Joint Opportunistic Network Coding and Opportunistic Routing for Correlated Data
Gathering in Wireless Sensor Network
Chong Tan1,2, Junni Zou2, Min Wang2
1Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences
2Department of Communication Engineering, Shanghai University, Shanghai, 200072, P.R. China Emails: {dudumaotc, zoujn, wangmin}@shu.edu.cn
Abstract—In this paper, we study the problem of correlated data gathering in wireless sensor networks. An opportunistic routing protocol joint with opportunistic network coding is proposed for correlated data gathering. In order to reduce the total transmission, we introduce the expected number of coded transmission (ECTX) as metric for the routing selection.
Moreover, we also define the coding gain for the network nodes to count the coding opportunistic, with which the throughput of the wireless sensor network is further increased. Numerical simulations are conducted for performance analysis with the proposed routing scheme.
Index Terms—Wireless sensor network, opportunistic network coding, opportunistic routing, correlated data gathering, dis- tributed source coding
I. INTRODUCTION
Due to typically battery-powered sensor nodes, effective data gathering from sensor nodes to end sites or sink nodes is crucial for energy-constrained wireless sensor networks. Since sensor nodes partially monitor the same spatial region and are often densely deployed, the data collected by nearby sensor nodes are either redundant or correlated. This data correlation can be exploited to reduce the amount of data transmitted in the network, resulting in energy savings. In this paper, we consider the data gathering scenario where data is sampled at a number of distributed correlated sources and needs to be routed to one or a few sink nodes.
The data gathering for correlated sources can be discussed in the prior works. Slepian-Wolf coding (S-W coding) is a distributed source coding that can remove data redundancy without requiring inter sensor communication. However, S-W coding is based on the assumption that each sensor node has a priori knowledge of the correlation structure, which depends on the distances between sensor nodes and the characteristics of the observed phenomenon. Unfortunately, S-W coding requires a perfect prior knowledge of the whole network which is not scalable in large networks. In this paper, we adapt a localized version of S-W coding from [1], such that only local correlation information is required at each sensor node.
Network coding has demonstrated a wide range of applica- tions for improving the performance of wireless networks [2].
However, a packet gained by a relay node has to wait to be
network-coded with others which results in large delay and packet-loss rate. A novel network coding approach, referred as opportunistic network coding (ONC), is presented in [3]
to overcome these limitations. With the opportunistic network coding, the intermediate node can determine whether a packet is transmitted with or without network coding. As it is difficult and complicated to design dynamic scheduling and coding algorithms, a practical network coding protocol is proposed in [4] which is based on the opportunistic reception from the download nodes. Although different approaches to network coding are disused and illustrated in the previous works, they focus on how to apply network coding at the intermediate nodes. It is obvious that network coding can improve the network performance only when the bottleneck link occurs or the data flow is beyond the limited link capacity. Therefore, we consider joining the opportunistic network coding with the routing protocol to establish an effective data gathering framework for wireless networks.
Moreover, opportunistic routing emerges a promising tech- nique that achieves higher throughput than traditional de- terministic forwarding in the face of highly unpredictable and lossy wireless channels. Biswas et al. in [5] proposed an opportunistic protocol ExOR to send information through multiple relays and introduce delicate scheduling policies to reduce duplicate transmission. Chachulski et al. in [6]
developed an improved ExOR protocol called MORE, in which no specific scheduler is required and network coding is applied to avoid the unnecessary forwarding. However, the metric they adopted for the relay set selection is very simple (e.g. ETX metric) which largely limits their capability in improving the network throughput [7]. In [8], coding-aware routing protocol is proposed which takes into account network coding at network nodes in route selection. Ni et al. in [9]
defined the coding gain as the routing metric and proposed a coding-aware routing scheme with which the total number of coded transmissions can be reduced. However, the above coding-aware routing protocols only fix the route selection issue, and neglect how to apply the network coding at the network nodes. Hence, in the paper, we not only consider the opportunistic network coding to reduce the number of transmissions, but also take account into the opportunistic
978-1-4673-6187-3/13/$31.00 ©2013 IEEE
routing mechanism to improve the performance of the whole network.
Our main contributions in this paper are as follows. First, we join the opportunistic network coding and the opportunis- tic routing together to establish an efficient data gathering framework for correlated sources. Then, we consider both the number of coded transmissions and the network coding opportunistic to decrease the total number of transmissions.
The rest of this paper is organized as follows. Sec. II presents the network model, related constraints and formulates the problem. An opportunistic routing strategy joint with ONC is then proposed at Sec. III. Numerical results are presented in Sec.IV, and we conclude this article at the last section.
