Computer Networks 55 (2011) 2126–2137

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Computer Networks

journal homepage: www.elsevier .com/locate /comnet

Network lifetime optimization for wireless video sensor networkswith network coding/ARQ hybrid adaptive error-control scheme

Chong Tan a, Junni Zou a,⇑, Min Wang a, Ruifeng Zhang a,b

a Key Laboratory of Special Fiber Optics and Optical Access Networks, School of Communication and Information Engineering, Shanghai University,Shanghai 200072, Chinab Universit’e de Lyon, INRIA, INSA-Lyon, CITI, France

a r t i c l e i n f o

Article history:Received 20 June 2010Received in revised form 4 February 2011Accepted 18 February 2011Available online 2 March 2011Responsible Editor: I.F. Akyildiz

Keywords:Wireless video sensor networkNetwork lifetimePower consumptionNetwork codingConvex optimization

1389-1286/$ - see front matter � 2011 Elsevier B.Vdoi:10.1016/j.comnet.2011.02.014

⇑ Corresponding author.E-mail address: zoujn@shu.edu.cn (J. Zou).

a b s t r a c t

This paper addresses the performance optimization of network lifetime and resource allo-cation for wireless video sensor networks. Network flow control and video encoding bitrate are jointly optimized, aiming to maximize the network lifetime at a given power bud-get and video quality requirement. We develop a generalized power consumption modelfor video sensors, in which video encoding, data communication and error-control behav-ior are completely considered. To combat packet loss over wireless channels, a hybriderror-control scheme integrating network coding and ARQ protocol is introduced. It adap-tively adjusts the number of redundant coded packets according to ARQ feedbacks with afixed code structure and decoding algorithm. Through the Lagrange dual and subgradientapproach, a fully decentralized algorithm is proposed to solve the target convex problem.Finally, simulation results validate the convergence and performance of the proposed algo-rithm in a large-scale random topology as well as in a small static network.

� 2011 Elsevier B.V. All rights reserved.

1. Introduction

Wireless video sensor network (WVSN) is a special kindof wireless sensor network. It consists of geographicallydistributed video sensors, and is capable of capturing, pro-cessing visual information, and delivering them to the sinknodes for further analysis [1]. Typically, WVSNs have beenenvisioned for a wild range of important applicationsincluding security monitoring, emergence response, envi-ronmental tracking and health monitoring. In practice, bat-tery-powered video sensors are often deployed in remoteand unreachable locations. Therefore, minimizing powerconsumption to prolong the network lifetime and provid-ing high-quality video are of paramount importance inWVSNs.

Over the past few years, energy conservation schemesfor wireless sensor networks have been extensively

. All rights reserved.

studied [2–7]. Yang et al. in [2] proposed a mechanismthat utilizes sensors’ mobility to balance the energyconsumption so as to extend the lifetime of the entirenetwork. Zhao et al. [3] presented an optimal sensorscheduling and information routing scheme, in which theimpacts of the network geometry and the energy con-sumption in communications are taken into account.Targeting at saving the aggregate transmit power, anSNR-constrained power reduction scheme is presented in[4]. These methods effectively reduce sensors’ energy con-sumption, but fail to derive an optimal network lifetime.

From network performance perspective, the cross-layerdesign provides a promising approach for maximizing thenetwork lifetime. A joint optimal design of the physical,medium access control (MAC), and routing layers is devel-oped in [5]. It formulates the problem of optimal routingflow, link schedule, as well as link transmission powersas a non-linear optimization problem. The authors in [6]attempted to maximize the lifetime of energy constrainedWSNs with a mixed integer convex optimization solution,

C. Tan et al. / Computer Networks 55 (2011) 2126–2137 2127

where the time division multiple access (TDMA) mecha-nism is adopted in MAC layer, and the impacts of data rate,link access and routing are jointly considered. Also, theperformance tradeoff between fair rate allocation andmaximum network lifetime was investigated in [7].

The power consumption model adopted in existing re-search is constructed on the basis of conventional wirelesssensor networks, where the data processing function at thesensor node is very simple and the corresponding powerconsumption is assumed to be negligible. In WVSN, theraw video of high rate is required to be compressed beforebeing injected onto the channel. In this case, energy uti-lized in video encoding is significant and cannot be ne-glected anymore.

The power consumption on video encoding and datatransmission are intuitively paradoxical. If the encodingprocess occupies too much energy, the power left forthe transmission process will decrease, thus deterioratingthe received video quality. On the other hand, if thepower budget for data transmission is raised, the powerconsumption on video encoding will be curtailed, whichwill definitely influence the quality of the gatheredvideo. A power-rate-distortion (P-R-D) model that char-acterized the relationship between power consumptionof video encoding and its rate-distortion (R-D) perfor-mance, was developed by He et al. in [1]. Following thismodel, a distributed algorithm for maximizing the net-work lifetime of WVSNs is proposed in [8]. The scenarioit considered is very simple where not only the channelcapacity is assumed unlimited, but the channel interfer-ence is negligible. How to balance encoding power, rateand distortion, meanwhile, make a joint optimizationwith network lifetime have remained vastly unexploredin WVSNs.

