 Open Access
 Total Downloads : 234
 Authors : N. Prakash Rajan, P. Dhavakumar, S. Vijayalakshmi
 Paper ID : IJERTV3IS20150
 Volume & Issue : Volume 03, Issue 02 (February 2014)
 Published (First Online): 12022014
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Life Span Enrichment of Wireless Sensor Networks via Duty Cycle and Network Coding: A Survey
N. Prakash Rajan1, P. Dhavakumar2, S. Vijayalakshmi3
1,2,3. Assistant Professor/CSE,
1 ,3. RVS College of Engineering and Technology, Karaikal,PuducherryIndia
2. Periyar maniammai University, Thanjavur District, TamilnaduIndia.
Abstract Wireless sensor networks (WSNs) essential confront is to Enrich the network lifetime. The area something like the sink forms a bottleneck zone. There is stirring a heavy traffic flow. This Survey works attempts to develop the life time of wireless sensor networks by in view of Duty Cycle and Network Coding. A competent communication exemplar has been adopted in the bottleneck zone by the amalgamation of Duty Cycle and Network Coding. The aspiration of our Survey is discussed get better energy competence and raises the throughput in WSN. Exhaustive speculative analyses have been provided to demonstrate the efficiency of the proposed approach besides discussed.
Index TermsWireless Sensor Networks, network lifetime, energy efficiency, duty cycle, network coding.

INTRODUCTION
An elementary dispute in the design of wireless sensor networks (WSNs) is to augment the network life time. In the region of sink form a bottleneck zone appropriate to heavy traffic flow which restrictions the network existence in WSN. The sensor node in the bottleneck zone is alienated in to two groups: simple relay sensor and network coder sensor. The relay node just forward the received data, the network coder nodes convey using the network coding based algorithm [1].
There is a momentous amount of data flow near the
Sink. The area near the Sink is known as the bottleneck zone.
Fig.1. Traffic Flow, Bottleneck zone and role of sensor in a typical WSN.
Profound traffic load imposes on the sensor nodes near the Sink node. The nodes in the bottleneck zone diminish their energy very quickly, referred as energy hole problem in WSN. Collapse of such nodes inside the bottleneck zone leads to expenditure of network vigor and reduction of network steadfastness. The bottleneck zone needs extraordinary consideration for diminution of traffic which improves the network existence of the whole WSN.
Energy competence of the bottleneck zone increases because more degree of data will be transmitted to the sink with the same number of broadcast. Wireless sensor networks consist of sovereign sensor node that can be deployed for monitoring unfeasible areas, such as glaciers, woodland areas, deserts, deep bushel etc [2]. Sensor nodes are generally outfitted with a radio transceiver, a micro controller, a reminiscence unit, and a set of transducer using which they can obtain and process data from the deployed regions. These nodes can self systematize themselves to form multihope network and transmit the data to a sink. In a emblematic WSN, the network traffic exposure at the sink swelling S. (Fig.1).

ARBITRARILY DUTY CYCLE WSN ENERGETIC OF
EXPOSURE.
Wireless sensor networks that maneuver in low duty cycles, deliberate by the entitlement of time a feeler is on or active. The energetic change in topology as a result of such dutycycling has potentially disorderly consequence on the concert of the network. We perimeter our concentration to a class of scrutiny and monitoring applications and unsystematic dutycycling schemes, and scrutinize certain coverage chattels. Here deems exposure strength distinct as the prospect sharing of durations contained by which an intention or an event is revealed/unmonitored. Originate this allocation using a partiallyMarkov model, constructed using the superposition of discontinuous rejuvenation processes. The psychotherapy using the partiallyMarkov model serves as a tool with which we can unearth apposite arbitrary dutycycling schemes gratifying a given recital prerequisite and also show that there
is a close rapport among coverage passion and the appraise of lane accessibility, defined as the prospect division of durations inside which a path vestiges existing. Thus the consequences presented here are voluntarily pertinent to the cram of path accessibility in a short dutycycled sensor group.

