gðl ;j Þ of lnk l ;j can be determned based on the allocated transmsson opportunty duraton [5]. In addton, the experenced sgnal-to-nterference-nose rato (SINR) sðl ;j Þ can also be derved followng prevous channel estmaton approaches [19], [20]. We augment the SINR estmaton at the PHY layer wth the lnk-falure probablty fðl ;j Þ, whch represents the expected falure probablty for the duraton of the vdeo streamng sesson. Even though lnk falures may be short-lved, t s safe to assume that all vdeo packets on a faled lnk are lost durng the occurrence of a falure due to the strngent delays of typcal vdeo streamng applcatons. In total, we defne the state vector for each lnk l ;j as c l ;j ¼ gl;j sl ;j fðl ;j Þ : ð1þ In our work, we assume that each node can actvely montor the state vector of each outgong lnk. However, lnk state nformaton beyond the mmedate neghborhood can only be estmated. Ths follows the noton of network horzons ntroduced n our recent work [5]. An example of ths prncple s pctorally shown n Fg. 1 for the sender node n0. Based on ths assumpton, all network condtons (for example, avalable bandwdth or packet loss rate) beyond the lnks of the sender node are expressed as statstcal expectatons, and ther exact value durng the network smulaton s unknown. 2.2 Vdeo Source Characterstcs At the applcaton layer, the vdeo stream to be transmtted s encapsulated n a sequence of vdeo packets. Each vdeo packet v s characterzed by ts deadlne d deadlne v, the packet sze L v, and the nduced dstorton reducton v at the vdeo decoder. These parameters are communcated from the applcaton to the MAC layer followng a multtrack hnt specfcaton [15]. The packet deadlne ensures that each node wll forward the packet only f t s stll useful atthe decoder; otherwse, the vdeo packet s dropped. Thepacket sze s useful durng the transmsson delay estmaton and the error probablty calculatons, as t wll v ¼ v 2 ð0; 1Þ; ð2þ where and are modelng parameters that depend on sequence characterstcs and the encodng parameters. As t wll be llustrated n the expermental part of the paper, ths model can approxmate the measured dstorton reducton for a varety of vdeo sequences encoded by a wavelet vdeo encoder by the approprate selecton of and for each. Notce that the strct dstorton reducton prortzaton expressed by the monotonc functon of (2) enables the exact analyss of the expected MAC operaton under smple network topologes snce packets are encapsulated n MAC Servce Data Unts (MSDUs) n a predetermned order based on ther dstorton reducton. Ths s an mportant aspect of our work snce, unlke related work wth nonscalable codng [2], [7], [21], our preestablshed prortzaton mechansm leads to a very low-complexty soluton. Ths fact, combned wth the ndvdual MSDU acknowledgments receved at the MAC layer, provdes a tractable soluton for determnng several optmal cross-layer parameters durng the real-tme vdeo streamng sesson. 2.3 Expected Transmsson Error Probablty and Delay Estmaton at the MAC Layer Based on the above defntons, the MAC-layer probablty of error for packet v of sze L v bts over lnk l ;j can be gven as e l;j ðl v Þ¼ eðl ;j Þ L v ; where eðl ;j Þ expresses the MAC-layer BER of lnk l ;j, whch can be estmated based on the chosen modulaton mðl ;j Þ and the observed SINR sðl ;j Þ [19], [20]. Smlarly, the probablty of error for one transmsson over path p s Ywtotal e p ðl v Þ¼1 j¼1 el;j ð L v j¼1 ð3þ Þ Ywtotal ¼ eðl;j Þ L v : Let Np max be the maxmum number of retransmssons for packet v over path p. The average number of transmssons over path p untl the packet s successfully transmtted or the retransmsson lmt s reached can then be evaluated as follows [18]: 2. For smplcty and wthout loss of generalty, we assume that delay deadlnes are assocated wth the structure of the vdeo coder. Smaller delays can be accommodated followng the noton of subflows [5]. ð4þ

4 1346 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 6, NO. 12, DECEMBER 2007 N mean p Nmax ¼ Xp p j¼1 þ1 j 1 j e p ðl v Þ ep ðl v Þ h þ Np max þ 1 e p ðl v Þ p þ1 ð5þ j¼1 ¼ e p ðl v Þ Nmax p þ1 : ð6þ e p ðl v Þ Thus, the average end-to-end delay of a packet wth sze L v over p s d p L v ;Np mean Np max ¼ Xwtotal Np mean Np max L v gðl ;j Þ þ T overhead þ Xwtotal ð7þ d queue ðl ;j Þ; j¼1 where T overhead accounts for the delay and protocol overheads nvolved n the packet transmsson. The last equaton derves the end-to-end delay estmate by jonng all lnks of path p va the summaton terms, thereby formng a vrtual lnk from the sender to the recever node n the multhop network. We follow ths approach snce the maxmum number of retransmssons T max p requred on each path p can only be defned from end to end based on the maxmum permssble delay from the sender node to the recever. We remark that, n our experments, the retransmsson lmt for any part of a path or even for one lnk l ;j s set equal to T max p snce, n prncple, all possble retransmssons (untl the MSDU expres due to delay volaton) could occur at an ndvdual lnk. Followng the analyss of (4)-(7), t s straghtforward to defne the average MSDU transmssons and the expected delay for subpaths that nclude only a subset of lnks or even for an ndvdual lnk. Ths wll be proven to be very useful for some of the dervatons. Wth the knowledge of the packets scheduled for transmsson over a certan lnk l ;j, denoted by v queue ðl ;j Þ, we can calculate the queung delay for that lnk. For each packet w n v queue ðl ;j Þ, the product of the expected number of transmssons of the packet (gven by (6)) wth the transmsson duraton gves the average delay to transmt the packet under the partcular network condtons (quantfed by bandwdth gðl ;j Þ and packet loss rate e p ðl w Þ from (4)). The result s d queue ðl ;j Þ¼ X 8w2v