Reliable communication over time-varying and error-prone wireless channels currently is still challenging. Auto-matic repeat request (ARQ) and forward error correction(FEC) are two popular error-control mechanisms. ARQadopts feedback and retransmission scheme, thus is notsuited for delay-sensitive video applications [9]. Packet-level FEC, (e.g., Reed-Solomon Erasure (RSE) code [10]),which deals with erasures instead of bit errors, is moresuitable to reliable communication over wireless networks[11,12]. In most FEC-based schemes, the maximum error-control redundancy is upper-bounded by the FEC-codesymbol size, which may still lead to decoding failureswhen the channel loss probabilities increase tremendously[13]. Choi et al. [14] proposed a class of adaptive error-control schemes, in which the number of FEC code seg-ments and the frame length are chosen adaptively basedon the estimated channel condition. However, differentencoding/decoding structures are required for variousredundancy levels. And the implementation complexity istoo high to be applicable to real systems. Furthermore,many FEC schemes have been investigated in a hop-by-hop fashion that requires each relay to execute bothdecoding and encoding operation [8]. Such power con-sumption is magnificent and becomes impossible inlarge-scale WSVNs.

Recently, the combination of network coding with mul-tipath routing [15,16] has exhibited some unique advanta-

ges in coping with the unreliability: (1) It can be performedin a decentralized way, requiring no coordination amongnodes; (2) It can be operated ratelessly, i.e. it can run indef-initely until successful decoding. (3) Flows of linearly inde-pendent, instead of same copies traversing multiple pathsmay reduce the transmission redundancy [17]. In thisstudy, we will develop a network coding/ARQ hybrid er-ror-control scheme with low implementation complexityand high throughput efficiency. It can dynamically adjustthe error-control redundancy levels according to theinstantaneous channel condition.

The motivation of this paper is to address the perfor-mance optimization of network lifetime and resource allo-cation for wireless video sensor networks. Our maincontributions are as follows. First, absorbing the general-ized power consumption model of network coding in ourprevious work [18], we construct a power consumptionmodel for video sensors, in which video encoding, datacommunication and error-control behavior are completelyconsidered. Second, we propose a joint optimization ofvideo coding rate, aggregate power consumption and flowcontrol to maximize the network lifetime and meet videoquality requirements. To combat packet loss over wirelesschannels, a hybrid error-control scheme integrating net-work coding and ARQ protocol is introduced. It adaptivelyadjusts the number of redundant coded packets accordingto ARQ feedbacks with a fixed code structure and decodingalgorithm. Last, using Lagrange dual and subgradient ap-proach, we solve the target convex optimization problemin a fully decentralized manner, and evaluate its perfor-mance in a large-scale random topology as well as in asmall static network.

The rest of the paper is organized as follows: Section 2defines the system model and related network constraints.Section 3 presents the proposed hybrid error-controlscheme. Section 5 formulates the optimization problemof network lifetime and rate allocation, and proposes afully decentralized algorithm over lossy wireless channels.Finally, simulation results are presented in Section 6.

2. System modeling

2.1. Network model

A static wireless video sensor network can be modeledas a directed graph G(V,E), where V is the set of sensornodes and E is the set of directed links betweennodes. The set V consists of two disjoint subsets S andT(V = S [ T), representing video sensor nodes and sinknodes respectively. Sensor nodes perform video capture,video encoding and packets routing, while sink nodes aredestinations of WVSN. All sensor nodes have a maximumtransmission range dx. So a directed link (i, j) 2 E existsbetween node i and node j if their distance dij satisfiesdij 6 dx. Suppose there are multiple alternative paths J(s)existed between sensor node s and the sink node. Andeach node s is associated with a matrix Hs to reflect therelationship between its paths and related links. LetHsm

ij ¼ 1 if path m 2 J(s) of sensor node s uses link (i, j), orelse Hsm

ij ¼ 0.

2128 C. Tan et al. / Computer Networks 55 (2011) 2126–2137

2.2. Power-rate-distortion model

According to the analytic power-rate-distortion (P-R-D)model in [1,27], the relationship of source coding bit rate R,coding power consumption P, and the corresponding dis-tortion Dc can be described as:

DcðR; PÞ ¼ r2e�c�R�P23 ; ð1Þ

where r2 is the input variance, c is a model parameterrelated to encoding efficiency. It should be noted that thepower-rate-distortion model is intended to characterizethe P-R-D behavior of the encoder at relatively large scales,i.e., a group of video pictures (GOP), instead of a singlevideo frame [1]. To be concrete, the average P-R-Dmodeling at the GOP level is commonly used to capturethe power consumption behavior of a wireless video sen-sor for efficient power management within a relativelylong period of time, e.g., hours or even days.

It is observed that a given encoding distortion can beguaranteed by controlling both the source rate and theencoding power. However, if we simply adjust the sourcerate or the encoding power to a very low or very high level,the encoding distortion will inevitably become large, mean-while, the total power consumed at the sensor node willfast increase [1]. Thus, an optimal allocation of R and Pshould be established to achieve the required video quality.