Coverage Passion
In this slice will sculpt the on/off schedules of individual sensors as sporadic Markov revitalization processes (MRP), and scrutinize the superposition of numerous such processes. While revitalization theory is a wellreputable subject [3], there are moderately less outcome on sporadic revitalization Processes. In [4] the superposition of sporadic revitalization processes was deliberate with a relevance to arithmetical multiplexing of fracture traffic sources. In this part occupy the approach used in [6] to obtain coverage passion. We too there a beginner's partiallyMarkov model with a linear state space, while the model based on [4] has an exponential state liberty.

Markov revitalization Processes

We will presume distinct time, and thus the on and off periods are integervalued and selected from certain prospect mass functions (pmf) (having finite support) fon i (k) and foff i (k), k = 1, 2K, for some K, correspondingly. The same loom can be applied to nonstop time in a similar manner. Consider n, n 2sovereign discretetime MRPs. Each MRP has only 2 states off (denoted as state 1) and on (denoted as state 2). The ith MRP is characterized by a partiallyMarkov essence Gi(k) = [gi(x, y, k)] defined over the set of states {1, 2}, where gi(x, y, k) is the prospect that the ith process goes
from state x to state y in k slots where x, y {1, 2}. Thus we have.
Fig. 2. A circumstances transition example when there are n = 2 MRPs. State
Â½ is the off/on state.
A superposed state is given by the ntuple
[(x1, t1), (x2, t2),,(xn, tn)], xi {1, 2}, ti {0, 1} (2) where xi is the state of the ith process pragmatic immediatelyafter a transition occurs in the superposed process, and ti indicates whether the ith process has untouched state when this transition occurs, with ti = 1 iff process i has changed state and ti = 0 otherwise. Symbolize by S the state space of the superposed process. The state space consists of all possible combinations of n pairs except when ti = 0, i, in which case no component process has a state transition and then the superposed process cannot have a state transition. The total number of states is thus 2n (2n 1). Figure 2 exemplify a model of the superposition of two component MRPs (n = 2), and the equivalent state space S.
A state u S is given by u = [(x1(u), t1(u)),(x2(u), t2(u)), , (xn(u), tn(u))], where the ith pair defines the state of the ith component process when the superposed process
gi (1,1, k)gi (1,2, k) 0
fioff (k )
changeover to state u. accordingly we will also refer to the ith
Gi =
=
(1)
pair (xi(u), ti(u)) as the state of the ith component process
gi (2,1, k)gi (2,2, k) fpon(k ) 0
The superposition of n sovereign MRPs is modeled as a partiallyMarkov process. Communication that this is a guess since the future superposed state may depend not only on the present state and the time the superposed process has spent in the present state, but also on past states2. Delineate the state transition of the superposed process to arise at time instants when one or more of the constituent processes familiarity a state transition.
when the state of the superposed process is u. For example, if the superposed states are u = [(2, 1), (2, 0)] and = [(1, 0), (1,
1)], then we have (x1(u) = 2, t1 (u) = 1) and (x1(v) = 1, t1 (v) = 0).
Toward attain the allotment of the time the superposed process expend in state u before transitioning to state v, u, v S, we begin with the following notations.
gi(x, y, k): the probability that the ith component process stays in state x for k slots before transitioning to state y, where x and y signify the individual on/off states, x, y {1, 2}. This was formerly agreed in Equation (1).


