WIRELESS video sensor networks (WVSNs) are capable

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1 1182 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 60, NO. 3, MARCH 2011 Lifetie and Distortion Optiization With Joint Source/Channel Rate Adaptation and Network Coding-Based Error Control in Wireless Video Sensor Networks Junni Zou, Meber, IEEE, Hongkai Xiong, Senior Meber, IEEE, Chenglin Li, Ruifeng Zhang, Meber, IEEE, and Zhihai He, Senior Meber, IEEE Abstract In this paper, we study joint perforance optiization on network lifetie and video distortion for an energyconstrained wireless video sensor network WVSN). To seek an appropriate tradeoff between axiu network lifetie and iniu video distortion, a fraework for joint source/channel rate adaptation is proposed, where the video encoding rate, link rate, and power consuption are jointly considered, forulating a weighted convex optiization proble. In the context of lossy wireless channels, an efficient error control schee that couples network coding and ultipath routing is explored. Moreover, an integrated power consuption odel, including power dissipation on video copression, error control, and data counication, is specifically developed for the video sensor node. By prial decoposition, the original proble is decoposed into a two-level optiization procedure, with the high-level procedure for source adaptation source rate optiization) and the low-level procedure for channel adaptation network resource allocation). Finally, a fully decentralized iterative algorith is developed to resolve the target optiization proble. Extensive siulation results evaluate the convergence perforance of the proposed algorith and deonstrate the best tradeoff perforance. Index Ters Lifetie, power rate distortion P-R-D), resource allocation, wireless video sensor networks WVSNs). I. INTRODUCTION WIRELESS video sensor networks WVSNs) are capable of capturing and processing visual inforation and delivering the to the sink over wireless channels [1]. In typical scenarios, such as target tracking and video surveillance, Manuscript received August 19, 2010; revised Noveber 28, 2010; accepted January 5, Date of publication February 4, 2011; date of current version March 21, This work was supported in part by the National Natural Science Foundation of China under Grant , Grant , Grant , and Grant , by the Progra for New Century Excellent Talents in University under Grant NCET , and by the National High Technology Research and Developent Progra of China under Grant 2006AA01Z322. The review of this paper was coordinated by Dr. C. Yuen. J. Zou and R. Zhang are with the Key Laboratory of Special Fiber Optics and Optical Access Networks, Shanghai University, Shanghai , China e-ail: zoujn@shu.edu.cn). H. Xiong and C. Li are with the Departent of Electronic Engineering, Shanghai Jiao Tong University, Shanghai , China e-ail: xionghongkai@sjtu.edu.cn; lcl1985@sjtu.edu.cn). Z. He is with the Departent of Electrical and Coputer Engineering, University of Missouri, Colubia, MO USA e-ail: hezhi@issouri.edu). Color versions of one or ore of the figures in this paper are available online at Digital Object Identifier /TVT a WVSN is supposed to support high data rates and provide high-quality video. High data rates necessitate a huge power consuption at the video sensor. However, battery-powered video sensors are often deployed in reote and unreachable locations, where battery replaceent is ipossible. Hence, there is an inherent tradeoff between using iniu power and achieving the highest video quality. The focus of this paper is on the design of adaptive power consuption, source coding rate, transission rate, and ultipath coding, achieving joint perforance optiization on network lifetie and video distortion. Over the past few years, a variety of power control, rate allocation, scheduling, and routing schees have been proposed to axiize the lifetie of wireless sensor networks [2] [7]. For instance, distributed algoriths for axiu lifetie routing have been studied in [2] and [3]. Wang et al. [4] investigated a cross-layer design approach for iniizing the energy consuption of a ultiple-source and single-sink wireless sensor network. Lifetie optiization with joint power and rate control in interference-liited ad hoc networks has been considered in [5] and [6]. In [7], the authors exploited the interaction between network lifetie axiization and fair rate allocation. The power consuption odel adopted in the foregoing literature is constructed on the basis of conventional sensor networks, where the data processing function at the sensor node is very siple, and the corresponding power consuption is assued to be negligible. In WVSNs, the raw video of high rate is required to be copressed before being injected onto the channel. In this case, the energy utilized in video copression is significant and cannot be neglected anyore. In our previous work [1], a power rate distortion P-R-D) analytical odel has been developed to characterize the relationship between power consuption of video encoding and its rate distortion perforance. Following this odel, He et al. [8] proposed a distributed algorith for axiizing the network lifetie of WVSNs. The scenario they considered is very siple, where the channel capacity is assued unliited, and the quality required for the reconstructed video is prescribed. When the video quality and the network lifetie concurrently becoe the targets, the cases would be ore coplicated and paradoxical since the video quality can be iproved at the price /$ IEEE

2 ZOU et al.: LIFETIME AND DISTORTION WITH RATE ADAPTATION AND NETWORK CODING CONTROL IN WVSNs 1183 of the network lifetie, and vice versa. How to establish an appropriate tradeoff between these two conflicting properties has reained vastly unexplored in WVSNs. Rate/channel adaptation has been proven as an effective eans of enhancing the wireless network efficiency [9] [11]. In channel adaptation, the data being counicated are considered to be generic and, thus, are generally encoded at the source with fixed rates. A cobination of flexible channel adaptation with predeterined source rate is hard to fully utilize network resources. When the source rate exceeds the instantaneous channel capacity, network congestion would occur and could never be prevented by any rate adaptation schee. On the contrary, the channel would be underutilized. The authors of [12] envisaged the nature of source data and proposed adaptive source encoding rates to satisfy the distortion constraints. However, their approach addressed the lifetie axiization proble for a single-hop wireless syste. In this paper, we present a joint source/channel rate adaptation fraework for ultihop ultipath WVSNs. It allows both the source rate and the transission rate to vary with both channel conditions and distortion requireents. Quality degradation arising fro packet loss is quite challenging for wireless video transission. Autoatic repeat request adopts a feedback and retransission schee that is not suitable for delay-sensitive video applications [13]. Packetlevel forward error correction e.g., Reed Soloon erasure RSE) code [14]), which deals with erasures instead of bit errors, introduces check packets that require extra energy consuption. Recently, the cobination of network coding with ultipath routing also