2.3. Flow conservation and network coding constraint

For any video session s originating from sensor s withsource rate Rs, its information flow must flow at rate Rs

to the sink node. For each link (i, j), let xsmij denote the infor-

mation flow rate of session s over path m, the informationflow conservation constraint at each node i can be ex-pressed as:Xj:ði;jÞ2E

Xm2JðsÞ

Hsmij � xsm

ij �X

j:ðj;iÞ2E

Xm2JðsÞ

Hsmji � xsm

ji ¼ qi; 8i 2 S;

where qi ¼Rs for i 2 S;

�Rs for i 2 T;

0 otherwise:

8><>: ð2Þ

To ensure the successful decoding, the actual physicalflow rate of any session on each link should be no less thanits corresponding information rate. Let f s

ij represent thephysical flow rate of session s on link (i, j), the relationshipbetween information flow and physical flow can be ex-pressed as:Xm2JðsÞ

Hsmij � xsm

ij 6 f sij ; 8ði; jÞ 2 E; 8s 2 S: ð3Þ

2.4. Channel interference constraint

Consider a WVSN with a shared medium of capacity C.Suppose any link originating from node k will interferewith link (i, j) if dki < (1 + D)dij or dkj < (1 + D)dij. Here,D > 0 specifies the interference range. Also define W(i, j)for each link (i, j) as the cluster of links that cannot transmit

as long as link (i, j) is active, then the wireless networkchannel interference constraint can be defines as [20]:Xs2S

f sij þ

Xs2S

Xðp;qÞ2Wði;jÞ

f spq 6 C; 8ði; jÞ 2 E: ð4Þ

2.5. Power consumption model

In general, the total power of a video sensor is used forfour important processes: video coding, data transmission,data reception, and error-control. The video coding powerconsumption can be computed by the P-R-D model. Fol-lowing an extensively used power consumption model inwireless sensor networks [7], the transmission power con-sumption at a node i is formulated as:

Pti ¼ �ij �

Xs2S

Xj:ði;jÞ2E

f sij ; ð5Þ

where �ij = h + g � (dij)a is the transmission energy con-sumption cost of link (i, j), h is the energy cost of transmitelectronics, g is a coefficient term corresponding to the en-ergy cost of transmit amplifier, and a is the path loss factor.

The reception power consumption at a node i is givenby:

Pri ¼ n �

Xs2S

Xj:ði;jÞ2E

f sji ; ð6Þ

where n is the energy consumption cost of the radioreceiver.

The propose network coding/ARQ hybrid error-controlscheme will be detailed in the following section. The net-work coding power consumption at a node i is given by:

Peni ¼ u �

Xs2S

Xm2JðsÞ

Xj:ði;jÞ2E

Hsmij � xsm

ji ; ð7Þ

where u = [e⁄ � q2 � h + e+ � (h � 1)] is the power consump-tion cost of network coding for each bit, q is the Galois Fieldsize, and h is the generation size [19]. Note that this modelis an analytic one that is developed in our previous work.Please also refer to [18] for the detailed information.

Based on the above analysis, the total power dissipationat a sensor node i is given by:

Pi ¼ Psi þ Pt

i þ Pri þ Pen

i ¼ Psi þ �ij �

Xs2S

Xj:ði;jÞ2E

f sij

þ n �Xs2S

Xj:ðj;iÞ2E

f sji þu �

Xs2S

Xm2JðsÞ

Xj:ði;jÞ2E

Hsmij � xsm

ji ; ð8Þ

where Psi represents the video coding power of node i.

3. Network coding/ARQ hybrid error-control scheme

In this session, we present an error-control scheme thatcombines network coding with ARQ mechanism to combatthe packet loss over the wireless channels.

3.1. A hybrid of network coding and ARQ

The main idea of a hybrid of network coding and ARQis that, the sink node attempts to recover the current

Generationnumber

AC

K/N

AC

K

Number of packets received

Checksum

2 bytes 1 byte 2 bytes 1byte

Fig. 2. Structure of an ACK/NACK packet.

C. Tan et al. / Computer Networks 55 (2011) 2126–2137 2129

generation with the received coded packets first, and ifthe decoding operation fails, retransmission is requested.Responsively, in the next generation, the coded packetsissued from the source will be increased. More precisely,

(1) At the source node, each generation i of h packets arecoded together by random linear network coding,creating n0 coded packets. Generally, n0 is largerthan h, and n0 � h is referred to as redundantpackets for handling packet loss problem. These n0

packets then are injected on outgoing links alongmultiple paths. In this way, flows traversing differ-ent paths are linearly independent rather than iden-tical copies.

(2) At the relay node, packets from different paths of thesame session can be coded again to provide diverseinformation. Here network coding across differentsessions is forbidden to reduce the complexity.

(3) At the sink node, when any h linearly independentpackets of generation i are received, this generationis assumed to be successfully received. Then anacknowledgement (ACK) is sent to the sourcenode. Or else, a negative acknowledgement (NACK)is sent back. In an ACK/NACK feedback, the numberof received linearly independent packets should beappended, upon which the source could decidethe number of coded packets sent in the nextgeneration.

(4) The source node keeps transmitting generationswithout waiting for ACK/NACK of those generationsalready transmitted, i.e., we use the selective-repeatARQ in this study [14]. If NACK of a transmittedgeneration i is received, which means the channelconditions are getting deteriorated and the redun-dancy of n0 � h is not enough for the recovery ofgeneration i, the source node will increase the num-ber of coded packets to n1 for the next generationbased on the NACK information. As for generationi, the motion estimation and motion compensationcan be applied to the decoder while the video qualityacquired drops a little [21]. On the contrary, whenACKs is consecutively received within a presetinterval, the source node considers if it is time todecrease the number of coded packets so as to avoidunnecessary redundancy.