NETWORK INFORMATION FLOOD
Network Information Flood (NIF) introduces a new class of tribulations called network information flood which is stirred by computer network applications. Regard as a point topoint communication network on which a number of information sources are to be multicast to influenced sets of goals. Presuppose that the information sources are reciprocally independent. The problem is to characterize the permissible coding rate province. This model includes all formerly premeditated models along the same line. In this paper, learning the problem with one information source, and we have attain a simple characterization of the permissible
coding rate province. Our result can be staring as the Max flow Mincut Theorem for network information flood [8].
Divergent to ones insight, our work divulge that it is in general not optimal to regard the information to be multicast as a fluid which can simply be running scared or imitation. Fairly, by employing coding at the nodes, which we refer to as network coding, bandwidth can in general be saved. This verdict may have momentous impact on future design of switching systems [8].
In obtainable computer networks, each node functions as a switch in the sense that it moreover relays information from an input link to an output link, or it replicates information received from an input link and sends it to a certain set of output links. From the informationtheoretic point of view, there is no reason to hamper the function of a node to that of a switch. fairly, a node can function as an encoder in the sense that it receives information from all the input links, encodes, and sends information to all the output links. Commencing this point of view, a switch is a special case of an encoder. In the continuation, we will refer to coding at a node in a network as network coding.
Let Rij be a nonnegative real number allied with the edge (i,j), and let R=[Rij,(i,j)E]. For a fixed set of multicast
requirements, a vector R is admissible if and only if there exists a coding scheme rewarding the set of multicast
requirements such that the coding rate from node i to node j is less than or equal to Rij for all (i,j) E . In graph theory, Rij is called the aptitude of the edge (i,j). Our goal is to characterize
the tolerable coding rate province, R i.e., the set of all admissible R, for any graph G and multicast requirements a,b and h.
The model we have described includes both multilevel assortment coding (without deformation) [5], [6] and distributed source coding [7] as special suitcases. As an illustration, let us show how the multilevel miscellany coding system in Fig. 1 can be formulated as a special case of our model. In this system, there are two sources, X1and X2. Decoder 1 renovates X1 only, while all other decoders renovate both X1 and X2. Let ri be the coding rate of Encoder i,i=1,2,3. In our model, the system is represented by the graph G in Fig. 2. In this graph, node 1 represents the source, nodes 2, 3, and 4 represent the inputs of Encoders 1, 2, and 3, respectively, nodes 5, 6, and 7 represent the outputs of Encoders 1, 2, and 3, respectively, while nodes 8, 9, 10, and
11 represent the inputs of Decoders 1, 2, 3,and 4, respectively. The mappings and are precise as
Fig.4. The graph G representing the coding system in Fig.3.
And h = [pp] represents the information rates of X1 and X2. Now all the edges in G except for (2, 5), (3, 6), (4, 7) match to straight connections in Fig. 3, so there is no constraint on the coding rate in these edges. Therefore, in order to influential R, the set of all permissible R for the graph G (with the set of
multicast requirements precise by a,b and h), we set Rij=
for all edges in G except for (2,5), (3,6), (4,7) to obtain the permissible coding rate region of the quandary in Fig. 3.
A major pronouncement in this paper is that, dissimilar to ones suspicion, it is in general not optimal to consider the information to be multicast in a network as a fluid which can simply be routed or pretend at the middle nodes. Fairly, network coding has to be employed to accomplish optimality.
In the respite of the paper spotlight our debate on problems with m=1, which we collectively refer to as the singlesource problem. For problems with m 2, we refer to them communally as the multisource problem. The respite of the paper is structured as track.
A. A MaxFlow MinCut Theorem
In this part propose a theorem which characterizes the permissible coding rate district for the singlesource problem. For this problem, we let a (1) =s, and b (1) = {t1, Tl} In other words, the information source X1 is generated at node and is multicast to nodes. We will call the source and t1, Tl the sinks of the graph G.
and
a (1)=1 a (2)=1
b (1)= {8,9,10,11} b(2){9,10,11}
Fig.3. A multilevel diversity coding system
Fig.5. A singlelevel diversity coding system
Fig.6.The graph representing the coding system in Fig.3
For a explicit L, the problem will be referred to as the one source Lsink problem.
Let us first identify some notations and terminology which will be used in the respite of the paper. Let G= (V, E) be a graph with source and sinks t1… tL. The capability of an
edge (i,j)E is given by Rij, and let R=[Rij, (i,j) E]. The
sub graph of G from s to tl, l=1, refers to the graph Gl= (V,El), where
El={(i,j) E: (i,j) is on a directed path from s to tl}.
F=[Fij, (i,j) E ] is a flow in G from s to tl if for all (i,j) E.
0 Fij Rij
Such that for all i V except for s and tl.
a general sensor network circumstances. Then, the effect of the bottleneck zone on network performance is scrutinized by construe performance bounds compulsory by the energy resources available indoors the bottleneck precinct. In this epistle, both the concert hurdle in stipulations of network existence and the performance hurdle in terms of information collection are discovering.
Fig.7. Functionalities of the sensor nodes in the bottleneck zone.