referred to as ultipath network coding) has eerged as a proising technique for reliable counication [15] [17]. Most of the previous studies in this area focused on code design and paraeter selection to guarantee successful decoding at the destination [18]. To the best of our knowledge, the power consuption behavior of network coding has not been investigated in the literature. In this paper, we develop a generalized power consuption odel for network coding. Based on this odel, the power consued on ultipath network coding could be incorporated with source coding and data counication power dissipation, foring an integrated power consuption odel for the video sensor node. The otivation of this paper is to address a joint perforance optiization of network lifetie and video quality for energyconstrained WVSNs. To seek an optial tradeoff between axiu network lifetie and iniu video distortion, we consider joint video encoding rate, aggregate power consuption, along with link rate allocation, forulating a weighted constrained convex optiization proble. Within the context of lossy wireless channels, an efficient error control schee that couples network coding and ultipath routing is explored. By prial decoposition, the original proble is decoposed into a two-level optiization procedure, with the high-level procedure for source adaptation and the low-level procedure for channel adaptation. Using the Lagrange dual approach, the lowlevel procedure is further decoupled into three subprobles: 1) rate control proble; 2) distortion control proble; and 3) energy conservation proble, which are solved separately and coordinated by Lagrange ultipliers. Finally, a fully decentralized iterative algorith is developed to solve the target optiization proble. Copared with existing lifetie optiization approaches, the proposed algorith is specifically developed for WVSNs and has the following ajor advantages: 1) Distributed joint optiization of network lifetie and video distortion. The previous work on perforance optiization for a wireless sensor network ostly focused on extending the lifetie of the network. In WVSNs, not only the network lifetie but the video distortion is the ajor concern as well. We forulate the joint optiization of these two conflicting objectives as a weighted convex proble and propose a distributed algorith with low counication overhead to resolve it. 2) Joint source/channel rate adaptation. To increase the resource utilization, we propose a fraework for joint source/channel rate adaptation. The channel adaptation network resource allocation) is achieved by solving rate control, distortion control, and energy conservation subprobles at individual sensor nodes and wireless links. Based on the resource allocation results in channel adaptation, each video source independently perfors source adaptation source rate optiization) by solving a localized optiization proble. 3) Source coding, data counication, and error control integrated power consuption odel. Unlike the power consuption odel of a conventional wireless sensor network, we consider power dissipation on video copression, ultipath network coding-based error control, as well as data counication, establishing an integrated power consuption odel for the video sensor node. The rest of this paper is organized as follows: The network odel and related specifications are presented in Section II. In Section III, the network coding-based error control schee and its power consuption odel are developed. In Section IV, we forulate the tradeoff proble of axiizing network lifetie and iniizing video distortion as a weighted convex optiization proble. A decentralized algorith for joint rate allocation, distortion control, and energy conservation is proposed. We also prove the convergence of the iterative algorith for updating the network lifetie and discuss an efficient ipleentation schee. Experiental results are presented in Section V. Finally, we suarize this paper in Section VI. II. SYSTEM MODELING A. Network Model A WVSN can be odeled as a directed graph GV,E), where V is the set of network nodes, and E is the set of directed links between nodes. The set V consists of two disjoint subsets S and T representing video sensor nodes and sink node, respectively. Video sensor nodes perfor video capturing, video encoding, and packet routing. Sink nodes are reote control units or huan interface devices acting as destinations of the WVSN. The transission between each source sink pair is called a session in this paper. All the sensor nodes have a axiu transission range d ax. A directed link i, j) E

3 1184 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 60, NO. 3, MARCH 2011 Fig. 1. Relationship of video encoding power, rate, and distortion. exists between nodes i and j if their distance d ij satisfies d ij d ax. Suppose that there exist ultiple alternative paths Js) between sensor node s and the sink node. Each node s is associated with a atrix H s to reflect the relationship between its path and related links. Let Hij s =1if path Js) of sensor node s uses link i, j), orelsehij s =0. B. P-R-D Model In video counication over lossy channels, the end-toend distortion D is divided into two parts: 1) source coding distortion D c caused by video copression and 2) transission distortion D t arising fro channel errors. Since the encoding and transission errors are generally uncorrelated, we have D = D c + D t. 1) This distortion odel is proposed in [19]. Thereafter, it is widely used to estiate the end-to-end distortion in the literature [1], [20]. An analytic P-R-D odel has already been developed in [1]. It characterizes the relationship of video coding power consuption P, source rate R, and its distortion D c as D c R, P )=σ 2 e γ R P 2 3 where σ 2 is the average input variance, and γ is a odel paraeter related to the encoding efficiency. Fig. 1 plots the encoding distortion D c, easured in ean square error MSE), as a function of source rate R and encoding power P. Clearly, a given encoding distortion can be guaranteed by controlling both the source rate and the encoding power. If we decrease the encoding power P or the source rate R, then the distortion D c increases for the sake of insufficient copression power. On the other hand, if we increase the encoding power P, then the power used for transission decreases, which also results in the increase of the distortion D c. Further, if we siply adjust the encoding power or the source rate to a very low or very high level, then the encoding distortion will becoe large. Meanwhile, the total power consued at the sensor node will increase fast [1]. Thus, an optial allocation of R and P should be aintained to save the power consuption and control the video distortion. 