II. SYSTEMMODEL
A wireless sensor network is represented by a directed graph G = (V, E), where V is the set of nodes, E is the set of wireless links, S ∈ V = {s1, s2, ..., sNs} and T ∈ V = {t1, t2, ..., tNt} denote the set of sensor nodes and sink nodes, respectively. Each node i ∈ V has a radio range di and can communicate with other nodes within its range. We denote a link either by a single index l or by the directed pair (i, j) of nodes it connects. And each link (i, j) ∈ E has a fixed finite capacity C. uij andrij are the flow rate and the packet reception ratio of the link (i, j) ∈ E, respectively.
For a sensor nodesi ∈ S, Tiis the set of sink nodes which can gain data from node si; For a sink nodetj∈ T , Sj is the set of source nodes with the same sink node tj.
Each source si periodically measures a continuous random observation Xi. The values of the sources are drawn from some joint distribution p(X1 = x1) = p(x1) and can be either continuous or discrete. The joint source vector X = {X1, ..., XNS} is characterized by a joint probability distributionp(X1= x1, ..., XNS = xNS) = p(x1, ..., xNS).
A. Distributed Source Coding
To quantify the performance of the aggregation scheme, we need to quantify the amount of information generated by the sources. LetH(Xi) denote the entropy of observation Xi
collected by sensor si, H(Xi) = −
p(Xi) log2p(Xi)dXi. Once, the source nodes transmit enough information to the terminals, then they can recover the original data, losslessly.
Intuitively, each source si can code its data at a rate Ri
which is greater than or equal to their respective entropy, Ri≥ H(Xi).
With S-W coding, the correlated data from different sensor nodes can be coded independently without communication with each other, Ri≥ H(Xi|Xic), where Xicis the correlated data with Xi and gained by other sensors. The S-W region specifies the minimum encoding rate that the sensor nodes must meet in order to transmit all independent information to the sink nodes. It is satisfied when any subset of sensor nodes encode their collected data at a total rate exceeding their joint entropy.
However, the rate admissibility constraints require each sensor node to have global correlation information, which is
not scalable in large networks. Here, a localized version of S- W coding is adapted to relax the rate admissibility constraints, such that only local correlation information is required at each sensor node. Here, we describe the localized S-W coding as:
Rtsji ≥ H(Xsi|Nsi) tj ∈ Ti (1) whereNsi is a subset of the sensors within the neighborhood of sensorsi. For each nodei ∈ Nsi,i is the one-hop neighbor ofsiand can connect withsidirectly. Moreover, eachi ∈ Nsi has the same sink nodetj as si.
B. Minimum Cut Capacity Constraints
The capacity region of the terminal tj with respect to Sj
as:
Ctj = {(Rt1j, ..., RtNjS) :
∀B ⊆ Sj,
i∈BRtij ≤ min − cut(B, tj)}. (2) Thus,Ctj consists of inequalities that define the maximum flow from each subset of Sj to the terminal tj. A rate vector (Rt1j, ..., RtNjS) ∈ Ctj can be transmitted from the source nodes s1, ..., sNS to terminaltj.
Definition 1 (Traffic matrix) We call the traffic matrixA of a graphG, the elements of the NS× NR square matrix A is given by:
Aij =
1, if source i is transmitted to sink j,
0, else. (3)
With this notation,Ti= {j : Aij = 1} and Sj= {i : Aij = 1}.
C. Channel Interference Constraint
Suppose any link originating from nodek ∈ V will interfere with link (i, j) if dki< (1+Δ)dij ordkj< (1+Δ)dij. Here, Δ > 0 specifies the interference range. Also define Ψi,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 network channel interference constraint can be defined as:
uij+
(p,q)∈Ψij
upq≤ C, j ∈ Vout(i) (4)
D. Network Coding Constraints
With network coding, flows from different sources to differ- ent sinks are allowed to share the network capacity by coding together at the intermediate nodes. For any intermediate node i, if network coding is applied, the actual physical flow sent by nodei to its next hop j is only to be the maximum of the received information flows. That is
uij =
⎧⎨
⎩
maxs,t Bijst· Rts if network coding is applied,
s,tBijst· Rts otherwise.
(5) where,Bstij is defined as the path matrix for source s by:
P22
P2
P12
P1
P11
P21
Fig. 1. Example of NC-aware OR for correlated sources
Bijst=
1, if source s to sink t occupied link (i, j), 0, else.