queue ðl ;j Þ N mean p p L w gðl ;j Þ þ T overhead : 2.4 Elementary Cells n Multhop Wreless Networks A Dvde and Conquer Strategy Although the estmatons of packet error probablty and delay of the prevous secton may be accurate for the outgong lnks of each node, the uncertanty ntroduced for remote lnks n the multhop topology, combned wth the approxmatons 3 necessary for makng practcal predctons based on (5)-(8), makes the analyss of the full topology very 3. For example, one has to assume a constant (nomnal) packet sze, known lnk and path error probablty, and so forth. ð8þ Fg. 2. Two examples of multhop wreless network elementary cells. dffcult. In fact, our prevous research has already shown that such estmaton-based schemes may lead to sgnfcant gaps n performance n comparson to the end-to-end optmzaton of vdeo streamng under full knowledge of the network condtons. On the other hand, optmzaton under the knowledge of the local network status performed reasonably well [5], even when compared to end-to-end optmzaton. Followng ths lead, n ths paper, we extend the concept of lmted-horzon vdeo streamng optmzaton for multhop networks to optmzaton wthn a multhop wreless network elementary cell. Pctoral examples of such elementary cells are gven n Fg. 2. In the elementary cell n Fg. 2a, node n0 (source node) has only two state vectors, cðl 1;1 Þ and cðl 2;1 Þ. Fg. 2b can be consdered as a specal case of Fg. 2a n whch node n2 and n3 (destnaton node) are collapsed nto one node. Based on an overlay network nfrastructure at the applcaton layer [14], each source node of an elementary cell n the overall multhop topology operates assumng that the vdeo sender and recever are located n the startng and termnatng nodes of ts cell and vdeo packets can be routed from the sender to the recever node followng a specfc path. In ths way, path dversty wthn an elementary cell becomes feasble; also, t s sgnfcantly smpler n comparson to the drect analyss of path dversty over large multhop networks. Fnally, ths approach allows for an analytcal study of the merts and dsadvantages of path dversty under realstc condtons for the MAC and PHY layers snce t corresponds to the basc scenaro where two nonoverlappng paths (wth uncertan condtons) are avalable n the wreless multhop network for the vdeo flow. When consdered wthn the overall multhop network topology, a certan network node may be the orgn of more

5 TONG ET AL.: DISTORTION-DRIVEN VIDEO STREAMING OVER MULTIHOP WIRELESS NETWORKS WITH PATH DIVERSITY 1347 ntermedate node of the cell), r v s updated based on the remanng (expected) probablty of error for the transmsson of the packet n the remanng part of the elementary cell beyond the nformaton horzon. Consder the topology n Fg. 2a. When packet v s successfully transmtted over path p 1, an acknowledgment MSDU frame s receved from n1. Then, we can evaluate r v as r v ¼ v Efe l1;2 ð Þg: ð9þ L v Fg. 3. (a) The two ntal elementary cells emergng from n0 (source node). (b) The subsequent network cell from the ntermedate network node n2 to the fnal destnaton node n6. Notce that, n the case ndcated n (b), node n2 s the source node for the elementary cell. than one elementary cell. Moreover, ntermedate nodes of an elementary cell may also be the source nodes of subsequent cells. Ths s llustrated n the example n Fg. 3. In ths way, wreless multhop network topologes can be decomposed n elementary cells ntroduced n Fg. 2a. Ths also covers the cases where more than two nodes are connected wth a source node, as shown for node n0 n Fg. 3. In the remander of the paper, the term elementary cell refers to cells of the type ntroduced n Fg. 2a and dsplayed n the examples n Fg PATH DIVERSITY STUDY IN ELEMENTARY CELLS Ths secton proposes cross-layer optmzed vdeo streamng wth path dversty n the proposed framework of a wreless multhop elementary cell topology. Although we focus our attenton on the multhop elementary cell n Fg. 2a, our analyss s applcable n a broad range of smlar confguratons. Sectons 3.1 and 3.2 dscuss the case of falure-free elementary cells, and Secton 3.3 presents the equvalent optmzaton under the occurrence of lnk falures. Fnally, Secton 3.4 dscusses the extenson of the optmzaton under an elementary cell nto larger multhop topologes. 3.1 Proposed Cross-Layer Optmzaton for an Elementary Cell wthout Lnk Falures To realze the optmal packet dversty wthn each elementary cell under no lnk falures, we ntroduced a new network-aware dstorton reducton metrc r v as an extenson of v of (2). Pror to the ntal packet transmsson, we have r v ¼ v. Each tme the packet s successfully transmtted from the source node of the current cell (that s, an acknowledgment MSDU frame s receved from an The last equaton ndcates that, f we expect the packet to be dropped by lnk l 1;2, that s, Efe l1;2 ðl v Þg ¼ 1, there s a remanng beneft (utlty) n retransmttng the same packet over the alternate path ðp 2 Þ, whch s gven by r v ¼ v. Conversely, f Efe l1;2 ðl v Þg ¼ 0, there s no remanng beneft n retransmttng packet v. Therefore, r v captures the expected dstorton reducton achevable f a networkaware path dversty s chosen for packet v. Our overall objectve s to maxmze the expected dstorton reducton at the destnaton node of each elementary cell under the constrant of lmted network resource and the deadlne constrant of the vdeo streamng applcaton. Smlar to our prevous work [5], ths s acheved by fndng the best path as well as the crosslayer parameters for the lnk correspondng to that path: h v p p ¼ arg max p 2P;v2v schedule ðn0þ mðl ;j Þ nh o e p ðl v Þ Nmax p r v ; ð10þ where v schedule ðn0þ s the set of nonexpred packets n the buffer of source node n0. The expected end-to-end delay of the path should be smaller