Generation 1 Generation 2 3 noitareneG

NACK ACK

Fig. 1. Network coding/ARQ hyb

The proposed hybrid error-control scheme is shown inFig. 1. Since it is performed based on the channel state esti-mation provided by the ACK/NACK feedbacks, it might notbe able to deal with short-term channel variations, but iseffective for long-term ones.

An ACK/NACK packet consists of 6 bytes shown in Fig. 2.The first two bytes specify the generation number associ-ated with the ACK/NACK. The third byte denotes whetherit is an ACK or NACK. The following two bytes are to informthe number of linear independent packets received for thespecified generation. And the last byte is a checksum. Ifeach generation contains 50 IP packets, and an average IPpacket is about 1400 bytes, the overhead of ACK/NACK isthen less than 0.009%.

3.2. Performance analysis

It is known that the more redundant packets is sentfrom the source, the more lost packets can be recoveredat the destination. However, it would make little sense togenerate much more redundant information when thepacket loss rate (PLR) is very low. Thus, the redundancylevel would be adapted to the time-vary channelconditions.

Fig. 3 shows the relationship between the PLR and theappropriate number of coded packets required, assumingthere are 100 original packets for delivering. It is observedthat the redundant packets are increased with the PLR ofthe wireless channel. When the PLR is less than 10�3, thelower bound of the required packets is almost near 100.When the channel conditions get worse, the source node

1 noitareneG4 noitareneG

NACK ACK

rid error-control scheme.

Fig. 3. Relationship between PLR and the required coded packets.

Fig. 4. Relationship between PLR and the throughput efficiency.

2130 C. Tan et al. / Computer Networks 55 (2011) 2126–2137

has to add more redundant packets to avoid any decodingfailure.

Fig. 4 compares the throughput efficiency of networkcoding based error-control scheme to its RSE counter-part [12]. An (N,K) RSE code takes N packets as a trans-mit block which consists K data packets and N � Kredundant (parity) packets. And rc = K/N is defined asthe coding rate. A lower coding rate means more redun-dant packets and stronger error recovery capability. It isclear that (255,254) RSE scheme with a coding rate of0.996 has a very high throughput efficiency, but its pack-et recovery capability is quite limited. For a coding rateof 0.9, when the PLR is higher than 0.012, it could notprovide a valid transmission. Although (255,204) RSEand (255,178) RSE codes can guarantee a successfulpacket recovery, their efficiency is relatively lower. Incontrast, the proposed network coding scheme can notonly ensure a reliable communication, but offer a higherthroughput efficiency.

4. Problem statement

For battery-powered WVSNs, maximizing the networklifetime is a critical issue. In this section, we formulatethe network lifetime optimization problem as optimal flowcontrol and energy conservation problems, and develop afully distributed solution.

4.1. Optimization problem

In this work, we aim to seek the maximum network life-time and optimal rate allocation for a WVSN, where theinitial power budget of video sensors and the required vi-deo quality are given. Mathematically, it can be formulatedas follows:

P1 : maximize Tnet ð9Þsubject to :

ð1ÞX

j:ði;jÞ2E

Xm2JðsÞ

Hsmij � xsm

ij �X

j:ðj;iÞ2E

Xm2JðsÞ

Hsmj;i � xsm

ji ¼ qi; 8i 2 V ;

where qi ¼Rs; if i 2 S;

�Rs; if i 2 T;

0; otherwise:

8><>:

ð2ÞX

m2JðsÞHsm

ij � xsmij 6

hnl� f s

ij ; 8ði; jÞ 2 E; 8s 2 S;

ð3ÞXs2S

f sij þ

Xs2S

Xðp;qÞ2Wði;jÞ

f spq 6 C; 8ði; jÞ 2 E;

ð4Þ Ti ¼ Ei=Pi; 8i 2 S;

ð5Þ r2e�c�Rs �ðPsÞ2=36 Ds; 8s 2 S:

Assuming that each sensor node i has an initial energyEi, the lifetime of sensor node i can be formulated asTi = Ei/Pi. Also assume all video sensors are of equal impor-tance. Hence, the network lifetime of WVSN is given by:Tnet = mini2STi = mini2SEi/Pi. For conventional wireless sen-sor networks, there exists several different definitions ofnetwork lifetime in the literature, such as the time beforethe first node runs out of energy, the time until a certainfraction of nodes survive in the network, or the time tothe first loss of coverage, etc. Among these definitions, thatthe time until the first sensor exhausts its battery energy isa standard and extensively used one, e.g. in [7,8]. More-over, this definition is fairly suited for visual monitoringapplications, and makes the analysis tractable for manydifferent scenarios. Take a security monitoring applicationfor example, if any of the sensor node fails due to theexhaustion of energy, the intruder can break into the mon-itored area covered by that node. In such case, the entiresecurity monitoring system loses its effectiveness even ifall the other sensor nodes are still working. From thispoint, we can say that once a node is down, the whole net-work is down. Therefore, in our study, each video sensornode is viewed of equal importance, and the energyexhaustion of any node will result in the failure of thewhole network.

Constraint (2) specifies the relationship between infor-mation flow and physical flow over lossy channels. Unlikethe error-free channel defined in Eq. (3), here we take thepacket loss into account. Assume the source node codes horiginal packets of each generation into nl packets in termsof instantaneous ACK/NACK feedbacks. So if the number of

C. Tan et al. / Computer Networks 55 (2011) 2126–2137 2131

the coded packets gained by the sink is larger than h, theoriginal generation can be recovered.