2) C. Channel Interference Constraint When a standard ediu access control MAC) protocol, e.g., IEEE , is adopted to coordinate the sensors access to a shared channel, the counication activities aong the links are no longer independent. Suppose any link originating fro node k will interfere with link i, j) if d kj < 1 + Δ)d ij or d ki < 1 + Δ)d ij. Here, Δ 0 specifies the interference range. In other words, when node i is counicating with node j, any node whose distance to i or j is less than 1 + Δ) ties that between i and j has to keep quiet. In addition, defining Ψi, j) for each link i, j) E as the cluster of links that cannot transit as long as link i, j) is active, then the wireless network channel interference constraint can be defined as [21] fij s + fpq s C 3) s S s S p,q) Ψi,j) where fij s is the transission rate of session s over link i, j), fpq s is the transission rate of session s along link p, q) Ψi, j) that would interfere with link i, j), and C represents the axiu rate supported by the wireless shared ediu. III. NETWORK CODING-BASED ERROR CONTROL AND ITS POWER CONSUMPTION A. Multipath Network Coding Schee Transission errors, such as packet loss and packet corruption, frequently happen over wireless fading channels. To iprove the reliability and reduce the transission distortion D t, we now present an efficient error control schee based on ultipath network coding. Define the strea fro its source to the sink as a separate session. Hence, the video data gathering in the sensor network is accoplished through ultiple independent unicast sessions. Suppose that the original strea at the source is divided into generations [22], with each generation containing h packets denoted as X 1,X 2,...,X h. Using rando linear coding, each outgoing packet Y i is a linear cobination of these original packets, naely h Y i = g ij X j 4) j=1 where the set of coefficients g =[g i1,...,g ih ], which is also called the global encoding vector, is randoly picked fro field GF 2 q ). Since network coding across different generations ay increase the processing delay and coputational coplexity, we liit coding operations within the sae generation. Consequently, packets of each generation can be decoded independently at the sink. At the source node, the original packets are coded together before being injected on the outgoing links. With a ultipath routing protocol e.g., traditional disjoint ultipath echanis [23]), the coded streas traverse through ultiple paths toward the sink node. A relay sensor, helping forward packets for other sensors, stores incoing packets into its buffer for a certain period. Packets that belong to the sae generation but fro different paths can be further cobined at the relay sensor to

4 ZOU et al.: LIFETIME AND DISTORTION WITH RATE ADAPTATION AND NETWORK CODING CONTROL IN WVSNs 1185 increase the inforation diversity. When the sink receives h packets with linearly independent global encoding vectors, it can perfor decoding by Gaussian eliination and recover the original packets. For any video session s originating fro sensor s, suppose that there are, respectively, A s ij τ) and Bs ij τ) coded packets injected and received on link i, j) at a tie period of τ. Ifthe packet loss rate on link i, j) is p ij, then we have Bij s τ) = k=1 As ij τ)z k, where Z k is a Bernoulli rando variable with PrZ k =0)=p ij. If the packets are injected and received on link i, j) at the average rates of fij s and xs ij, then we have [17] x s Bij s ij = li τ) = li τ τ τ = li τ A s ij τ) k=1 Z k τ A s ij τ) k=1 Z k A s ij τ) As ij τ) =1 p ij ) f s τ ij. 5) It is entioned that the packet loss rate p ij of link i, j can be estiated at nodes i and j if real-tie transport protocol/realtie transport control protocol is eployed at each node. In the preceding forulation, the linear correlation aong different encoding vectors is not taken into account. Therefore, the coded data received at each node are decodable as long as the flows injected and received on any link i, j) are equivalent. Since there exists a sall probability of linear correlation aong the encoding vectors, we introduce a slack factor κ and let κ x s ij =1 p ij ) f s ij 6) where κ>1. This way, for each link i, j), the injected flow rate f s ij would be larger than the received flow rate xs ij, with their difference offsetting the linear correlation. B. Integrated Power Consuption Model 1) Power Consuption Model on Data Counication: In our design, the total power of a video sensor is ainly used for four iportant processes: 1) video copression; 2) data transission; 3) data reception; and 4) ultipath network coding. The video copression power consuption can be calculated by the P-R-D odel. Based on the power consuption odel extensively used in wireless sensor networks [7], [8], the transission power consuption at node i can be defined as Pi t = ɛ ij fij s 7) s S j:i,j) E where ɛ ij = θ + η d ij ) α is the transission energy consuption cost of link i, j), θ is the energy cost of transit electronics, η is a coefficient ter corresponding to the energy cost of transit aplifier, and α is the path loss factor. The reception power consuption at a node i can be forulated as = ξ fji s 8) P r i s S j:j,i) E where ξ is the energy consuption cost of the radio receiver. 2) Power Consuption Model of Network Coding: Assue that each packet consists of L bits. Letting GF 2 q ) represent the Galois field, then each q consecutive bits of a packet can be viewed as a sybol over field GF 2 q ). In addition, assuing that L is a ultiple of q, then each packet is coposed of a vector of L/q sybols. To obtain a coded packet Y i defined in 4), it is observed that h L/q) ties of ultiplication and h 1) L/q) ties of addition should be perfored in GF 2 q ). Although soe practical coding ethods have recently been eployed in wireless protocols e.g., XOR coding in a MAC extension known as COPE [24]), we just develop a generalized odel for theoretical network coding, upon which siplified versions can easily be obtained. Let ε q 3 and ε + q denote the energy consuption per q-bit ultiplication and addition, respectively. Here, ε and ε + are energy consuption cost deterined by specific copleentary etal oxide-seiconductor CMOS) technology [25]. Thus, the energy consued on packet Y i can be forulated as ϕ p = ε q 3 h L/q)+ε + q h 1) L/q). 9) The unit power consuption cost is then given by ϕ = ε q 3 h L/q)+ε + q h 1) L/q)L = ε q 2 h + ε + h 1). 10) Correspondingly, the network coding power consuption at node i is forulated as = ϕ x s ji. 11) P nc i s S j:j,i) E Fro 10), we can find that the power consuption cost is ainly deterined by the Galois field size q and the generation size h. It would be true that the encoding vectors are linearly independent if they are generated randoly fro a Galois field of sufficient size. The field size q, however, cannot be too large, since not only the cost of the power consuption but the coplexity of the code also grows with the field size. It has been proven that if q is 8, then the probability that the atrix of the encoding vectors received at the sink node has full rank is at least 99.6% [22]. Fig. 2 shows the relationship of generation size h and power consuption cost, where we have ε = W/MHz) and ε + = W/MHz), easured on 0.18-μ 2.5-V CMOS platfor, and the arithetic circuit is siulated by the gate-level siulator ean estiator of density [25]. It is observed that the power consuption cost is approxiately in proportion to the generation size h. This iplies that h should not be too large. Fig. 3 shows the ipact of h on the counication overhead of network coding, i.e., the overhead of transitting extra h encoding vectors in each packet. Here, an average packet is supposed to be about 1400 B for realistic Internet settings. As shown in Fig. 3, the counication overhead increases fast with the generation size h and the field size q. With relatively sall h and q e.g., h =50and q =8), the overhead is tolerant and is only about 3%.

