Wireless Pers Commun (2014) 77:87–99 DOI 10.1007/s11277-013-1496-y
A Novel Network Coding and Multi-path Routing Approach for Wireless Sensor Network Baolin Sun · Chao Gui · Ying Song · Hua Chen
Published online: 6 November 2013 © Springer Science+Business Media New York 2013
Abstract In recent times, there have been many advances in the field of information theory and wireless sensor network (WSN) technologies. Network coding is a new paradigm in data transport and promises to change many aspects of WSN. This paper proposes a network coding multipath routing algorithm in WSN (NC-WSN). It is typically proposed in order to increase the reliability of data transmission or to provide load balancing. We evaluate and compare our technique with several existing approaches by a set of simulations, using different scenarios and topologies. The simulations results suggest that the multipath diversity achieved with our proposition can significantly improve the network response time. Keywords
Wireless sensor network · Multipath routing · Network coding
1 Introduction A wireless sensor network (WSN) is a collection of wireless sensor nodes relying neither on fixed communication infrastructures nor on any base stations to provide connectivity [1–11]. Each node in the WSN acts as both a host and a router. If two nodes are not within the transmission range of each other, other nodes are needed to serve as intermediate routers for
B. Sun (B) · C. Gui · Y. Song School of Information Management, Hubei University of Economics, Wuhan 430205, China e-mail:
[email protected] C. Gui e-mail:
[email protected] Y. Song e-mail:
[email protected] H. Chen College of Mathematics and Computer Science, Wuhan Textile University, Wuhan 430073, China e-mail:
[email protected]
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the communication between the two nodes. The hosts are free to move around randomly, and hence the network topology may change dynamically over time. Therefore, the routing protocols for a WSN must be adaptive and capable of maintaining routes as the characteristics of the network connectivity change. Designing an efficient and reliable routing protocol for such networks is a challenging issue [1–11]. The paradigm of routing is also referred as storeand-forward, that is, every intermediate node in the network transmits out messages of the same contents as its received messages. This natural transport mode is inherited from commodity transport, including postal service. However, this seemingly natural mode does not optimize the bandwidth utility. Data transport simply does better than commodity transport does. Network coding (NC) [5] is a technique that successfully increases transmission capacity of a network by mixing together data from different sources and by broadcasting the coded data. Proposed by Ahlswede et al. [5], Network coding promises to offer benefits along very diverse dimensions of communication networks, such as throughput, wireless resources, security, complexity, and resilience to link failures. For the problem of multipath under WSN environment, using network coding at the multipath can achieve the network capacity. Recently, network coding in wired networks with stable topologies has been concerned extensively, but the research and application of network coding in WSNs are still in the primary stage. A great deal of attention has been focused on dealing with practical issues and developing implementable protocols with network coding [5–15]. Generally speaking, network coding techniques in wireless networks can be divided into two categories: inter-flow network coding and intra-flow network coding. In the former, coding is operated on packets from different flows; while in the latter, coding is done over the packets belonging to the same flow. These two network coding techniques can increase the overall throughput of wireless networks from different aspects as we will explain next. COPE [6] is the first practical wireless network coding scheme designed to deal with inter-flow traffic in wireless networks. With opportunistic listening and opportunistic coding, COPE intends to exploit the shared nature of wireless medium. By combining what one neighbor wants with what other neighbors have, a router with COPE can transmit multiple packets to different neighbors in a single transmission. Experiments have shown that COPE can significantly improve network throughput [6]. Hou et al. [7] propose AdapCode, a reliable data dissemination protocol that uses adaptive network coding to reduce broadcast traffic in the process of code updates. Packets on every node are coded by linear combination and decoded by Gaussian elimination. The core idea in AdapCode is to adaptively change the coding scheme according to the link quality. Fragouli et al. [8] proposed an instant primer on network coding, the author explain what network coding does and how it does it, and also discuss the implications of theoretical results on network coding for realistic settings and show how network coding can be used in practice. Vazintari et al. [9] proposes an effective NC scheme intended for sparse DTNs comprising nodes of limited storage capacity. The scheme employs a memory management algorithm that makes optimal use of the limited storage capacity and focuses on unicast sessions where source and intermediate nodes combine only packets belonging to the same generation and destined for the same destination node. Lu et al. [10] propose an energy-efficient multipath routing protocol for wireless sensor networks that balances energy load among nodes so that a minimum energy level is maintained among nodes and the network life increases. Feng et al. [11] consider the realistic two-dimensional (2D) scenario where nodes are distributed in rectangular space and derive an optimal transmission range in rectangular ad hoc networks. In our scheme, the source node as well as intermediate relay nodes encode native/incoming packets by using random linear network coding and broadcast them to all downstream nodes.
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Fig. 1 Wireless sensor network coding
Where we keep the packet sender combine the packets randomly in a local area along the route, create more coding opportunities by introducing network coding. The rest of the paper is organized as follows. In Sect. 2, we briefly review the main theorem of network coding. Section 3 presents network coding policy in WSN. Some simulating results are provided in Sect. 4. Finally, the paper concludes and future work in Sect. 5.