To make our problem be a convex one, we introduce anew variable ti = 1/Ti. So constraint (4) can make a equiva-lent transformation of Ei � ti = Pi. Actually, ti can be regardedas the normalized power consumption of node i with re-spect to its energy budget Ei. Maximizing the minimumlifetime of all sensor nodes is therefore equivalent to min-imize the maximum normalized power consumption overall sensor nodes: Tnet = mini2S Ti = maxi2Sti.

Constraint (5) reflects the relationship of the encodingrate, encoding power and encoding distortion, where Ds

is the upper bound of the received video distortion for ses-sion s.

Note that in Problem P1, xsmij ; f

sij ; Ti, and Rs are optimiza-

tion variables. r2 (average input variance of the videosequence in MSE), c (equivalent encoding efficiency coeffi-cient), �ij (transmission energy consumption cost of link(ij)), n (energy consumption cost of the radio receiver), q(Galois Field size), h (generation size), nl (the number ofthe coded packets issued), C (capacity of the wirelessshared-medium), and Ei (initial power of sensor node i)are design parameters.

For each sensor node s, its path set J(s) to the sink nodeis not an optimization variable, but determined at the ini-tialization phase of the optimization procedure. In the ini-tialization phase, using the multi-path routing protocol,each sensor s finds a set of paths J(s) to the sink node. Thensensor s sends a message containing the value of Hsm

ij toeach link. For any link (i, j) included in the mth path of nodes, it has Hsm

ij ¼ 1, or else Hsmij ¼ 0.

Since our target function is not differentiable and needsthe knowledge of global information of the whole network,it is difficult to solve this problem in a fully distributedmanner. Thus, we use a simple approach, to replace themax norm by an q-norm [24]:

maxi2S

ti ¼ ktk1 ¼ limq!þ1

ktkq ¼ limq!1

Xi2S

tqi

!1q

: ð10Þ

When q is a sufficiently large integer, ktkqmight approxi-mate to ktk1. Therefore, Problem P1 can be re-written as:

P2 : minimize ktkqq ð11Þ

subject to :

ð1ÞX

m2JðsÞHsm

ij � Rsm6

hnl� f s

ij ; 8ði; jÞ 2 E; 8s 2 S;

ð2ÞXs2S

f sij þ

Xs2S

Xðp;qÞ2Wði;jÞ

f spq 6 C; 8ði; jÞ 2 E;

ð3Þ 1c� ln r2

Ds

� �� ðPsÞ�2=3

6 Rs; 8s 2 S;

ð4Þ E � ti ¼ Psi þXs2S

Xj:ði;jÞ2E

eij � f sij þ n �

Xs2S

Xj:ðj;iÞ2E

f sji

þu �X

m2JðsÞRsm

Problem P2 is a convex optimization problem, as theobjective function and the constraint sets are convex[22]. Traditional centralized solutions require global infor-mation and coordination among all nodes, which is

sometimes infeasible in practice. In the following section,we will develop a fully distributed solution based ondecomposition and Lagrange dual theory [23].

4.2. Fully distributed algorithm

To simplify our optimization problem, the originalProblem P2 can be decoupled into a set of subproblemswith distributed solutions. Therefor, we relax constraintsets and formulate the following Lagrangian:

Lðk;l;g;t;R;P;fÞ¼Xs2S

tqs

!þXs2S

Xði;jÞ2E

ksij

�X

m2JðsÞHsm

ij �Rsm� h

nlf sij

" #

þXs2S

ls �1c� lnðr

2

Ds� ðPsÞ�

23Þ�Rs

� �

þXði;jÞ2E

gij �Xs2S

f sij þXs2S

Xðp;qÞ2Wði;jÞ

f spq�C

" #

ð12Þ

where k, l and g are Lagrange multipliers. And the corre-sponding Lagrange dual function is

gðk;l;gÞ ¼ inft;R;P;f

Lðk;l;g; t;R;P; fÞ ð13Þ

subject to : Psi ðtiÞ ¼ Eti �

Xs2S

Xj:ði;jÞ2E

eijf sij � n

Xs2S

Xj:ðj;iÞ2E

f sji

�u �X

m2JðsÞRsm: ð14Þ

The Lagrange dual problem of Problem P2 is then definedas:

maximize gðk;l;gÞ ð15Þsubject to : k P 0; l P 0;g P 0:

As the objective function of the primal Problem P2 isnot strictly convex, the dual function may not be differen-tiable everywhere [22]. We hence use a subgradient algo-rithm to update the primal and dual variables.