5 1186 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 60, NO. 3, MARCH 2011 Fig. 2. Power consuption cost versus generation size. A. Optiization Proble For an energy-constrained wireless sensor network, one ajor concern is how to optiize the energy utilization and prolong the lifetie of the network. Supposing that each sensor i has an initial energy E i and a lifetie of T i = E i /P i, we define the lifetie of the network as T net = in i S T i = in i S E i /P i. Note that this definition akes the analysis tractable for any different scenarios and has been extensively used, e.g., [6] [8]. Hence, the objective of axiizing the network lifetie is ax T net = axin i S T i ). Equivalently, the axiization objective can be reforulated as a iniization objective, i.e., in T net = in in i S T i ). On the other hand, the key issue for video transission is how to iprove the video quality reconstructed at the destination. It iplies that we should iniize the end-toend video distortion at all sink nodes, i.e., in i S D i = in i S Dc i + Dt i ). Note that, by using the proposed error control schee, nearly all the coded packets fro the source are expected to be successfully recovered at the sink. Therefore, transission distortion is negligible, and we have in i S Dc i. According to the foregoing analysis, axiizing the network lifetie and iniizing the total video distortion can both be forulated as constrained iniization probles. Hence, the tradeoff between the can be forulated as a ultiobjective prograing proble. A siple and efficient way to achieve the desired tradeoff is the weighting ethod [26]. That is, we introduce a weighted syste paraeter α [0, 1] and cobine these two objective functions together into a single objective function, i.e., in{α i S Dc i +1 α)[ in i S T i )]}. With the previously introduced constraints, the balance proble can be forulated as follows: { P1 : in α } Di c 1 α) in T i 13) i S i S Fig. 3. Counication overhead versus generation size and field size. Based on the preceding analysis, the total power dissipation at a sensor node i is given by where P c i P i = Pi c + Pi t + Pi r + Pi nc = Pi c + ɛ ij + ξ s S j:i,j) E s S j:j,i) E f s ij f s ji + ϕ s S j:j,i) E represents the video encoding power at node i. IV. PROBLEM STATEMENT x s ji 12) s.t. 1) Js) xs R s s S; 2) κ Js) Hs ij xs =1 p ij ) fij s i, j) E s S; 3) s S f ij s + s S p,q) Ψi,j) f pq s C i, j) E; 4) T i = E i /P i i S; 5) σ 2 e γ R i Pi c)2/3 Di c i S where x s, fij s, T i, R i, and Di c are the nonnegative optiization variables, and x s is the allocated rate on the th path of sensor node s. Constraint 2 shows that fij s is a duy variable that can be expressed by the functions of x s, i.e., fij s = Js) η ij Hij sxs Δ, where we let η ij = κ/1 pij ) to siplify the expression. Constraint 4 is not convex and usually hard to solve in practice. Therefore, we introduce a new variable t i =1/T i and ake an equivalent transforation of E i t i = P i. Note that t i can be interpreted as node i s noralized power consuption with respect to its initial energy budget E i. Naely, axin i S T i ) = inax i S t i ). As for Constraint 5, we siplify it by a logarithic transforation logσ 2 /Di c)=γ Pi c)2/3 R i. In the objective function, the axiu function ax i S t i is not differentiable and is difficult to solve in a distributed anner. Following the sae analysis in [2], we can obtain ax i S t i = t t k = ) 1/k t k i. 14) It can be verified that t k uniforly converges to t at a large k. See also in Section IV-D. In addition, in a reasonable way, we slightly rewrite the objective function t k to t k k, and Proble P1 can be rewritten as P2 : in α i S i S D c i +1 α ) i S t k i 15)

6 ZOU et al.: LIFETIME AND DISTORTION WITH RATE ADAPTATION AND NETWORK CODING CONTROL IN WVSNs 1187 s.t. 1) Js) xs R s s S; 2) s S p,q) Ψi,j) Js) η pq Hpq s x s + s S Js) η ij Hij sxs C i, j) E; 3) E i t i =Pi c+ s S j:i,j) E Js) η ijɛ ij Hij s + s S j:j,i) E Js) η jiξ Hji sxs + ϕ Hji sxs ) i S; 4) 1/γR i ) logσ 2 /Di c) P i c)2/3 i S where x s, t i, R i, and Di c are the optiization variables. xs B. Distributed Algorith To solve Proble P2 in a distributed anner, we use the prial decoposition approach [27] and propose a two-level optiization procedure, i.e., P2a : in α i D c i +1 α ) i t k i 16) s.t. 1) Js) xs R s s S; 2) s η ij Hij sxs + s S p,q) η pq Hpq s x s C i, j) E; 3) E i t i = Pi c + s j:i,j) η ijɛ ij Hij sxs + s j:j,i) η jiξ Hji sxs +ϕ Hji sxs ) i S; 4) 1/γR i ) logσ 2 /Di c) P i c)2/3 i S. P2b : in U R) s.t. R i 0 i S. 17) Proble P2a perfors channel adaptation by allocating appropriate network resource i.e., transission rate and power budget) to video sessions such that they can be accoodated by the wireless channel. Proble P2b perfors source adaptation to channel conditions and sensor states by adjusting the source coding rate on the basis of resource allocation results in Proble P2a. Proble P2a is a low-level optiization, which achieves the optial solution under the condition that R is fixed. Proble P2b is a high-level optiization that is responsible for updating the coupling variable R. The objective value of the low-level optiization is locally optial. It approxiates to the global optiality using the result of the high-level optiization. 