Network coding.
Network coding is a technique which allows the intermediate nodes to encode data packets received from its
adjoining nodes in a network. The encoding and decoding process of linear network coding are depicting underneath. [1].
i!:(i!,i )E
Fi!i =
j:(i, j )E
Fij

Encoding maneuver
A node, that desires to transmit encoded packets, prefer a

., the total flow into node is identical to the total flow out of node i. Fij is referred to as the value of F in the edge (i,j). The value of F is distinct as
progression of coefficients q = (q1, q2… qn), called encoding vector, from GF (2s). A set of n packets Gi (i =
1, 2, 3, 4… n) that are customary at a node are linearly encoded into a solitary output packet. The output encoded
j:( s, j )E
Fsj –
i:(i,s )E
Fis
packet is prearranged by
n
This is equal to
Y= qiGi
i1
qiGF (2s) (3)
F is a maxflow from s to t1 in G if F is a floe form s to tl whose value is greater than or equal to any other flow from s to tl. Manifestly, a maxflow from s to tl in Gi is also a max flow from s to tl in. For a graph with one source and one value of a maxflow from the source to the sink is called the capacity of the graph.




TAILBACK ZONE
I WSN nodes roughly the sink devour more vitality than those further disappeared. It is not unusual that limited energy resources available at the nodes around the sink befall the bottleneck which limitations the routine of the intact network. In this epistle initially present our measured bottleneck zone in
The coded packets are conveying with the n coefficients in the network. The encoding vector is used at the receiver to decode the encoded data packets.

Decoding maneuver
A receiver node decipher a set of linear equations to salvage the original packets from the received coded packets. The encoding vector q is received by the receiver sensor nodes with the encoded data. Let, a set (q1, Y 1)… (qm, Y m) has been received by a node. The cipher Yj and qj denote the information pictogram and the coding vector for the jth received packet respectively. A node solves the go after set of linear equations (4) with m equations and n unknowns for decoding progression.
n
Y j=
i1
qjiGi, j= 1 m (4)

Energy Expenditure Model with Duty Cycle.
A sensor node devours energy at different states, such as, sensing and generating data, transmitting, receiving and
As minimum n linearly independent coded packets must be
received by the recipients for apposite decode of the inventive packets. The merely unknown, Gi, restrain the original packets that are transmitted in the network. The n number of original packets can be retrieved by decipher the linear system in equation (4) after getting n linearly independent packets. The XOR network coding, a special case of linear network coding has been used in this exertion. The coded packets that are transmitted in the network are rudiments in GF (2) = {0, 1} and bitwise XOR in GF (2) is used as an operation.
B. Duty Cycle
The sensor nodes accumulate energy by switching between active and quiescent (i.e. sleep) states. The quotient between the time during which a sensor node is in energetic state and the totality time of active/quiescent states is called duty cycle. The duty cycle depends on the node solidity of the scrutinize area for better exposure and connectivity. Habitually for a intense WSN the duty cycle of a node is very stumpy [10].
A duty cycled WSN can be droopily categorized into two main types: random dutycycled WSN [10] and co ordinate duty cycled WSN [11]. In previous the sensor nodes are crooked on and off separately in random trend. In afterward the sensor nodes synchronize amid themselves via communication and control message interactions. They are potentially proficient for communication. Conversely it requires additional information replace to propagate the active
/ snooze agenda of each lump.
The random dutycycled WSNs are simple to blueprint as no additional slide is required. The principally goal is to gain certain systematic understanding on the upper bound of the network lifetime. Consequently, the random duty cycle based WSN has been measured for its effortlessness in design. Expressly, the problem of lessening of passage in the bottleneck zone has been painstaking [10].