At the kth iteration, the primal variables are updated asfollows:

Rsmðkþ 1Þ ¼ RsmðkÞ � hðRÞ � @LðRsmÞ@Rsm ðkÞ

� �þ; ð16Þ

tiðkþ 1Þ ¼ tiðkÞ � hðtÞ � @LðtiÞ@tiðkÞ

� �þ; ð17Þ

f sijðkþ 1Þ ¼ f s

ijðkÞ � hðf Þ �@Lðf s

ijÞ@f s

ij

ðkÞ" #þ

; ð18Þ

Psi ðkþ 1Þ ¼ E � tiðkþ 1Þ �

Xs2S

Xj:ði;jÞ2E

eij � f sij

� n �Xs2S

Xj:ðj;iÞ2E

f sji �u �

Xm2JðsÞ

Rsm; ð19Þ

where h(R), h(t) and h(f) are positive step sizes, and [�]+ rep-resents the projection onto the set of non-negative realnumbers. The partial derivatives of the above primal vari-ables are given by

2132 C. Tan et al. / Computer Networks 55 (2011) 2126–2137

@LðRsmÞ@Rsm ðkÞ ¼

Xði;jÞ2E

ksijðkÞH

smij � lsðkÞ;

@LðtiÞ@tiðkÞ ¼ q � tq�1

i � 23

E � li �1c� ln r2

Di

� �� ðPs

i Þ�4=3

;

@Lðf sijÞ

@f sij

¼ �ksij �

m0

n0þ gij þ

Xðp;qÞ2Wði;jÞ

gpq

!:

Similarly, the dual variables are updated as follows:

ksijðkþ1Þ ¼ ks

ijðkÞþ hðkÞ �X

m2JðsÞHsm

ij �RsmðkÞ�m0

n0f sijðkÞ

!" #þ;

ð20Þ

lsðkþ1Þ¼ lsðkÞþhðlÞ � 1c� ln r2

Ds� ðPsðkÞÞ�

23

� ��RsðkÞ

� �� �þ;

ð21Þ

gijðkþ1Þ ¼ gijðkÞþ hðgÞ �Xs2S

f sijðkÞþ

Xs2S

Xðp;qÞ2Wði;jÞ

f spqðkÞ�C

!" #þ;

ð22Þ

where h(k), h(l) and h(g) are the corresponding positivestep size.

The update of the primal and dual variables can solvethree correlated subproblems, i.e., P-R-D balance problem,rate control problem and energy conservation problem. Fora required video distortion, the source coding rate controlis mainly performed by the update of Rsm, where ks

ij canbe viewed as the encoding price at sensor node s. For eachsensor node s, if the source coding rate

Pm2JðsÞR

sm exceedsthe supply flow, the encoding price ks

ij will rise to reducethe allocated rate. Or else, ks

ij will decrease to meet the ratedemand to balance the power allocation between thetransmission consumption and the video encodingconsumption.

The energy conservation at each sensor is achieved byadjusting the value of Rsmand ti, with li working as the en-ergy consumption cost. If the total energy utilized at node iexceeds the current energy budget, li will rise. As a re-sponse, the communication rate Rsm will slow down to savethe energy. Meanwhile, the normalized power consump-tion ti will rise, signifying the reduction of the lifetime.Otherwise, the opposite changes will happen.

Similarly, gij can be viewed as the congestion price atlink (i, j), For each link (i, j), if the total demand exceedsthe supply C, namely, the capacity of wireless shared-medium is not sufficient to support current data flowstravelling, the price gij will rise to reduce the data flows.Or else, gij will decrease to attract more flows to occupythe free bandwidth.

Clearly, all the updating steps of Problem P2 can bedecentralized performed using only the local information.

4.3. Convergence analysis

The solution of Problem P2 provides a lower bound toapproximate the optimal solution of Problem P1 in respectto the normalized power consumption t.

Proposition 1. Let t̂ and t̂ðqÞ denote the optimal solutioncorresponding to Problem P1 and P2 respectively, we have

kt̂k1 6 kt̂ðqÞk1 6 jSj1q � kt̂k1 ð23Þ

where jSj is the number of sensor nodes in the WVSN. Theproof can be obtained by following the similar analysis in[24] . As q ?1, we have jSj

1q ! 1 and kt̂ðqÞk1 ! kt̂k1. It im-

plies that the bound provides by Problem P2 is very tight withrespect to Problem P1 at a sufficiently large q.

4.4. Implementation of distributed algorithm

To implement the proposed distributed algorithm, eachlink and each sensor node is considered as a processor of adistributed computation system. Assume that the proces-sor for link (i, j) keeps track of variables f s

ij ; ksij and gij, while

the processor for node i keeps track of variables Rim, ti, Pii

and li. A decentralized implementation of the proposedalgorithm can be summarized below. Since the update ofthe primal and dual variables only require the local infor-mation, the communication overhead and the convergencebehavior would not greatly increase with the networkscales.

Algorithm 1. Implementation of the proposeddistributed algorithm

Initialization:set k ¼ 0; Rsmð0Þ; tsð0Þ; Psð0Þ; f s

ijð0Þ, and

ksijð0Þ;lið0Þ;gijð0Þ to some non-negative value for all

i, j, k and the iteration stepsize.At times k = 1,2, . . .

At link (i, j)Receives Rsm(n) and Ps(n) from all nodes use link (i, j);Fetches ks

ijðnÞ and f sijðkÞ stored in the local processor;

Updates rate congestion price ksijðnÞ;

Broadcasts the new price ksijðnÞ to all nodes use link (i, j);

Gain the new price ksijðnÞ

Updates the date flow f sijðkÞ

At sensor node sReceives from the network the price ks

ijðnÞ;Fetches ls(n) stored in the local processor;Updates ts(n), Rsm(n), Ps(n), and price ls(n);Broadcasts the new price ls(n) to all links.