1) Low-Level Optiization Channel Adaptation): To solve the low-level optiization, we relax constraints 1, 2, and 4, and forulate the following Lagrangian [28]: Lλ, υ, μ, x, D, t) = α i + s Di c +1 α ) t k i i λ s ) x s + R s + υ ij i,j) s η ij Hij s x s + s + i η pq Hpq s x s C p,q) 1 σ 2 μ i log γr i D c i ) ) Pi c ) ) where λ, υ, and μ are Lagrange ultipliers. In addition, the corresponding Lagrange dual function is s.t. E i t i = Pi c + s + s gλ, υ, μ) = inf Lλ, υ, μ, x, D, t) x,d,t j:j,i) j:i,j) η ij ɛ ij Hij s x s ηji ξ H s ji x s + ϕ Hji s x s). 19) The Lagrange dual proble of P2a is then defined as ax gλ, υ, μ). 20) The corresponding Lagrange ultiplier proble can be solved with the subgradient ethod as [ λ s n+1) = λ s n)+τn) )] + x s +R s 21) υ ij n+1) = υ ij n)+τn) η ij Hij s x s s S + s Js) η pq Hpq s x s C p,q) + 22) [ ) )] 1 σ 2 + μ i n+1) = μ i n)+τn) log γr i Di c Pi c ) ) where [ ] + denotes the projection onto the set of nonnegative real nubers, and τn) is a positive step size. In addition, the channel adaptation proble [see 16)] can further be decoposed into three separate subprobles, i.e., P2a 1 in λ s s x s +R s Js) + υ ij i,j) s S + s S Js) p,q) Ψi,j) Js) η ij Hij s x s η pq Hpq s x s C 24)

7 1188 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 60, NO. 3, MARCH 2011 P2a 2 in α i D c i + i ) 1 σ 2 μ i log γr i D c i 25) P2a 3 in1 α ) i t k i i μ i P c i ) ) s.t. E i t i = P c i + s + s j:i,j) j:j,i) η ij ɛ ij Hij s x s ηji ξ Hji s x s + ϕ Hji s x s). Fig. 4. Scheatic diagra of joint source/channel adaptation schee. Subproble P2a 1 is a rate control proble, in which both the rate allocation at the transport layer and the channel interference at the MAC layer are involved. P2a 2 ais to control and iniize the video distortion. P2a 3 keeps an energy conservation in wireless sensor networks. These three probles are solved separately and coordinated by Lagrange ultipliers λ, υ, and μ. Rate control proble: P2a 1 is siilar to the classical rate control proble in wired networks [29], but it takes into account the wireless channel interference. P2a 1 is an unconstrained convex proble, in which the objective function is still not strictly convex. Thus, we use the subgradient ethod and have x s n +1)=[x s n) ẋ s ] + [ ] + = x s Lλ, υ, μ, x, D, t) n) τn) x s. 27) The derivative of x s is given by ẋ s = τn) λ s + υ ij η ij Hij s i,j) + i,j) p,q) Ψi,j) υ ij η pq H s. 28) In this case, rate control is ainly perfored by the update of x s, where υ ij can be viewed as the congestion price at link i, j). For each link i, j), if the total deand s η ij Hij sxs + s p,q) η pq Hpq s x s exceeds the supply C, naely, the capacity of wireless shared ediu is not sufficient to support current data flows traveling within a cluster, then the price υ ij will rise to reduce the allocated rate x s and the transission rate at link i, j). Otherwise, υ ij will decrease to attract ore flows to occupy the free bandwidth. Distortion control proble: The objective function of P2a 2 is still not strictly convex. Using the sae subgradient algorith, the iniu video distortion can be obtained by D c i n +1)= [ Di c n) τn) α μ )] + i 1 γr i Di cn). 29) pq Energy conservation proble: Again, the variable t i in P2a 3 can be solved using the subgradient algorith as [ t i n+1)= t i n) τn) 1 α )kt k 1 i 2 )] + 3 μ ie i Pi c ) 1 3 wherewehave P c i = E i t i s s j:j,i) j:i,j) η ij ɛ ij Hij s x s 30) ηji ξ Hji s x s + ϕ Hji s x s). 31) The energy conservation at each sensor i is achieved by adjusting the value of x s and t i, with μ i working as the energy consuption price. If the total energy utilized at node i exceeds the current energy budget, then μ i will rise. As a response, the counication rate x s will slow down to save the energy. Meanwhile, the noralized power consuption t i will rise, signaling the reduction of the lifetie. Otherwise, the opposite changes will happen. 2) High-Level Optiization Source Adaptation): We now discuss how to adapt source rate R in the high-level optiization to the channel conditions. As previously entioned, the objective function U R) in P2b is the optial value of P2a for the given R. In addition, the high-level optiization is iteratively executed to update the value of R. For an initial source rate R i at sensor node i, the optial value of P2 is a function of R i that can be resolved by in U R i ). 32) R i 0 Unlike the fixed source rate echanis, the video sensor in our design can achieve the source adaptation by independently solving a localized optiization proble [see 32)], where the instantaneous source rate R i can vary with the congestion price υ ij, energy consuption price μ i, and λ i that are obtained fro channel adaptation, as shown in Fig. 4. The integration of channel adaptation network resource allocation) with source adaptation source rate optiization) finally leads to an optial perforance on network lifetie and video quality.