UPPER BOUND OF NETWORK LIFETIME USING DUTY
CYCLE.
The system model has been depicting in this sector. Based on the system replica, an energy utilization model for duty cycle based WSN has been urbanized. The upper bound of the network life span has been anticipated and energy savings due to duty cycle has also been exposed [13].
A. System Model
A system is painstaking with N sensor nodes sprinkled unvaryingly in vicinity A. The area A with a traffic jam zone B with radius D is exposed in Fig. 1. All the N sensor nodes are duty cycle enabled (i.e. switching between active and dormant states). The nodes are named based on their roles in the network as shown in Fig. 1. In the zone B, the nodes are discriminate into two groups, such as, relay sensor and network coder sensor nodes. [13] The (active) relay sensor nodes (R) transmit data which are generated outside as well as inside the traffic jam zone. The (active) network coder sensor nodes (N) encode the unprocessed native data which are coming from faint the zone B before transmission.
sleeping state. In this work, the radio model [13] has been personalized for a duty cycle based WSN. Energy investments are done at the node level through switching between active and
Fig.8. State transition diagram of a node substitute as a source (only inside the rectangle) and a node substitute as a relay (the whole state diagram) with transition probabilities (TPs) in a WSN. PSL SL: TP from sleep state to the same state, PSL SN: TP from sleep to sense state, PSN SN: TP from sense state to the same state, PSN Tx : TP from sense to transmit (Tx) state,
PTx Tx: TP from Tx to the same state, PTx SL: TP from Tx to the sleep state, PSL Rx: TP from sleep to receive (Rx) state, PRx Rx: TP from Rx to Rx state and PRx SL: TP from Rx to sleep state.
Snooze states. Energy expenditure by a source node per second across a distance d with path loss proponent n is,
Etx = Rd (11 + 2dn) (5)
Where Rd is the transceiver relay data rate, 11 is the energy addicted per bit by the transmitter electronics and 2 is the energy extreme per bit in the transmit opamp [11]. Besides, the total energy utilization in time t (i.e. duration [0, t]) by a source node (leaf node) lacking acting as a relay (intermediate node) is
ES = t [p (rses + Etx) + (1 p)Esleep] (6)
somewhere Esleep is the sleep state energy utilization of a sensor node per second, rs is the average sensing rate of each sensor node and it is same for all the nodes, es is the energy utilization of a node to sense a bit, the probability p is the average quantity of time t (in the duration [0,t]) that the sensor node devotes in active state. Thus, p is the dutycycle.
C. Energy utilization and Upper Bound of Network life span.
Total energy utilization in the bottleneck zone are scrutiny as three parts, namely, energy utilization (i) to relay the data bits which are received from outside of the bottleneck zone (E1)
(ii) due to sensing maneuver of the (relay) nodes inside the bottleneck zone (E2) (iii) to relay the data bits which are spawn inside the bottleneck zone (E3).
which are nearest to the Sink and diminish their energy quickly) in the bottleneck zone transmits using network coding based announcement. The other group of nodes in the bottleneck zone acts as simple relay nodes. These relay nodes help the Sink to decode the encoded packets. Every time a node in the bottleneck zone receives a packet, it checks its role (refer Fig. 7). The node follows the Algorithm1 to process a packet.
Fig.9. (a) Reception of redundant data bits by the boundary relay nodes in the bottleneck zone (b) A scenario of XORnetwork coding in the network coding layer of the bottleneck zone.
As shown in Fig. 9, sensor nodes in the bottleneck zone may receive multiple copies of the same data bits transmitted from exterior of zone B. So, the superfluous bits which affect the network life span are transmitted within the zone B.
The performance of a WSN austerely depends on the failure information of the sensor nodes. The failure pattern of sensor nodes depends on the rate of depletion of energy. The network life span demands that the total energy utilization is no greater than the primary energy reserve in the network. The upper bound on network life span can be realize when the total battery vigor (N Â·Eb) obtainable in a WSN is exhausted completely. The following unfairness holds to conjecture the Upperbound of the network life span for a duty cycle pedestal WSN.
ED NB Eb t dm BEb = TuD (7) A Qx
Fig.10. Network lifetime upper bounds in duty cycle based WSN.