than the deadlne of the packet; otherwse, the packet s dropped. Ths constrant can be expressed as 8v; and 8p 2P: Np max d deadlne 6 v E d queue ðl ;2 Þ 1þ þ : L v gðl ;j Þ Efgðl;j Þg 2 T overhead ð11þ Notce that the bandwdth lmtaton of each lnk s only consdered n the constrant of (11) and s not explctly expressed n the optmzaton of (10) snce each vdeo packet s transmtted at the MAC layer untl an acknowledgment s receved or the delay deadlne for the vdeo packet s reached. The algorthm n Fg. 4 can be deployed at the source node of each elementary cell n order to solve (10) under the constrant of (11). Note that, f multple copes of the same packet come nto the queue of an elementary cell source node from prevous cells, we retan only one packet for transmsson wthn the current cell. Fnally, f the source node can utlze more than one cell, such as n the case n Fg. 3a, the algorthm n Fg. 4 s appled for all avalable outgong lnks and, once a path has been chosen, the packet s consdered wthn the correspondng elementary cell. 3.2 Theoretcal Analyss of the Falure-Free Case Under the optmzaton of (10), f the two paths have unequal error probabltes, then the path p wth the lower

6 1348 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 6, NO. 12, DECEMBER 2007 vdeo packets arrve at the ntermedate nodes followng a Posson process arrval rate total, and each packet ndependently chooses path p at the sender node wth probablty Prfp g. Thus, the packets arrve at each ntermedate node n ð ¼ 1; 2Þ wth average rate ¼ total Prfp g. By the Pollaczek-Khnchn (P-K) formula [22] and after some straghtforward manpulatons, the expected queung delay d queue ðp Þ s gven as n o E X;serv 2 d queue ðp Þ¼ ; ð14þ 21 E X ;serv where EfX ;serv g¼ Np X max n L n v Efgðl ;2Þg E e n l ;2 L v E el;2 L v n¼1 þ L v p þ 1 E e l;2 ðl v Þ E gðl ;2 Þ p ; o ð15þ Fg. 4. Soluton of cross-layer optmzaton of (10) for the sender node of an elementary cell. The utlzed modulaton strategy for lnk adaptaton at Step 5 s derved based on prevous modelng work for lnk adaptaton strateges [19], [20]. error probablty wll be used to transmt packets, whch wll lead to a larger queung delay for that path and, thereby, a smaller value for Np max (from (11)). Thus, the term ½ e p ðl v Þ Nmax p Š wll decrease and, eventually, the alternate path p 3 n the elementary cell wll be chosen. Consequently, n the steady-state operaton of each elementary cell, we may assume that 4 p e p1 ðl v Þ 1 p ¼ e p2 ðl v Þ 2 ; ð12þ where L v s the nomnal (average) packet sze and e p ¼ e l;1 L v E el;2 L v Lv Lv ð13þ ¼ eðl ;1 Þ E eðl;2 Þ ¼ 1; 2: Notce that Np max ðl v Þ can be determned based on (11) under the equalty condton Estmaton of the Average Number of Successfully Transmtted Vdeo Packets The queung delay over path p, that s, d queue ðp Þ, ¼ 1; 2, can be evaluated by modelng each path s ntermedate nodes as an M/G/1 queung system. We assume that the 4. Equaton (12) does not hold only under the trval case when the capacty of one path s suffcent to transmt all the vdeo packets (under the same deadlne) wth a smaller error probablty than that of another path. In ths case, no path dversty s benefcal. n o E X;serv 2 ¼ Np X max 2 nl v n E e Efgðl ;2 Þg l;2 L v E el;2 L v n¼1 þ! 2 L v p þ 1 E e l;2 L v E gðl ;2 Þ p ð16þ are the frst and second moments of the servce tme X ;serv correspondng to the queue of path p. Wth the knowledge of d queue ðp Þ from (14), we can establsh Np mean ðnp max Þ from (11) and (6). Then, the expected delay ncurred by the bottleneck lnk of the path s gven by n d bottleneck ðp Þ¼Np mean Np max 1 L v max gðl ;1 Þ ; o 1 Efgðl ;2 Þg ð17þ based on the fact that each packet s transmtted on average Np mean ðnp max Þ tmes at the MAC layer of each lnk, as calculated by the analyss of (3)-(6). We can now establsh the expected number of transmtted packets n the duraton of one (that s, under the transmsson deadlne) as S ¼ d deadlne 1 v d bottleneck ðp 1 Þ þ 1 : ð18þ d bottleneck ðp 2 Þ Dstorton Reducton under Falure-Free Transmsson wth and wthout Path Dversty Gven that S packets are transmtted, based on the predetermned dstorton prortzaton scheme, the receved dstorton reducton when no lnk falure happens and wthout path dversty s gven as ffal-free; no-dverstyg ¼ XS ½ v Š¼ v¼1 Sþ1 ; ð19þ

7 TONG ET AL.: DISTORTION-DRIVEN VIDEO STREAMING OVER MULTIHOP WIRELESS NETWORKS WITH PATH DIVERSITY 1349 where we utlzed the proposed packet dstorton reducton model of (2). Under the use of path dversty, before attemptng to retransmt packet v over the alternate path, we assume to have transmtted k dp subsequent packets, that s, packet v þ 1 to packet v þ k dp, whose dstorton reducton s greater than r v calculated n Step 8 n Fg. 4. Obvously, k dp depends on the dstorton reductons f vþ1 ;...; vþkdp g and r v. In the steady state, f packet v s to be attempted over one path, t has a pror expected dstorton reducton (that s, dstorton reducton wthout knowng f an acknowledgment wll be receved or not) r v ¼ v e p1 ðl v Þ p 1 ¼ v p e p2 ðl v Þ 2 ð20þ snce both paths are balanced. We can compute an estmate of k dp by equalzng r v of packet v expressed by (20) wth the (ntal) dstorton reducton of packet v þ k dp : v p e p1 ðl v Þ 1 ¼ vþkdp ; ¼f1; 2g; ð21þ whch gves j k p k dp ¼ log e p1 ðl v Þ 1 ; ¼ 1; 2: ð22þ Under the steady-state assumpton, the derved k dp of (22) expresses the average number of packets between the orgnal transmsson of packet v and ts retransmsson over the alternate path. Eventually, all ntal packets of the current wll be retransmtted to the alternate path except for the last packets fs k dp ;...;S g, whch wll expre before they can be replcated n the alternate path. In addton, n the steady-state case, each path s expected to