8 ZOU et al.: LIFETIME AND DISTORTION WITH RATE ADAPTATION AND NETWORK CODING CONTROL IN WVSNs 1189 C. Ipleentation Proble A decentralized ipleentation of the proposed two-level iterative algorith is suarized in Algorith 1. For each sensor s, its path set Js) to the sink is generated at the initialization phase of the optiization procedure. Precisely, in the initialization phase, using the ultipath routing protocol, each sensor s finds a set of paths Js) to the sink. In turn, the sensor s sends a essage containing the value of Hij s to each link. For any link i, j) included in the th path of node s, it has Hij s =1,orelse,Hij s =0. Algorith 1 Distributed two-level optiization algorith Initialization Set n =0, n =0, and x s 0), t s 0), R s 0), Ds0), c λ s 0), υ ij 0), μ s 0) to soe nonnegative value for all i, j, s,. repeat Updating at link i, j) in low-level ipleentation: Receives x s n) fro sensor nodes {s S H s 1 or H s pq ij = =1, p, q) Ψi, j)}; Fetches υ ij n) stored in the local processor; Updates congestion price υ ij n) by Eq. 22); Sends new price υ ij n+1) to sensor nodes {s S H s 1 or Hpq s =1, p, q) Ψi, j)}. Updating at sensor node s in low-level ipleentation: E H s ij ij = Receives the congestion price υ ij n) fro links {i, j) =1or Hpq s =1, p, q) Ψi, j)}; Fetches λ s n) and μ s n) stored in the local processor; Updatesx s n),d sn)andt c s n)byeq.27),29),and30); Updatesλ s n)andenergypriceμ s n)byeq.21)and23); Sends new rate x s n+1) to links {i, j) E Hij s = 1 or Hpq s =1, p, q) Ψi, j)}. Updating at source node s in high-level ipleentation: Sensor s adjusts source rate R s n ) according to Eq. 32). until All variables converge to the optius. Within the ipleentation of network coding, practical rando network coding [22] is used to distribute the source packets of ultiple generations. Here, we assue that intrasession network coding [30] is ipleented within each unicast session to ensure easy operation. During data transission, each video sensor cobines its received packets of the sae generation of the sae source node fro different upstrea links. To cope with asynchronous transission, we use the buffer odel [22] to synchronize the packet arrival and departure. In the buffer odel of relay nodes, packets that arrive at a node on any of the incoing links are put into a single buffer sorted by the generation nuber and the source node nuber. Subsequently, whenever there is a transission opportunity at an outgoing link, the nuber of packets of every source node s every generation in the buffer is checked, and a packet is generated containing a rando linear cobination of all the packets that belong to the generation with the largest nuber of packets. After the generated packet is transitted to the outgoing link, Fig. 5. Topology of the WVSN with the illustration of aggregate link rates. TABLE I CONFIGURATION OF MODEL PARAMETERS IN WVSN certain old packets are flushed fro the buffer according to the flushing policy. D. Convergence Analysis It is straightforward to see that the two-level optiization proble has a unique solution following the foregoing distributed procedures. A foral proof of the convergence directly follows fro the properties of the decoposition principle [27] and is oitted in this paper. In addition, the solution of Proble P2 provides a lower bound to approxiate the optial solution of P1 with respect to the noralized power consuption t. Proposition 1: Letting ˆt and t k) denote the optial noralized power consuption corresponding to Probles P1 and P2, respectively, we have ˆt ˆt k) S 1 k ˆt where S is the nuber of sensor nodes in the WVSN. The proof can be followed with a siilar analysis in [2]. As k,wehave S 1/k 1 and ˆt k) ˆt.Itiplies that the bound provided by P2 is very tight with respect to P1 at a sufficiently large k. In general, either constant step sizes or diinishing step sizes can be used for a subgradient algorith [28]. A constant step size is ore convenient for distributed ipleentation, whereas the corresponding subgradient algorith will only converge to soe suboptial solution within any given sall neighborhood around the optiu [27]. Using a diinishing step size, the

9 1190 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 60, NO. 3, MARCH 2011 Fig. 6. Convergence behavior of the proposed distributed algorith, where a), b), and c) show the low-level iterations of variables x, D, andt, respectively, and d) illustrates the high-level iteration of the coupling variable R. convergence to the optiu can be guaranteed. Accordingly, we have the following result. Proposition 2: If the step size τn) satisfies li τn) =0, n τn) = n=0 then for the sequence {t k) n)} generated by the iterative algorith given in 30), we have li t k) n) ˆt =0. n,k V. S IMULATION RESULTS In this section, we present siulation results to deonstrate the perforance of the proposed distributed algorith. We consider a static WVSN with ten nodes randoly distributed in a square region of 50 50, as illustrated in Fig. 5, where node 10 is set to the sink, and the other nodes are video sensors. Each sensor has a axiu transission range of 30. For every sensor node, we find two shortest paths to the sink, and all nine sensors encode the videos and transit the to the sink through ultiple paths. Nuerically, the values of all the related odel paraeters are tentatively listed in Table I. In Fig. 5, we also depict the aggregate link rates solved by the proposed distributed algorith for the set of links E. The thickness of an edge is proportional to the aount of aggregate flow at the corresponding link. The traffic generated fro all sensors is transported by the rando network coding schee via ultiple paths helping reduce the transission distortion. A. Convergence Behavior of the Proposed Algorith The convergence results of both low-level and high-level optiization iterations are shown in Fig. 6. In accordance with the three low-level subprobles P2a 1 P2a 3, Fig. 6a) c) shows the convergence behavior of the corresponding optiization variables x, D, and t during the lowlevel optiization update at a fixed step size of Here, we set k =10and α = in the optiization objective. Specifically, Fig. 6a) illustrates the low-level iteration of allocated rates on the sensors paths, and the convergence of the video distortion and the power dissipation 1/T i ) at each sensor node is shown in Fig. 6b) and c). It can be seen that all these three types of optiization variables can achieve optial values after about 100 iterations. The convergence behavior of high-level optiization is shown in Fig. 6d), where we present the coupling variable R for illustration. We can observe that the video encoding bit rate R i for each sensor can