UPPER BOUNDS OF NETWORK LIFE SPAN VIA
NETWORK CODING AND DUTY CYCLE
The network life span has been anticipated with a proposed network coding algorithm for a nnduty cycled WSN. Besides, network coding and random duty Cycles have been combined to guess the network life span in a duty cycled WSN. Here, the lifetime upper bounds have been resultant while consider a fraction of total passage flows during the network coder nodes in the bottleneck zone.
A network coding layer (refer Fig.1 and Fig. 9 (b) containing network coder nodes has been initiate around the Sink. The network coding layer is the most congested region (i.e. vulnerable region) of the bottleneck zone. So, diminution of energy utilization of the coding layer leads to higher network life span. A group of unarmed nodes (i.e. the nodes
The packet processing process of a node in the network coding layer of the bottleneck zone has been given in Algorithm1. Each node in the network coding layer maintains a established queue (RecvQueue()) and a sensed queue (SensQueue()). On receiving a packet Pi, a node put the packet in RecvQueue(Pi). If the packet is already processed by the node than it is discarded, otherwise the nodes process the packet auxiliary. The node prove its role from EncoderNodeSet(), whether it is an encoder or a simple relay node. If the packet is a native (noncoded) packet and the node is an encoder, the node invokes the method XorEncode(). Specify method of encoded packet making is given in Algorithm2.

Algorithm 1
Packet practice (Pi): Packet processing at a node inside the network coding layer.
Require: Packet transmission and reception starts, received packets inserted into the RecvQueue ()
Ensure: Encoded packet transmitted or discarded

Pick a packet pi from RecvQueue(Pi )

If Packet Pi ForwardPacketSet(Pi ) exit;

If Node n EncoderNodeSet() continue;

If native(Pi ) then

CN =XorEncode();

Node n transmits the coded packet CN to Sink

Insert the processed packet Pi to ForwardPacketSet();

Else

Discard(Pi);

Endif

Else

Node n acts as relay and transmits the packet Pi to the Sink;

Endif

Endif

If (RecvQueue() _= empty)

goto step 1;

else exit;

endif


Algorithm 2:
XorEncode() : Encoding algorithm
Require: A received queue RecvQueue() and a sensed queue
SensQueue() is maintained at an encoder node.
Ensure: Invention of network coded packet CN.

If SensQueue() is not empty then continue;

Pick a packet Pi from head of the RecvQueue();

Pick a packet Pj from head of the SensQueue();

CN = Pi Pj ;

Else

Pick next packet Pi+1 from the RecvQueue();

CN = Pi sPi+1;

endif;

return CNs

A portion of the traffic engender inside traffic jam zone may also relay through the network coder sensor nodes. Imagine that the traffic engender inside the bottleneck zone are not encoded and the network coder sensor node functions as a common relay node. So, the energy utilization in the traffic jam zone to relay the data bits engender inside the zone is given by
cycle, (ii) network coding and (iii) amalgamation of duty cycle and network coding. It has been pragmatic that there is a lessening in energy utilization in the traffic jam zone with the planned approach. This in twirl will lead to enlarge in network life span. The packet delivery ratio and packet latency for the planned approach have also been scrutinize with packet wounded at the Sink. As a conservatory of the current exertion, life span time analysis can be complete. Auxiliary, the planned scrutiny and approach too confer in this appraisal.
REFERENCES
[1]. Enhancement of Lifetime using Duty Cycle andNetwork Coding in Wireless Sensor Networks Rashmi Ranjan Rout, Student Member, IEEE, and Soumya K. Ghosh,
E3NC= N r s t
B
A
E3NC = N r s t
l(x)dS
n x dS (8)
B
Member, IEEE.
[2]. I. F. Akyildiz, W. Su, Y. Sankarasubramaniam, and E. Cayirci, Wireless sensor networks: a survey, Computer Networks, vol. 38, no. 4, pp. 393422, 2002. [3]. D. Cox, Renewal Theory. Methuen and Co. LTD Science Paperbacks, 1970. [4]. K. M. F. Elsayed and H. G. Perros, The superposition of discretetimeA n1 dm
Fig.11. Lifetime upper bounds by combining network coding and duty cycle.