successfully transmt S 2 packets n total. Hence, n the path dversty case wth no lnk falures, the expected number of successfully receved unque (that s, nonreplcated) vdeo packets from both paths s dff; fal-free S ¼ S þ k dp : ð23þ 2 Consequently, the receved dstorton reducton for the path dversty scheme can be calculated by ffal-free; dverstyg ¼ dff; fal-free þ1 S ¼ : X Sdff; fal-free v¼1 ½ v Š ð24þ The comparson between the cases wth no dversty and the case where path dversty s used can be performed by comparng ffal-free; dverstyg from (24) and ffal-free; no-dverstyg gven n (19). The theoretcal comparson reveals that path dversty wll never ncrease the expected dstorton reducton at the decoder snce ffal-free; dverstyg > ð25þ ffal-free; no-dverstyg ff k dp >S : However, from the defnton of k dp, k dp S. Consequently, path dversty should not be used under the crosslayer optmzaton n Fg. 4 when no falures occur n the multhop elementary cell. Ths concluson s expermentally valdated by our smulatons and the correspondng analyss n Secton 4. Secton 3.3 examnes the usefulness of path dversty under the occurrence of random lnk falures n the elementary cell topology. 3.3 Retransmsson and Path Dversty Optmzaton n the Case of Elementary Cells wth Lnk Falures Under the occurrence of lnk falures beyond the horzon of the elementary cell topology, one cannot estmate the remanng dstorton reducton for each packet n a relable manner snce ths packet may be dropped n the ntermedate node of the elementary cell topology. Hence, nstead of usng path dversty for a vdeo packet based on the acknowledgment of the orgnal packet transmsson, we de facto retransmt a certan percentage of the most mportant vdeo packets on both paths. Consequently, the algorthm n Fg. 4 s also appled for ths case but wth the modfcaton that the orgnal dstorton reductons are used, that s, Step 10 n Fg. 4 s not appled. Moreover, the 100 percent most mportant packets ð0 < 1Þ n terms of dstorton reducton are attempted on both avalable lnks n the elementary cell topology. The analyss n ths secton derves the dependency of wth the expected dstorton reducton at the destnaton node. For the theoretcal study of ths approach, the expected dstorton reducton of the retransmsson scheme n the case of lnk falures can be evaluated as ffalure; dverstyg " ¼ ffal-free; no-dverstyg ð Effðl 1;2 ÞgÞð Effðl 2;2 ÞgÞ " ## þ X2 d deadlne v ð Effðl ;2 ÞgÞ Effðl 3 ;2 Þg ; d ¼1 bottleneck ðp ÞS ð26þ where E fðl ;2 Þ, ¼f1; 2g, s the expected falure rate of lnk l ;2, ffal-free; no-dverstyg s gven by (19), and d bottleneck ðp Þ s gven by (17). The last equaton descrbes the expected dstorton reducton under all possble combnatons of faled paths and under the case of falure-free transmsson. The percentage of packets usng path dversty should satsfy the followng constrant: 2 d deadlne v mn 100 percent ð27þ S ¼f1;2g d bottleneck ðp Þ because path dversty s nherently upper bounded by the bottleneck path. The last equaton demonstrates that the maxmum dversty can be acheved under equal congeston condtons on both paths, that s, d bottleneck ðp 1 Þ¼d bottleneck ðp 2 Þ; whch leads to 100 percent, that s, all vdeo packets of each path could be retransmtted va the alternate path. The number of packets usng path dversty s denoted by S dversty, and we have S dversty ¼ S. Smlarly, the number of unque vdeo packets transmtted va both paths n the case of falures s denoted by S dff;fal ¼ S ð 0:5Þ. S dff;fal, and we have

8 1350 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 6, NO. 12, DECEMBER 2007 To smplfy the notaton, we defne the expected number of packets transmtted through path p n the duraton of one as d deadlne v S ðp Þ¼ ;¼ 1; 2 ð28þ d bottleneck ðp Þ and we assume n the followng analyss that S and 1 2 S are ntegers. Based on the utlzed dstorton model, the expected receved dstorton reducton of the dversty scheme can then be wrtten as wth ffalure; dverstyg ¼ð1 Effðl 1;2 ÞgÞð Effðl 2;2 ÞgÞ Sdff; fal þ1 þ X2 ¼1 ð Effðl ;2 ÞgÞEffðl 3 ;2 Þg " 1 2 S 1 2 Sdversty dversty þ1 þ S ðp Þ 1 2 Sdversty S S dversty S S dversty þ1 ¼ b 1 Sð1 1 2 Þþ1 " þ b S þ1 þ S ðp 1 Þ 1 2 S S ð Þ # 1 2 S S S þ1 " þ b S þ1 þ S ðp 2 Þ 1 2 S S ð Þ # S 2 S S þ1 # ð29þ ð30þ 8 9 < b 1 ¼ð1 Effðl 1;2 ÞgÞð Effðl 2;2 ÞgÞ = b 2 ¼ð1 Effðl 1;2 ÞgÞEffðl 2;2 Þg : ; : ð31þ b 3 ¼ð1 Effðl 2;2 ÞgÞEffðl 1;2 Þg After some straghtforward manpulatons, the dstorton reducton expresson of (30) s smplfed to ffalure; dverstyg ¼ c 1 þ c 2 þ c S þ c 4 þ c S ; where 8 c 1 ¼ðb 1 þ b 2 þ b 3 Þ h 1 c 2 ¼ b 1 þ b 2 S ðp 1 Þ S þ b 3 S ðp 2 Þ S S þ1 >< 1 c 3 ¼ b 1 þ b2 2 þ b3 2 S þ1 h 1 c 4 ¼ b 2 S ðp 1 Þ S þ b 3 S ðp 2 Þ S ðb 2 þ b 3 Þ >: c 5 ¼ b 2þb ð32þ >= : ð33þ >; The expected dstorton reducton under path falures gven by (32) s a functon of the packet dversty percentage. Hence, gven the network parameters, we can analytcally determne to obtan the maxmum vdeo qualty at the decodng node of the elementary cell. For example, when p 1 and p 2 have the same delay bottleneck, that s, d bottleneck ðp 1 Þ¼d bottleneck ðp 2 Þ, we have S ðp 1 Þ¼ S ðp 2 Þ¼ 1 2 S from (28). Then, (32) s smplfed to ffalure; dverstyg ¼c 1 þ c S þ c S : ð34þ By settng the frst dervatve of ffalure; dverstyg to zero, we obtan the (optmal) percentage of vdeo packets usng path dversty that s expected to maxmze the dstorton reducton under path falures: ¼ 1 c 2 log S c 4 ¼ 1 2b 1 þ b 2 þ b 3 log S S b 2 þ b 3 : ð35þ Notce that the last expresson gves the optmal packet dversty percentage as a functon of the dstorton reducton model ðþ and the constants of (31), whch are expressng the expected falure condtons. However, the optmal value s nvarant to the scalng parameter of the dstorton model snce all the vdeo packets are equally nfluenced by