quickly converge to its optial value after 20 iterations. Based on the perforance of both low- and high-level optiizations, it can be seen that the proposed algorith can quickly converge to a steady state after a relatively short period of tie. B. Tradeoff Between Video Distortion and Network Lifetie The ipact of weighted syste paraeter α on the tradeoff between the total video distortion iniization and the network lifetie axiization is illustrated in Fig. 7. Fig. 7a) and b) illustrates the ipact of the weighted syste paraeter α on the average video distortion and the network lifetie. We can observe that as the weighted syste paraeter α decreases, the corresponding optial network lifetie increases with the increent of the video distortion. On the contrary, the network lifetie decreases and the average video distortion decreases as the increent of α. Fig. 7c) shows the tradeoff between the average video distortion and the network lifetie when α varies. We can observe that when α reduces to an extreely sall value, e.g., α = , the network lifetie approxiately achieves its axial value, since at this tie the network lifetie axiization proble is the doinant proble, which can approxiate the original optiization proble. For the sae reason, when α increases to an relatively large value, e.g., α = , the original optiization proble transfors to the total distortion iniization proble. C. Coparison of NC With RSE Fig. 8 copares the siulation results solved by the proposed algorith with NC and the algorith with typical link-by-link RSE coding schee [8] under different configurations of energy consuption odel paraeters. In the first case, the network coding power consuption cost is set to 0.12 J/Mb, whereas the RSE encoding and decoding power consuption cost are set to 0.08 and 0.21 J/Mb [8]. It can be seen that the algorith with network coding only slightly outperfors that with RSE error control schee. The reason is that under this paraeter configuration, the power consuption of both network coding and the RSE schee is quite sall in coparison with the video coding power consuption and, thus, takes up a inor

10 ZOU et al.: LIFETIME AND DISTORTION WITH RATE ADAPTATION AND NETWORK CODING CONTROL IN WVSNs 1191 Fig. 7. Ipact of weighted syste paraeter α on a) the average video distortion, b) the network lifetie, and c) the tradeoff between the average video distortion and the network lifetie. Fig. 8. Coparison of a) the video distortion and b) the lifetie at each sensor node. part of the entire node power consuption. To ore explicitly show the difference of siulation results, in the second case, we enlarge the network coding power consuption cost to 1.2 J/Mb, and accordingly, the encoding and decoding power consuption costs of RSE are extended to 0.8 and 2.1 J/Mb. Here, we observe that network coding perfors better than the RSE schee with both lower video distortion and longer node lifetie for each sensor node. D. Ipact of Source Rate Adaptation In this section, we copare the perforance achieved by source rate adaptation of the high-level optiization and that Fig. 9. Siulation results under different source rate R i. a) Average video distortion and b) network lifetie. with fixed source rate R i.e., where the high-level optiization is negligible). For each sensor node i, the fixed source rate R i varies fro 50 to 400 kb/s, and the results of average video distortion and network lifetie are shown in Fig. 9. Utilizing the proposed algorith with both low- and high-level iterations, the optial average video distortion and network lifetie can be obtained when the source rate is 310 kb/s, which are accordingly arked by a red line in both Fig. 9a) and b), respectively. Fig. 9 can also be interpreted in another way as the illustration of high-level convergence, i.e., when the proposed algorith initially starts fro either side of to the left or to the right of) 310 kb/s, it will converge rightward or leftward)

11 1192 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 60, NO. 3, MARCH 2011 Fig. 11. Siulation results for each sensor node in rando network with 20 nodes. a) Video distortion and b) the node lifetie. Fig. 12. Siulation results for each sensor node in rando network with 30 nodes. a) Video distortion and b) the node lifetie. Fig. 10. Convergence behavior of the proposed algoriths when network fluctuation occurs. a) Average video distortion and b) the axiu power dissipation, i.e., 1/T net. to the global optiality when the source rate in high-level iteration ends up with R i = 310 kb/s. Although both average video distortion and network lifetie are better when the fixed source rate is larger than 310 kb/s, it cannot be achieved since at this tie, the wireless network channel interference constraint is violated. E. Ipact of Dynaic Network Change We study the convergence behavior of the proposed distributed algorith under the dynaic change of the video content and network topology, and the results are shown in Fig. 10. We characterize the video content with the average input variance σ 2. Initially, the optiization iteration begins with σ 2 = At iteration 100, nodes 8 and 9 leave the network, and the average input variance is reduced to Meanwhile, both the average video distortion and the axiu power dissipation aong all sensor nodes 1/T net ) adapt theselves to this change and quickly converge to another steady state after about five iterations. At iteration 200, nodes 8 and 9 rejoin the network, and σ 2 is varied fro 3500 to The values of the average video distortion and the axiu power dissipation transit fro the previous steady state to a new steady state after about ten iterations. At iteration 300, node 9 leaves the network again, and σ 2 increases to Siilarly, the values of the average video distortion and the axiu power dissipation converge fro the previous steady state to a new steady state after about five iterations. In conclusion, the results in Fig. 10 deonstrate that the proposed distributed algorith can quickly reconverge to a steady state under dynaic change of network conditions. F. Ipact of Network Scale To evaluate the ipact of network scale, we vary the size of the networks and accordingly ipleent the proposed algorith on two larger networks, where 20 and 30 nodes are randoly located in the square regions of and , respectively. With regard to the video distortion and lifetie of each node, Figs. 11 and 12 show the siulation results on the two network topologies. In addition, we copare the siulation results of the proposed algorith on different network scales, and the coparison of the achieved average video distortion and network lifetie is shown in Fig. 13a) and b). We observe that as the scale of the network increases, the duty of data relaying at each sensor node becoes heavier, and thus relay nodes will consue higher power in the transission, reception, and network coding, which results in the worse network perforance with higher average video distortion and shorter network lifetie. G. Ipact of Packet Loss Rate By varying the average packet loss rate of each wireless link fro 5% to 30%, the average video distortion and the network lifetie solved by the proposed algorith are shown in Fig. 14a) and b), respectively. It can be seen that, as the average packet loss rate increases, the average video distortion increases, and the network lifetie decreases. The reason is