RECITAL SCRUTINY AND PONDERING
The routine metrics other than the energy competence are packet delivery ratio (PDR) and packet latency (PL) [15][16]. Thus, the metrics PDR and PL are used to appraise the recital of the network with the proposed network coding based algorithm in a duty cycled WSN. Packet delivery ratio (PDR) is the ratio of the successfully distribute packets to the total number of packets sent to the Sink [15]. Lest of multihop communication with multipath forwarding tactic, multiple nodes or link dislodge paths survive connecting a pair of source and the Sink [17] [18] to afford definite dependability.

CONCLUSIONS
We comprise survey in this paper in a wireless sensor network (WSN), the region roughly the Sink forms a traffic jam zone where the traffic flow is ceiling. Thus, the life span of the WSN network is utter by the life span of the traffic jam zone. The lifetime upper bounds have been predictable with (i) duty
Markov renewal processes with an application to statistical multiplexing of bursty traffic sources, Applied Mathematics and Computation (Kluwer Academic Publisher), 2000.
[5]. R.W. Yeung, Multilevel diversity coding with distortion, IEEE Trans.Inform. Theory, vol. 41, pp. 412422, Mar. 1995. [6]. R. W. Yeung and Z. Zhang, On symmetrical multilevel diversity coding, IEEE Trans. Inform. Theory, vol. 45, pp. 609621, Mar. 1999. [7]. Distributed source coding for satellite communications, IEEE Trans.Inform. Theory, vol. 45, pp. 11111120, May 1999.
[8]. R. Ahlswede, N. Cai, S. Y. R. Li, and R. Yeung, Network information flow, IEEE Trans. Inf. Theory, vol. 46, no. 4, pp. 12041216, July 2000. [9]. Q. Wang and T. Zhang, Bottleneck zone analysis in energyconstrained wireless sensor networks, IEEE Commun. Lett., vol. 13, no. 6, pp. 423 425, June 2009. [10]. C. F. Hsin and M. Liu, Randomly dutycycled wireless sensor networks: dynamic of coverage, IEEE Trans. Wireless Commun., vol. 5, no. 11, pp. 31823192, 2006. [11]. X. Y. Wang, R. K. Dokania, and A. Apsel, PCObased synchronization for cognitive dutycycled impulse radio sensor networks, IEEE Sensors J., vol. 11, no. 3, pp. 555563, 2011. [12]. M. Bhardwaj, T. Garnett, and A. Chandrakasan, Upper bounds on the lifetime of sensor networks, in Proc. 2001 IEEE ICC, pp. 785790. [13]. H. Zhang and J. C. Hou, On the upper bound of lifetime for large sensor networks, ACM Trans. Sen. Netw., vol. 1, no. 2, pp. 272300, 2005. [14]. E. Felemban, C. G. Lee, and E. Ekici, Mmspeed: multipath multispeed protocol for QoS guarantee of reliability and timeliness in wireless sensor networks, IEEE Trans. Mob. Comput., vol. 5, no. 6, pp. 738 754, 2006. [15]. P. K. K. Loh, H. W. Jing, and Y. Pan, Performance evaluation of efficient and reliable routing protocols for fixedpower sensor networks, IEEE Trans. Wireless Commun., vol. 8, no. 5, pp. 2328 2335, 2009. [16]. A. Cerpa and D. Estrin, Ascent: adaptive selfconfiguring sensor networks topologies, IEEE Trans. Mob. Comput., vol. 3, no. 3, pp. 272285, 2004.