t. 3.4 Extensons to Large Topologes Large topologes consstng of 7-20 nodes can be decomposed nto overlappng elementary cells, as shown n the example n Fg. 3. For each elementary cell, the sender node faces the stuaton dscussed prevously for the basc topology, that s, t has accurate nformaton for ts outgong lnks and estmated nformaton for the remander of the elementary cell. We can categorze elementary cells nto falure-free cells and cells wth lnk falures. Each case follows the analyss presented prevously n ths secton. Although analytcally tractable, vdeo streamng followng the elementary cell approach may lead to locally optmal solutons that do not correspond to the globally optmal vdeo streamng approach that consders the network parameters for the entre multhop topology. However, one wll need to cope wth the large uncertanty n the parameter estmaton when the entre multhop topology s consdered due to frequent varatons n the lnk condtons n wreless multhop networks. Although ths may be partally allevated f the sender node receves frequent updates for each lnk s condton, such an approach may ncur sgnfcant bandwdth overheads and delays. The elementary cell approach provdes the ntermedate soluton, that s, hgh performance wth reasonable feedback requrements about the network status. However, snce the performance gap from the end-to-end optmzed soluton may become sgnfcant when large topologes are consdered n the followng secton, we quantfy the performance of the elementary cell approach aganst the upper bound oracle approach that assumes nstantaneous feedback about the lnk condtons of the entre network (ncludng precse knowledge of lnk falures) and apples the cross-layer optmzaton of Fg. 4 for the entre topology.

9 TONG ET AL.: DISTORTION-DRIVEN VIDEO STREAMING OVER MULTIHOP WIRELESS NETWORKS WITH PATH DIVERSITY SIMULATION RESULTS In our experments, we used a fully scalable codec [23] and the produced btstream for each vdeo sequence was extracted at an average bt rate of 2 megabts per second (Mbps) for CIF resoluton sequences at 30 frames per second. Based on the rate-dstorton hnt track specfcaton [15], each vdeo btstream was packetzed nto MSDUs of data payload no larger than 1,000 bytes. Each was set to 16 vdeo frames. The end-to-end delay for the MSDUs of each was set to sec, whch corresponds to the replay duraton of one (at 30 Hz) and s also an acceptable latency for the majorty of real-tme vdeo streamng applcatons. For the expermental study of the elementary cell topology, we smulated the case of the multhop network shown n Fg. 2a. Moreover, we also consdered the larger multhop network n Fg. 3 n order to valdate our study of elementary cells wthn a larger multhop topology. In all cases, we assume that the central coordnator [11] or the dstrbuted overlay nfrastructure [12], [13] provdes predetermned transmsson ntervals for each lnk correspondng to the ndcated applcaton-layer bandwdth (n Kbps) for each experment. Under the knowledge of the SINR of each lnk and the utlzed modulaton strategy, ths leads to known guaranteed bandwdth and BER per lnk. However, snce each lnk s SINR may vary unpredctably, n our theoretcal analyss, we always use the average SINR of each lnk that leads to the expected packet loss rate and the average guaranteed bandwdth under the predetermned transmsson nterval for the vdeo flow. In order to make a realstc evaluaton of the dynamcs of multhop wreless topologes, we performed a parameterzed smulaton that takes nto account the dfferent optons and settngs for the varous layers, such as varyng SINR at the PHY layer, transmsson overheads at the MAC layer due to MSDU acknowledgments, and pollng, as well as queung and propagaton delays n the varous lnks of the multhop network. In order to ncorporate the effect of nose and nterference, we performed 50 smulatons per topology/vdeo sequence/chosen transmsson settng usng random values for the SINR of each lnk, chosen between 17 and 23 db. Ths range was selected such that the a modulaton strateges at the PHY provde reasonable packet loss rates wth enough PHY layer throughput to support vdeo applcatons (see the modulaton curves n [19] and [20] for more detals on packet loss rates and throughput versus SINR). In Secton 4.1, we frst valdate the utlzed dstorton reducton model of (2) usng typcal vdeo sequences. Then, Sectons 4.2 and 4.3 examne the elementary cell topology and valdate the proposed theoretcal analyss for the falure-free case and under the case of lnk falures. Fnally, Secton 4.4 presents results for vdeo streamng under a larger multhop topology when the optmzaton s performed wthn elementary cells. A comparson s made wth the globally optmzed streamng soluton, whch assumes exact knowledge of the network condtons. Fg. 5. Mnmum mean square error (MSE) fttng of the model and real vdeo trace for (a) an entre and (b) two groups of packets (pecewse approxmaton). The sequence Foreman was used, and the decodng bt rate was 2 Mbps. 4.1 Valdaton of the Vdeo Packet Dstorton Reducton Model Fg. 5a shows a typcal comparson between the expermental dstorton reducton of the packets n one (computed by the vdeo decoder for a of sequence Foreman ) and the dstorton reducton gven by the proposed model. Smlar results have been obtaned for all s of all the remanng vdeo sequences of our experments and under a varety of decodng bt rates. Under the proper selecton of the model parameters for each (that s, a and of (2)), we always obtan a suffcent approxmaton of the dstorton reducton for each packet. In addton, a pecewse dstorton model can provde even hgher accuracy, as shown n the example n Fg. 5b. In ths case, the packets of each are dvded nto I G groups, and each group s approxmated by the proposed model: ¼ XI G ¼1 v m 2ð0; 1Þ; v¼ 1; 2; 3;...; ð36þ where and are the model parameters for the th group of vdeo packets and m s the packet number of the frst packet n the th group, wth m 1 ¼ 1. In the partcular