(6) III. OPPORTUNISTICROUTINGSCHEME FORCORRELATED
SOURCE
In this section, we consider the data gathering scenarios where an opportunistic routing mechanism joint with oppor- tunistic network coding is applied to increase the network throughput and reduce the number of transmissions in wireless video sensor networks. According to the localized S-W region, each node can compress its data with the sensors belong to its one-hop neighbor set. During the transmission, sensor node attempts to broadcast its data packet. With opportunistic network coding, the packets can potentially be compressed again at the intermediate nodes, packetized, and forwarded to the corresponding sinks.
The proposed opportunistic routing scheme addresses two important issues: candidate selection and relay priority as- signment. An example is present in Fig.1 to illustrate the opportunistic routing scheme. Both sources s1 and s2 want to send packets to its corresponding sink. The packets sent by nodes1 can be received by{v2, v3, t2}, and the packets from s2can be received by{v1, v2, t1}. With opportunistic network coding, the data froms1ands2 can combined at nodev2. So, node v2 is selected as the relay node for both the of sources.
Then we calculate the expected coded transmission (ECTX) and select the node with a small ECTX opportunity as the forwarder in each packet transmission.
A. Forwarding Node Selection
When a node has packets to send, it first broadcasts a RTC to its neighbors which can be considered as the forwarding candidates. Each node in the candidate set calculates its ECTX and reports it to the sender with a CTS. With the information gained from its candidates, the sender can select a node as its relay node to transmit its packets.
In the previous routing schemes without network coding, the routing metric most commonly used is minimum hop count, such as expected transmission count (ETX). According to the ETX metric, for a single link (i, j) with the delivery probability rijthe value of expected number of transmissions on the link is 1/rij. With network coding, the expected number
s1 s2 s3
v
t1 t2
Fig. 2. Example of intermediate node gain data from different sources
of coded transmissions is defined to capture the number of transmissions required to make the coded packet received successfully.
As shown in Fig.1, without network coding, node s1 can gain two ETXs from its forwarding candidates, {r1
s1v2 +
rv2t11 ,rs1v31 +r1
v3t1}. In order to reduce the number of trans- mission, the candidate with lower ETX can be chosen as the relay node by s1. And s2 can choose its relay node as the same ass1. With network coding, node v2 can gain the data from boths1 ands2. Then, the ECTX is presented as
(ECT X) = 1
minl∈Vin(v)rlv + 1
mink∈Vout(v)rvk (7) Comparing with the ETX, the number of transmissions for both sources reduced by network coding is denoted as min{r 1
s1v2rv2t1,rs1v31rv3t1}+min{r 1
s2v2rv2t2,rs2v31rv3t2}−
min{rs1v21 rs2v2} +min{r 1
v2t1rv2t2}. B. Opportunistic Network Coding
However, another problem we have to consider is which packets should be coded at the intermediate node. Once, there are several senders send their data simultaneously and the intermediate node can receive the data from different sources as shown in Fig.2. We assume that the intermediate node has several data buffers to sort the packets from different sources to different sink nodes. As shown in Fig.2, a relay nodev has three buffers and can receive data froms1, s2, s3.
We assume that sensors1ands2 delivery their data to sink t1, s2 ands3 to sink t2. Therefore, for sink nodet1, the set of source nodeS1= {s1, s2}, and S2= {s2, s3} for sink t2. And the traffic matrix is
A3×2=
⎡
⎣ 1 0 1 1 0 1
⎤
⎦ .
Random linear coding scheme can be applied at interme- diate nodes. For each intermediate node, the packets on its outgoing links are random linear combinations of the packets on its incoming links. Therefore, node v has four probable combinations of data coding, as shown in table 1.
whereρiv is defined as the network coding gain. Obviously, the relay node can choose the combination with the highest
TABLE I
THE CASES FOR INTERMEDIATE NODE V TO COMPRESS THE DATA Rts11 Rts12
Rts22 ρ1v ρ2v Rts23 ρ3v ρ4v
*HQHUDWLRQB,' 6RXFHB,' 'HVWLQDWLRQB,'
&RGHYHFWRUV 5HOD\OLVW
Fig. 3. The format of the packet header
network coding gain, if the decoding is feasible at the sink node. Therefore, the coding gain of correlated sources can be defined as:
ρv= max{ρiv} = max
k∈Vin(v)ukv− max ukv
k∈Vin(v)ukv (8) where ukv=
si∈S
tj∈TiRtsjiBkvsitj, for k ∈ Vin(v).
With the coding policy, the relay node can combine the packets with high coding gain when several packets from different sources are received. The original source and desti- nation IP address and the list of nodes which could participate in forwarding it, as depicted in Fig.3. The sender keeps transmitting the coded packets of the current generation until it is recovered at the destination, and then it moves to the next generation.