5. Simulation results

In this section, simulation results are presented to dem-onstrate the performance of the proposed distributed algo-rithm. First, a small wireless video sensor network in Fig. 5is adopted, where eight video sensor nodes s1–s8 and onesink node t1 are deployed in a 50 m � 50 m square region.

The maximum transmission range dx for each node is25 m. The parameters for the power consumption modelare set as [7]: e = 0.25 J/Mb, n = 0.245 J/Mb, q = 10. The val-ues of source related parameters are estimated from thestatistics of the test sequence ‘‘Coastguard’’ at CIF (352 �288) resolution: c = 5 W(3/2)/Mbps and r2 = 15,625. It is

Fig. 5. Topology of a small wireless video sensor network.Fig. 7. The convergence of the encoding power.

Fig. 8. The convergence of the allocated rate at each link.

C. Tan et al. / Computer Networks 55 (2011) 2126–2137 2133

with a frame rate of 30 fps and a GOP-length of 32 frames.The initial power of each sensor node is 1 MJ. The capacityof the wireless shared-medium is 10 Mbps. The Rayleighfading model is applied to describe wireless channel fad-ing, where the envelope of the channel response is Ray-leigh distributed and has a probability density function:pðrÞ ¼ r

r2 expð� r2

2r2Þ ð0 6 r 61Þ. Each sensor nodes is al-lowed to perform random linear network coding overGF(28) with a generation size h of 50. Hence, the powerconsumption cost u of network coding is 0.12 mJ/Mb.

Fig. 5 shows the multipath routing from the sensornodes to the sink node, where sensor node s1 and s3 playas the source nodes, while other nodes act as both thesource nodes and the relay nodes. The convergence perfor-mance of the proposed algorithm are shown in Figs. 6–8.Given an upper bound of the encoding distortion Ds, mea-sured in average peak signal-to-noise ratio (PSNR =28.13 dB), the evolution of the encoding power and thesource rate at each sensor node are displayed in Figs. 6and 7, respectively. Here all step sizes are equally set to0.001. It is observed that all of the variables converges witha fast speed and reach their optimal values within 350iterations. Since the sensor nodes close to the sink node,e.g., node s7, have heavy duty on traffic forwarding, they

Fig. 6. The convergence of the source rate.

use a large part of the initial power on data communica-tion, thus leaving less power for video encoding. On thecontrary, those sensor nodes far away from the sink node,e.g., node s3, consume a larger video encoding power.

The convergence of the flow rates allocated at each linkis illustrated in Fig. 8. As the nodes closer to the sink trans-mit more video data, the outlinks of these nodes will beallocated higher data rates. For example, s5 helps forward-ing the data to the sink, and most of the outflows over link(s5, t1) are coming from other sensors. On the other hand,link (s1,s2) has been assigned a lower data rate, becauseit only needs to deliver partial video data for s1 which ful-fills video transmission through multiple paths.

Fig. 9 shows the normalized power consumption ti foreach sensor node. According to the bar chart, the powerconsumption difference among these sensor nodes is notprominent, which implies that all the sensors have veryclose lifetime. Therefore, the whole network would notlose its function fast due to the exhaustion of particularsensors.

Since the network lifetime and the collected videoquality are two paradoxical targets, i.e., the longer the

Fig. 10. Max–min fairness index vs. the required video quality.Fig. 9. Comparison of normalized power consumption on each sensornode.

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100

1

9

3

4

5

6

7

8

2

Fig. 11. The large-scale random topology of a WSVN.

2134 C. Tan et al. / Computer Networks 55 (2011) 2126–2137

network lifetime, the worse the obtained video quality, amaximum network lifetime would be achieved when theresulting video distortions approximate to the given upperbound. When the upper bound of the distortion Ds is set to100 in mean square error (MSE) (corresponding to a lowerbound of PSNR at 28.13), the resulting distortions of eachsensor are shown in Table 1. It is observed that the videodistortions at all the sensors are very close to the givenbound for maximizing the lifetime.

To evaluate the fairness performance of the proposedresource allocation scheme, we choose the popular max–min fairness criteria [25,26]. In accordance with the life-time maximization problem considered in this paper, wedefine our max–min fairness index as:

Max— min Fairness Index ¼ Tmin

Tmax;

where Tmin = min{T1, . . . ,T8} represents the minimum valueof all sensors’ lifetimes, and Tmax = max{T1, . . . ,T8} corre-sponds to the maximum lifetime among all the sensors.

Intuitively, Tmin would be generated from the sensorscloser to the sink node, because these sensors are likelyto exhaust their energy faster as they would help othersensors as well as deliver their own data. In contrast, Tmax

would probably come from the sensors far from the sinknode. Fig. 10 depicts the evolution of the fairness indexwith the required video quality. Clearly, when we requirea higher video quality, the sensor nodes have to increasetheir data rates. The sensors closer to the sink would corre-spondingly spend more energy in data forwarding. It leadsto their lifetimes dropping faster than those far from thesink node, thus resulting in the decrease of the fairnessindex. When we reduce the quality requirement, the

Table 1Resulting distortions of each sensor node.

No. sensor 1 2 3 4

MSE value 99.9761 99.9686 99.9761 99.97PSNR value 28.1318 28.1322 28.1318 28.13

opposite process would happen that achieves a largerfairness index.