10 1352 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 6, NO. 12, DECEMBER 2007 TABLE 1 Comparson between Smulaton Average and Theoretcally Estmated Results for Falure-Free Low and Hgh-Bandwdth Balanced Elementary Cells TABLE 2 Comparson between Smulaton Average and Theoretcally Estmated Results for Unbalanced Elementary Cells We ndcate the average receved number of packets and the normalzed dstorton reducton measured from the smulaton and estmated from the proposed formulaton. example n Fg. 5b where m 1 ¼ 1 and m 2 ¼ 26, the dstorton reducton of packets v ¼f1;...; 25g s approxmated by 1 ¼ 1:0 and 1 ¼ 0:916, and the dstorton reducton of packets v ¼f26;...; 200g s approxmated by 2 ¼ 0:119 and 2 ¼ 0:965 usng least squares fttng. Overall, we used I G ¼ 2 for all vdeo sequences, but the values for f1;2g and f1;2g are sequence-dependent and are defned based on least squares fttng wth the expermental dstorton estmates of the scalable codec, as produced durng the btstream extracton phase [23]. 4.2 Expermental Results and Model Valdaton for Falure-Free Elementary Cells In our frst round of experments, we separated our analyss nto two cases correspondng to low and hgh average bandwdth for the vdeo transmsson. Thereafter, we examne a balanced and an unbalanced topology (n terms of estmated avalable bandwdth for each path). Representatve results for the frst case are shown n Table 1. The average guaranteed bandwdth and average packet loss rate of each lnk dsplayed n the table were calculated based on the average SINR and the correspondng modulaton scheme for the average nterference case, although dfferent modulatons were utlzed durng the smulaton of the MSDU transmsson usng lnk adaptaton We ndcate the average receved number of packets and the dstorton reducton measured from the smulaton and estmated from the proposed formulaton. at the PHY layer [19], [20]. Although the channel condtons vary dependng on nterference, we fnd that, even wth unbalanced packet errors for the two paths, the receved packets are evenly dstrbuted over the two paths under the scenaros n Table 1. Ths s because we ncorporate the queung delay n the evaluaton of Np max n (11), and ths affects the expected packet loss of the optmzaton functon of (10). Hence, f too many packets are transmtted over one path, the queung delay of ths path wll grow, whch wll result n a lower maxmum packet retransmsson lmt and, thus, a larger path error rate. Then, the sender node wll swtch to the alternate path. The second set of our experments s outlned by the representatve results n Table 2. In scenaro 1, we found that on average there are packets transmtted over path 1 and packets transmtted over path 2; thus, the load s dstrbuted over the two paths accordng to the path bandwdth rato. Smlar results are observed for the scenaro wth larger error rates, dfferent bandwdths, and packet sze varaton. The results n Tables 1 and 2 ndcate that the proposed theoretcal estmaton captures the average smulated behavor accurately. Concernng the case of path dversty n the falure-free elementary cell topology, our smulaton valdated that t s not a benefcal approach. In fact, we observed that the proposed algorthm n Fg. 4 very rarely (f ever) selects to retransmt a vdeo packet on the alternate path, whch

11 TONG ET AL.: DISTORTION-DRIVEN VIDEO STREAMING OVER MULTIHOP WIRELESS NETWORKS WITH PATH DIVERSITY 1353 Fg. 6. Relatonshp of k dp (the average number of packets between the orgnal transmsson of packet v and ts retransmsson over the alternate path) wth the retransmsson lmt of each path ðnp max Þ and the path error probablty ðe p ðl v ÞÞ. The plots are generated based on (22), whch assumes a balanced elementary cell topology under a steady-state operaton, and we set ¼ 0:916, whch agrees wth expermentally measured dstorton reducton n typcal vdeo sequences. agrees wth the derved theoretcal outcome of (25). In order to elaborate further on why the proposed algorthm does not use the opton of path dversty, Fg. 6 examnes the relatonshp of the theoretcally predcted value of k dp from (22) wth the path error probablty for a sngle packet transmsson ðe p ðl v ÞÞ and under varous retransmsson lmts Np max, ¼f1; 2g. The plots clearly demonstrate that, even for very hgh path error probablty and for a large varety of retransmsson lmts (whch correspond to relaxed or strct delay deadlnes snce Np max s defned based on (11)), the theoretcal value of k dp s larger than the retransmsson lmt Np max for each path p. These results ndcate that, n falure-free multhop topologes and under a persstent MAC retransmsson framework that attempts to transmt the most mportant MSDUs (n terms of dstorton reducton) untl the delay deadlne s reached, path dversty does not provde an mproved dstorton performance, that s, t does not lead to hgher dstorton reducton at the decoder. 