12 ZOU et al.: LIFETIME AND DISTORTION WITH RATE ADAPTATION AND NETWORK CODING CONTROL IN WVSNs 1193 Fig. 13. Coparison of different network scales. a) Average video distortion and b) the network lifetie. a joint source/channel rate adaptation strategy is proposed, in which the channel adaptation is responsible for network resource allocation, whereas the source adaptation is eployed for source rate optiization. By jointly optiizing the video encoding rate, the transission rate, and the integrate power consuption, we forulated this tradeoff issue as a weighted convex prograing and then resolved it in a fully distributed anner by prial decoposition and Lagrange dual ethod. Through extensive nuerical and siulation experients, we evaluated the convergence perforance of the proposed algorith and deonstrated that the proposed algorith can provide the best tradeoff perforance in dynaic network settings and well support different network scales. Fig. 14. Coparison of different average packet loss rates. a) Average video distortion and b) the network lifetie. Fig. 15. Coparison between fixed average packet loss rates and link packet loss rate proportional to its distance. a) Video distortion and b) the node lifetie. as follows: For a successful decoding, the nuber of coded packets injected on link i, j) denoted by N Y ) should be sufficient to offset the packet loss rate of that link, and N Y should satisfy N Y h/1 p ij ). Therefore, N Y will increase as the increent of the average packet loss rate, which causes the worse perforance of the entire network. Furtherore, we investigate the perforance of the proposed algorith when the packet loss rate of each wireless link takes into consideration the distance of that link. Assue that the packet loss rate of each link is chosen between 10% and 30% and proportional to the distance of that link. Accordingly, the video distortion and lifetie of all sensor nodes are shown in Fig. 15. VI. 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Since 2006, she has been with the School of Counication and Inforation Engineering, Shanghai University, where she is an Associate Professor. She has published over 40 international journal/conference papers. Her research interests include distributed resource allocation, ultiedia counication, and network inforation theory. Dr. Zou is a eber of the Technical Coittee on Signal Processing of the Shanghai Institute of Electronics. Hongkai Xiong M 01 SM 10) received the Ph.D. degree in counication and inforation systes fro Shanghai Jiao Tong University SJTU), Shanghai, China, in Since 2003, he has been with the Departent of Electronic Engineering, SJTU, where he is an Associate Professor. In SJTU, he directs the Intelligent Video Modeling Laboratory and the Multiedia Counication area of the Key Laboratory of the Ministry of Education of China Intelligent Coputing and Intelligent Syste, which is also cogranted by Microsoft Research. Fro Deceber 2007 to Deceber 2008, he was a Research Scholar with the Departent of Electrical and Coputer Engineering, Carnegie Mellon University, Pittsburgh, PA. He has published over 90 international journal/conference papers. His research interests include source coding/network inforation theory, signal processing, coputer vision and graphics, and statistical achine learning. Dr. Xiong was the recipient of the New Century Excellent Talents in University in In 2008, he received the Young Scholar Award fro SJTU. He has served for various IEEE conferences as a Technical Progra Coittee eber. In addition, he is a eber of the Technical Coittee on Signal Processing of the Shanghai Institute of Electronics. Chenglin Li received the B.S. and M.S. degrees in electronic engineering in 2007 and 2009, respectively, fro Shanghai Jiao Tong University, Shanghai, China, where he is currently working toward the Ph.D. degree. His ain research interests include networkoriented iage/video processing and counication and network-based optiization for video sources. Ruifeng Zhang S 07 M 10) received the B.S. degree in electronics engineering fro Taiyuan University of Science and Technology, Taiyuan, China, in 1999, the M.S. degree in electronics engineering fro Shanghai University, Shanghai, China, in 2003, and the Ph.D. degree in inforation fro the Institute National des sciences appliques de Lyon, Lyon, France, in He is currently with the Key Laboratory of Special Fiber Optics and Optical Access Networks, Shanghai University. His research interests include wireless counications, cooperative opportunistic counications, wireless sensor networks, and ultiple-antenna wireless counication systes and networks. Zhihai He S 98 M 01 SM 06) received the B.S. degree in atheatics fro Beijing Noral University, Beijing, China, in 1994, the M.S. degree in atheatics fro the Institute of Coputational Matheatics, Chinese Acadey of Sciences, Beijing, in 1997, and the Ph.D. degree in electrical engineering fro the University of California, Santa Barbara, in In 2001, he was a Meber of Technical Staff with Sarnoff Corporation, Princeton, NJ. Since 2003, he has been an Assistant Professor with the Departent of Electrical and Coputer Engineering, University of Missouri, Colubia. His current research interests include iage/video processing and copression, network transission, wireless counication, coputer vision analysis, sensor networks, and ebedded syste design. Dr. He is a Meber of the Visual Signal Processing and Counication Technical Coittee of the IEEE Circuits and Systes Society and serves as a Technical Progra Coittee Meber or Session Chair for a nuber of international conferences. He currently serves as an Associate Editor for the IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY TCSVT) and the Journal of Visual Counication and Iage Representation. He is also a Guest Editor for the IEEE TCSVT Special Issue on Video Surveillance. He received the 2002 IEEE TCSVT Best Paper Award and the SPIE Visual Counications and Iage Processing Young Investigator Award in 2004.