2 Main Theorem of Network Coding (NC) 2.1 Main Developments of Network Coding Before exploring the implications of NC in wireless sensor networks, we provide a concise description of min-cut max-flow theorem, a multicast network problem statement, and the main theorem of NC. The value of the cut is the sum of the capacities of the edges on the cut. According to the multicast network problem statement, maximum flow from source to destinations in any network is equal to the size of min-cut [5,12]. As a result, there has been a great emphasis on linear network coding. For instance, Ho et al. [13] proposed a simple, practical code that achieves the min-cut of the network. They proposed that every node construct its linear code randomly and independently from all other nodes. This simple construction was shown to achieve capacity with probability exponentially approaching 1 with increasing field size. Network coding departs from the conventional store-and-forward paradigm by allowing mixture of information at the source and intermediate relays. Specifically, the source node splits the original data file into data blocks and then encode them with random linear codes [5]. Intermediate nodes can re-encode and forward the linearly independent blocks on hand. The destination is able to decode once it receives a sufficient number of coded blocks. For example, a wireless network coding scheme depicted in Fig. 1. In this example, two wireless nodes need to exchange packets a and b through a relay node. However, the network coding approach uses a store code and forward approach in which the two packets from the clients are combined by means of an XOR operation at the relay and broadcast to both clients simultaneously. The clients can then decode this coded packet to obtain the packets they need. The binary symbol a ⊕ b is a mathematical function of a and b. Calculation of a function from received data is called coding. Showing the merit of mixed coding among multiple messages at an intermediate node, a ⊕ b is called network coding (NC). In algebra, a ⊕ b is called the binary sum of a and b, interpreting in more general terms of linear algebra, the linear sum 1a + 1b over the binary field. Thus, the calculation of a ⊕ b is not only a form of coding but also a more restricted form of linear coding.
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2.2 Multipath Routing and Network Coding in WSN A propose multipath protocol called CHAMP (caching and multipath routing) [14] uses round-robin traffic allocation to keep routes fresh. It also employs cooperative packet caching to improve fault tolerance. Location-aided multipath routing (LAMR) [15] thus does not require the establishment or maintenance of routes. The nodes have neither to store routing tables nor to transmit messages to keep routing tables up-to-date. Generally, routing refers to the flow of data packets from source node(s) to destination node(s) where intermediate node(s) simply replicate and forward without any processing on received packets. NC allows each node to perform an operation, for example linear combinations of received data packets before forwarding on different transmission lines. Therefore, NC-aware routing is a special case of NC. NC-aware routing techniques take into account the availability of NC opportunities within a network during route selection for data transmission. Combining data packets from different flows along routes with more coding opportunities further improves network throughput. Simply, NC-based routing deals with the recoding of packets belonging to the same flow and is also known as intra-flow or intra-session coding. Protocols, i.e. NC-RMR [16], and PipelineOR [17] are related to NC-based routing and the use of NC reduces redundant data transmissions that lead to energy consumption reduction within wireless sensor networks. To address the issues related to the coding conditions and the number of packets to be coded Guo et al. [18] analyzed the performance of practical coding schemes to determine the number of packets that can been coded. They also defined generalized conditions that sufficiently identify actual coding points within a wireless network which ultimately possess compatibility and availability.
3 Network Coding Policy (NCP) 3.1 Network Model This paper will discard such an unrealistic assumption, and develop a practicable model for network coding. We will propose the WSN model by using Poisson point process in R2 . All the nodes in the network are represented as points which are uniformly distributed in a finite region B ⊂ R2 . Let Φ0 be a Poisson point process in R2 with intensity λ0 which characterizes the population of the nodes in the region B. Hence, there are λ0 nodes in the WSN in average. Let Φ1 , Φ2 , . . . , Φ N −1 be N − 1 2-dimensional independent Poisson processes with intensities, λ1 , λ2 , . . . , λ N −1 , which are also independent of Φ0 . N denotes the number of nodes. We will facilitate two lemmas in this section to derive the new theoretical analysis on the performance evaluation for the hierarchical networks. The following lemma will establish the foundation for the network performance measures regarding the routing query time (routing complexity) and the average network throughput. Lemma 1 The average number (first moment) of m i for 1 ≤ i ≤ N − 1 is expressed as E[m i ] =
λi−1 λi
(1)
Moreover, the average value (second moment) of m i2 , for 1 ≤ i ≤ N − 1 can be written as
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E[m i2 ] =
λ2 λi−1 + 1.3 i−1 λi λi2
(2)
The average number of li for 1 ≤ i ≤ N − 1 can also be derived as E[li ] =
λi−1 3/2
(3)
2λi
3.2 Network Coding Policy The network coding idea was introduced by Ahlswede et al. [5]. Usually, the routers or relay nodes just forward and duplicate the packets in the networks. However, network coding permits routers or relay nodes to encode the packets. In this paper, we use a linear network coding scheme [19]. Encoding: When a sender seizes the channel for data transmission, it first generates some NC-WSN packets using the network coding techniques described above. These NC-WSN packets belong to multipath with multipath ID assigned to them. Let k denote the number of NC-WSN packets in a batch, and k may vary in the different batches. Then, the sender creates different random linear combinations of the k NC-WSN packets in the current batch. The linear network coding scheme is an encoding method such that global coding vector gi = (gi1 , gi2 , . . . , gi N ) is given, each item gi j is randomly generated from a G F (Galois Field), gi j = 0, j = 1, . . . , N . and input packet M = (M1 , M2 , . . . , M N ) is converted into output packet Pi by the following expression [9]. Pi =
N
gi j M j
(4)
j=1
The destination node can decode input packets because the coding vector G = (g1 , g2 , . . . , g N ) and output packet data P = (P1 , P2 , . . . , PN ) are obtained from the received packets, and an inverse matrix exists in G. The sensor nodes communicated with it will upload the stored network coding packets and the related coding vector. This operation may be repeated at several nodes in WSN. Definition 1 (Success ratio of network coding packet) The success ratio of network coding packet is the probability that the network coding node successfully coding all the desired original data packet. Algorithm 1: Encoding (Pi ) Input: original data packet M j Output: combined network coding packet Pi for k = 1 to N Pk = 0 end for j = 1 to N randomly generate gi j from G F Pi = Pi + gi j M j end Then we have Lemma 2 In right arrival case, each sensor node with coding field size is enough to store the combined network coding packet which encode all the original data packets.