4.3 Expermental Results and Model Valdaton n Elementary Cells Exhbtng Path Falures We consder agan the low-bandwdth elementary cell ndcated n the low-bandwdth case n Table 1. All undetected falures occur n the dotted lnks and they are handled by usng path dversty as explaned n Secton 3.3. Although falures may also occur n the lnk connected to the source node n0, they are easly detected by the source node and, then, ths case essentally becomes a sngle-path transmsson problem. Hence, we focus our expermental study on falures for the unknown part of the multhop elementary cell, that s, beyond the frst lnk of each path. Fg. 7 shows the theoretcally expected dstorton reducton at the destnaton (decoder) node as a functon of Effðl 1;2 Þg (whch s equal to Effðl 2;2 Þg for ths analyss) and the percentage of dversty. Clearly, when Effðl 1;2 Þg ¼ 0, ths case rolls back to the prevous stuaton, and usng path dversty wll always lead to lower dstorton reducton Fg. 7. Analytcally evaluated dstorton reducton for dfferent lnk-falure probabltes as a functon of the percentage of packets usng path dversty for the low-bandwdth elementary cell topology. Fg. 8. Comparson of smulaton and theoretcal results for Effðl 1;2 Þg ¼ Effðl 2;2 Þg ¼ 0:05 n the low-bandwdth elementary topology. compared wth the no-path-dversty scheme (and the expected dstorton reducton s monotoncally decreasng as the percentage of packets usng path dversty ncreases). However, t appears that, even for modest values of Effðl 1;2 Þg, packet dversty can acheve hgher dstorton reducton f the percentage of packets usng dversty s chosen carefully. The theoretcal curves n Fg. 7 clearly demonstrate that there exsts a maxmum value for the percentage of packets usng path dversty, whch was expressed n the concluson of our analyss by (35). In addton, when path dversty s selected beyond the optmum pont, although the average dstorton reducton wll decrease, the varance of the decoded vdeo qualty wll also decrease, snce fewer vdeo packets are sacrfced durng the occurrence of a lnk falure. The detaled smulaton results and the correspondng theoretcal predcton for a varety of falure probabltes are presented n Fgs. 8 and 9. The analytcal model matches well wth the smulaton results. The bars n each fgure llustrate the range of the dstorton reducton observed n our smulatons wth each choce for path dversty percentage. Clearly, the varance of the dstorton reducton

12 1354 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 6, NO. 12, DECEMBER 2007 Fg. 9. Comparson of smulaton and theoretcal results for Effðl 1;2 Þg ¼ Effðl 2;2 Þg ¼ 0:10 n the low-bandwdth elementary topology. Fg. 12. Comparson of smulaton and theoretcal results for Effðl 1;2 Þg ¼ Effðl 2;2 Þg ¼ 0:10 n the hgh-bandwdth elementary topology. Fg. 10. Analytcally evaluated dstorton reducton for dfferent lnkfalure probabltes as a functon of the percentage of packets usng path dversty for the hgh-bandwdth elementary cell topology. Fg. 11. Comparson of smulaton and theoretcal results for Effðl 1;2 Þg ¼ Effðl 2;2 Þg ¼ 0:05 n the hgh-bandwdth elementary topology. at the decoder s reduced by ncreased percentages of packets usng path dversty. Concernng the hgh-bandwdth case n Table 1, the behavor under path falures s somewhat dfferent than n the case of low bandwdth. In the former case, there s suffcent bandwdth to transmt the most mportant Fg. 13. Smulaton results wth the multhop topology n Fg. 3 under the occurrence of lnk falures. packets of each on both paths. Consequently, even when a large number of vdeo packets use path dversty, there s no consderable decrease n average dstorton reducton, as shown n the theoretcal comparsons n Fgs. 10, 11, and 12. Smulaton results verfy ths fact and we fnd that, as the percentage of dversty becomes large, the receved dstorton reducton becomes very stable and the varance s neglgble n these cases. 4.4 Expermental Results for Larger Multhop Topologes We consder the entre multhop topology n Fg. 3 and smulate the case where all lnks operate wth 5 percent falure probablty for the duraton of the vdeo streamng sesson. For the reported experments, all falures are assumed to be short-lved, that s, lastng approxmately for an entre (16 frames at replay rate of 30 Hz, that s, 0.5 sec). The dstorton reducton as a functon of the percentage of packets utlzng path dversty s gven n Fg. 13. The top horzontal lne ndcates the performance bound, whch corresponds to the schedulng and crosslayer optmzaton that consders the end-to-end network parameters and assumes nstantaneous feedback concernng lnk falures. Ths corresponds to the end-to-end optmzaton case of our recent work [5] wth the addtonal

13 TONG ET AL.: DISTORTION-DRIVEN VIDEO STREAMING OVER MULTIHOP WIRELESS NETWORKS WITH PATH DIVERSITY 1355 TABLE 3 Smulaton Results for Two Vdeo Sequences under Varous Falure Probabltes and Varyng Percentage of Packets Utlzng Path Dversty decoder sde, the percentage of lost vdeo frames was quantfed based on the number of vdeo frames wth PSNR lower than 26 db, whch ndcates that the vdeo frame appears wth severe dstorton. The results ndcate that path dversty s benefcal when lnk falures are frequent. Moreover, a hgher percentage of vdeo packets utlzng path dversty ensures that fewer vdeo frames are severely dstorted. The bandwdth allocaton per lnk s ndcated n the top part. The correspondng packet loss rate of each lnk (for the falure-free ntervals) was varyng between 0.08 and 0.12, derved based on the average packet sze and the BER usng (3). knowledge of lnk-falure occurrences, whch s n general not easly feasble due to the feedback requrements. Smlar results have also been obtaned when the falure probablty s unformly dstrbuted wthn the range of [0, 10] percent, as well as when the lnk falures last longer. Overall, the results ndcate that our localzed optmzaton mechansm wthn overlappng elementary cells conssts of a good approxmaton of the globally optmal soluton that assumes exact knowledge of the network condtons and lnk falures for the entre network. In addton, n ths case, the man beneft of usng path dversty appears to be the reducton of the expected varance of the dstorton reducton at the destnaton node. We valdated these results by measurng the peak sgnalto-nose rato (PSNR) for two typcal Common Intermedate Format (CIF) vdeo sequences under the smulaton condtons n Table 3, as well as the average percentage of lost