We now consider a more complex wireless sensor net-work in Fig. 11, where 100 video sensors are randomlyplaced in a 100 m � 100 m square area, with a sink nodelocated in the center. The initial power of each sensor nodeis 10 MJ, the transmission and interference range are set to30 m, leaving other parameters unchangeable.

Fig. 12 shows the relationship between the videoquality requirement and the achievable maximum net-work lifetime under different channel conditions. It canbe seen that the quality and the lifetime is a paradoxical

5 6 7 8

69 99.5198 99.9769 99.4664 99.466418 28.1517 28.1318 28.1540 28.1540

Fig. 12. Relationship between video quality requirement and achievablemaximum network lifetime.

Fig. 13. Adaptive adjustment of the number of coded packets.

Fig. 14. Comparison of power consumption on network coding and FECscheme.

Fig. 15. Ratio of power consumption on video encoding to datatransmission.

C. Tan et al. / Computer Networks 55 (2011) 2126–2137 2135

property pair. High-quality video is achieved at the cost ofnetwork lifetime. Conversely, the network lifetime can beprolonged by moderately degrading the received videoquality. Further, as the channel state worsens, more andmore coded packets are required for a successful decoding.Consequently, more energy would be consumed onerror-control, which inevitably leads to the decrease ofthe network lifetime.

Fig. 13 shows the adaptive adjustment of the number oftransmitted coded packets with the ACK/NACK feedbacks.Assume the source node reduces the number of transmit-ted coded packets after receiving 10 consecutive ACK pack-ets. Clearly, the coded packets is observed to vary with theestimated channel condition. One can easily imagine thatthe moments of coded packet number climbs correspondto the bad channel condition, and vice versa.

For the selected 9 sensor nodes in Figs. 11 and 14 com-pares their power consumption on error-control by usingnetwork coding and hop-by-hop FEC scheme employed in[8]. We can find that network coding outperforms FEC

based error-control scheme. Using FEC scheme, each relaynode utilizes a large amount of energy on encoding anddecoding operation. For network coding based scheme,only the intersecting relay nodes along different pathsneed to perform further encoding, and network decodingis never required at any relay node. Moreover, FEC schemeintroduces redundant check codes which also consumemore power than network coding.

Given an required PSNR of 35 dB, Fig. 15 presents theratio of power consumption on video encoding to that ondata transmission for these nine sensors. Since a high-quality video is demanded, most power is thus used forvideo encoding, leaving a quite small part of power for datatransmission. Unlike other sensors, node 3 evenly allocatesits total power for two processes. The reason is thatnode 3 is located near the sink node, which has to act asthe relay for more sensors and uses more power for datatransmission.

2136 C. Tan et al. / Computer Networks 55 (2011) 2126–2137

6. Conclusion

This paper investigates the problem of network lifetimeoptimization for wireless video sensor networks, wherethe network employs link rate allocation, multipath net-work coding based error-control, as well as video encodingrate to jointly optimize the network lifetime. To achievereliable transmission as well as high throughput efficiencyover lossy wireless channels, a network coding/ARQ hybriderror-control scheme is developed. It allows the adaptationof the coded packets issued from the source to the esti-mated channel condition. We develop a fully decentralizedalgorithm by Lagrange dual and subgradient approach tosolve the objective convex problem. Simulation results val-idate the proposed algorithm from the convergence andperformance optimization.

Acknowledgements

The work has been partially supported by the NationalNatural Science Foundation of China under Grant Nos.60928003, 60736043, and 60802019.

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Chong Tan received the B.S. and M.S. degreein electronic engineering from Shanghai Uni-versity, Shanghai, China, in 2006 and 2009,respectively. She is currently working towardthe Ph.D. degree at Shanghai University. Hermain research interests include wireless sen-sor network, visual communication, and dis-tributed network optimization.

Junni Zou is currently an Associate Professorin the School of Communication and Infor-mation Engineering, Shanghai University(SHU), where she is undertaking the researchactivities in the area of multimedia trans-mission over wireless sensor networks. Sinceshe received Ph.D. degree in Communicationand Information System from SHU in 2006,she has been with the School of Communica-tion and Information Engineering, SHU. FromJanuary 2008 to May 2008, she was a ResearchScholar with the Department of Electrical

Engineering, Carnegie Mellon University (CMU), USA. Her researchinterests include distributed resource allocation, multimedia communi-cation and network information theory. She has published over 30

C. Tan et al. / Computer Networks 55 (2011) 2126–2137 2137

international journal/conference papers. Also, Dr. Zou acts as member ofTechnical Committee on Signal Processing of Shanghai Institute of Elec-tronics.

Min Wang is currently a Professor in theSchool of Communication and InformationEngineering, Shanghai University, Shanghai.He directs ‘‘Broadband Access Network’’ areain the National Key Laboratory of Special FiberOptics and Optical Access Networks. Hisresearch interests include broadband opticalaccess, wireless communication, and multi-media communication.

Ruifeng Zhang received the B.S. degree inElectronics Engineering from Taiyuan Univer-sity of Science and Technology, China, in 1999,and the M.S. degree in Electronics Engineeringfrom Shanghai University, China, in 2003, andthe Ph.D. degree in Information from InstituteNational des sciences appliqués (INSA) de Lyon,France, in 2009. His research interests includewireless communications, cooperative oppor-tunistic communications, wireless sensor net-works and multiple-antenna wireless commu-nication systems and networks.