C. Priority of Forwarder
The priority for each candidate is to choose the node with low ECTX to reduce the network transmissions. The forward- ing node can compress the data with a high coding gain to improve the end-to-end throughput. As defined in equation 8, the coding gain can be assigned to the intermediate node which predicts the throughput improvement of data transmission.
For each nodev, a max-coding gain problem is formulated as following:
P1: max
si∈S,tj∈Tiρv (9)
s.t. (1), (2), (4), (5).
Each nodesican choose a set of forwarding candidates with different priorities. The nodes within a source’s forwarding candidate set agree on that the highest priority node keeps the packet and all the other nodes drop the packet to prevent unnecessary multiple forwarding of the same packet. If the packet is not received by any node in the source’s candidate set, the source broadcasts the packet again until it is received by at least one node in the candidate set or the maximum number of trials is reached.
0 10 20 30 40 50
0 10 20 30 40 50
Fig. 4. The Grid topology for wireless sensor network
D. Complexity Analysis
Assume that a sensor node in the wireless network has an average degree D including both in-degree and out-degree, (D > 1). The time for the node to decide which packets should be coded is O(D(D − 1)). Moreover, a data sender needs O(D2) to select a relay node to forward its data to the sink node.
In the proposed routing mechanism, the time for constituting the optimal data gathering framework is O(D2).
IV. PERFORMANCEEVALUATION
In this section, we evaluate the performance of our routing scheme by simulation and compare the performance with the other exited routing protocols. As shown in Fig.4, we consider a wireless network with 10 sensor nodes and 2 sink nodes.
The source set to sinkt1 isS1= {s1, s3}, and S2= {s2, s4} takest2as the sink node. As all the sources are identically dis- tributed, we assume thatH(si) = 0.5Mbps and H(s1|Ns1) = 0.3Mbps, H(s2|Ns2) = 0.3Mbps, H(s3|Ns3) = 0.2Mbps.
Also, all the links have a static capacity 1M bps.
First, suppose that all the packets can be received correctly.
For SPT scheme, each source node transmits its data along the shortest path to it sink, although it has to compete the capacity of some link with other sources. As shown in Fig.5, link (n3, n6) is occupied by s2 ands3, simultaneously. Therefore, s2 and s3 have a low end-to-end throughput. With network coding, the data from s2 and s3 can be combined at node n3 and the capacity of link (n3, n6) can be shared by both sources. The coding is applied at the bottleneck link when it is necessary and passive with NC-based scheme. With the opportunistic routing joint with ONC scheme, the data sender takes into account the availability of coding opportunities during route selection and increases the throughput positively.
The data rate for sink nodet2 can gain its bound of min-cut.
To evaluate the performance of opportunistic routing in lossy wireless environments, we assume that each link has a packet reception rate randomly chosen in the range of [0, 1].
The end-to-end throughput for each source in lossy wireless network is illustrated in Fig.6. It is seen that the opportunistic routing joint with ONC scheme can significantly improve the
Fig. 5. The end-to-end throughput for each source with different routing scheme
Fig. 6. The end-to-end throughput for each source within lossy wireless network
end-to-end throughput as compared with the other routing schemes.
We assume that the flow for each source has a packet rate ranging from 0.5M bps to 1.5M bps. Clearly, in order to recover the original data losslessly, the average data rate must be no less than its entropy. Fig.7 shows the network throughput with SPT, NC-based OR and OR joint with ONC, respectively.
When the offered load is small, it is hard to create more coding opportunities. As a result, OR joint with ONC scheme performs similarly to SPT and NC-based OR. As the offered load increases, OR joint with ONC and NC-based OR achieve higher network throughput than SPT due to the introduction of network coding operations, which help reduce the number of transmissions. Furthermore, OR joint with ONC outperforms NC-based OR as it can create much more coding opportuni- ties through opportunistic forwarding. With the offered load increasing further, the network throughputs with OR joint with ONC and NC-based OR become close again because in this case paths for different flows become more likely to overlap.
Fig. 7. The network throughput under different offered load
V. CONCLUSION
The problem of correlated data gathering in wireless sensor networks is considered in this paper. In order to increase the network throughput and face the highly unpredictable wireless links, an opportunistic routing protocol joint with opportunistic network coding is proposed. We consider both the number of coded transmissions and the network coding opportunistic to decrease the total number of transmissions. With numerical simulations performance analysis are illustrated and good results are obtained using the proposed scheme.
VI. ACKNOWLEDGMENT
The work has been partially supported by the NSFC grants No. 61271211, No. 60632040, No. 60802019, and No.
60736043.
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