vdeo frames. Snce the qualty of a lost vdeo frame depends on the error concealment strategy appled at the 5 CONCLUSIONS Wreless multhop networks may emerge as mportant nfrastructures for vdeo streamng applcatons. In ths paper, we nvestgated the performance of such streamng applcatons under a cross-layer optmzaton framework that attempts to cope wth rapdly varyng network condtons and even complete lnk falures. Our approach splts the vdeo streamng problem nto ndependent transmsson problems wthn overlappng elementary cells n the multhop network. Each cell represents an elementary multhop topology that enables cross-layer optmzaton wth path dversty. By utlzng state-of-the-art vdeo codng wth predetermned dstorton reducton prortzaton for each vdeo packet, we modeled and analyzed the expected performance of the proposed framework under a varety of condtons. Our theoretcal dervatons demonstrate that, under the proposed cross-layer optmzaton framework, path dversty s not benefcal when lnk falures are not expected n the wreless multhop nfrastructure. On the other hand, path dversty s a useful approach for lowbandwdth transmsson over multhop networks f the percentage of vdeo packets utlzng dversty s chosen carefully. Fnally, for larger multhop topologes, the man beneft of utlzng path dversty appears to be the stablzaton of the decoded vdeo qualty. In ths case, the accurate choce of the percentage of vdeo packets to use path dversty s not so crtcal. Our conclusons are supported by smulaton studes wth a varety of vdeo sequences and a varety of network confguratons. The smulaton results addtonally ndcated that the proposed approach of usng elementary cells performs close to the upper bound that consders the entre network topology durng the cross-layer optmzaton and assumes nstantaneous feedback about the lnk condtons. ACKNOWLEDGMENTS The authors would lke to acknowledge the support from US Natonal Scence Foundaton Grants CCF and CNS At the tme of ths work, Y. Andreopoulos was wth the Department of Electrcal Engneerng, Unversty of Calforna, Los Angeles. REFERENCES [1] E. Setton, T. Yoo, X. Zhu, A. Goldsmth, and B. Grod, Cross- Layer Desgn of Ad Hoc Networks for Real-Tme Vdeo Streamng, IEEE Wreless Comm. Magazne, vol. 12, no. 4, pp , Aug [2] N. Gogate, D.-M. Chung, S.S. Panwar, and Y. Wang, Supportng Image and Vdeo Applcatons n a Multhop Rado Envronment Usng Path Dversty and Multple Descrpton Codng, IEEE Trans. Crcuts and Systems for Vdeo Technology, vol. 12, no. 9, pp , Sept

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Schelkens, In-Band Moton Compensated Temporal Flterng, Sgnal Processng: Image Communcaton, specal ssue on subband/wavelet nterframe vdeo codng, vol. 19, no. 7, pp , Aug Xaoln Tong receved the master s degree n electrcal engneerng from the Unversty of Calforna, Los Angeles n September He obtaned hs bachelor s and master s degrees n computer scence from the Bejng Unversty of Posts and Telecommuncatons and the Insttute of Computng Technology, Chnese Academy of Scences, n 2002 and 2005, respectvely. He s now wth the Corporate R&D Department, Qualcomm Inc. Yanns Andreopoulos receved the electrcal engneerng dploma and the MSc degree n sgnal processng systems from the Unversty of Patras, Greece, n 1999 and 2000, respectvely, and the PhD degree n appled scences from the Unversty of Brussels, Belgum, n May 2005, where he defended a thess on scalable vdeo codng and complexty modelng for multmeda systems. Durng hs thess work, he partcpated and was supported by the project MASCOT, a European Unon Future and Emergng Technologes (FET) project. Durng hs postdoctoral work at the Unversty of Calforna, Los Angeles, he performed research on cross-layer optmzaton of wreless meda systems, vdeo streamng, and theoretcal aspects of rate-dstortoncomplexty modelng for multmeda systems. Snce October 2006, he has been a lecturer at the Queen Mary Unversty of London, Unted Kngdom. Durng , he made several decsve contrbutons to the ISO/IEC JTC1/SC29/WG11 (Moton Pcture Experts Group (MPEG)) commttee n the early exploraton on scalable vdeo codng, whch has now moved nto the standardzaton phase. In 2007, he receved the Most Cted Paper Award from Sgnal Processng: Image Communcaton. He s a member of the IEEE. Mhaela van der Schaar receved the PhD degree from the Endhoven Unversty of Technology, the Netherlands, n She s currently an assocate professor n the Electrcal Engneerng Department at the Unversty of Calforna, Los Angeles. She has been an actve partcpant to the ISO Moton Pcture Expert Group (MPEG) standard snce 1999, to whch she made more than 50 contrbutons and for whch she receved three ISO recognton awards. She was also elected as a member of the Techncal Commttee on Multmeda Sgnal Processng and of the Techncal Commttee on Image and Multple Dmensonal Sgnal Processng, both of the IEEE Sgnal Processng Socety. She was an assocate edtor of the IEEE Transactons on Multmeda and SPIE Electronc Imagng Journal. Currently, she s an assocate edtor of IEEE Transactons on Crcuts and System for Vdeo Technology and IEEE Sgnal Processng Letters. She holds 28 granted US patents and has several more pendng. She receved the US Natonal Scence Foundaton Faculty Early Career Development (CAREER) Award n 2004, the IBM Faculty Award n 2005, the Okawa Foundaton Award n 2006, the Best IEEE Transactons on Crcuts and Systems for Vdeo Technology Paper Award n 2005, and the Most Cted Paper Award from Sgnal Processng: Image Communcaton between 2004 and She s also the edtor (wth Phl Chou) of the book Multmeda over IP and Wreless Networks: Compresson, Networkng, and Systems. She s a senor member of the IEEE.. For more nformaton on ths or any other computng topc, please vst our Dgtal Lbrary at