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Decoding: The encoding process is incremental. Decoding requires solving a set of linear equations. A node stores the encoded vectors it receives as well as its own original packets, row by row, in a so-called decoding matrix. When an encoded packet is received, it is inserted as last row into the decoding matrix. These packets yield a system of linear equations that need to be solved to retrieve the original native packets. Let us suppose that a node has received v encoded packets X 1 , X 2 , . . . , X v belonging to a given generation, with v ≤ N while g1 , g2 , . . . , gv representing the coding vectors corresponding to the encoded packets. The generic element of the decoding matrix G is given by: G i j = gi j where i = 1, . . . , v and j = 1, . . . , N . Let us denote the rank of G by R. When the matrix has full rank, i.e., R = v = N , for a given generation, then the node can solve the linear equations to retrieve all native packets belonging to that generation. In this case, the receiver can recover part of the source native packets belonging to the given generation. We finally observe that when a node receives a packet, it must check whether it is innovative or not, i.e., whether it increases the rank of the decoding matrix G. If not, the packet is dropped. Note that decoding does not need to be performed at all nodes of the network, but only at the receivers. Theorem 1 The success ratio of network coding data by network coding with coding field size to network coding all the data packets is 100 % (neglecting linear dependency of the coefficients). Proof When the network coding node arrives on time, from Lemma 2, each sensor node is enough to encode all original data packets. When the network coding node delays, the sensor nodes continue to encode the original data packets in the exist combined packets, so each sensor node can encode all the original data packets in the combined packets. If delays, the network coding node will contact sensor nodes to guarantee the decodable of the linear equations. The probability of decoding the combined packets are very close to 100 % for a large enough field size. 3.3 Analyses to NC-WSN In this section, we analytically characterize the packet delivery ratio for NC-WSN in a wireless lossy environment based on a simplified network topology. Here, the packet delivery ratio is defined as the ratio of the throughput for the common non-coding approach to the throughput for the network coding approach, which is equal to the ratio of the average number of transmissions required for common non-coding approach to the average number of transmissions required for network coding approach to deliver the same set of packets. To simplify the analysis, we have not taken the transmissions of ACKs into account because of the infrequent usage in our NC-WSN scheme and the negligible packet size. The analytical results can be used to study how lossy environment would impact the performance of wireless network coding schemes. In this paper, we study the simple topology illustrated in Fig. 2, where nodes S and D want to exchange packets with each other and p(0 < p < 1) is the delivery probability of each link in the network. Path 1: S → 1 → 4 → 6 → D, Path 2: S → 2 → 4 → 7 → D. NC-WSN requires each of node A send k packets to reach node B through multiple paths (path 1 and path 2). Here, the packets from path 1 are denoted as p11 , p12 , . . . , p1N , and those from path 2 are denoted as p21 , p22 , . . . , p2N . Router R encodes every pair of packets from path 1 and path 2, and produces k NC-WSN packets pi+ = p1i ⊕ p2i (i = 1, 2, . . . , N ). When router R is allowed to transmit, it creates a random linear combination of the k NCWSN packets and broadcasts it, which is in the form of Pi = Nj=1 gi j p j , where the gi j are random coefficients picked by router R, and pi ’s are packets obtained at the present time.
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Fig. 2 A simplified multipath for theoretical analysis
Let pn denote the probability that router R needs exactly n transmissions to deliver p + successfully. Then, we have pn = p(1 − p)n−1 · p(1 − p)n−1
(5)
The event εn can also happen when both nodes S and D receive kth NC-WSN packet in the nth transmission. Then, we have n−1 n−1 p k−1 (1 − p)(n−1)−(k−1) p (6) Pr = p k−1 (1 − p)(n−1)−(k−1) p · k−1 k−1 The average number of transmissions for router R ensure that at least k NC-WSN packets to ∞ have reached D can be obtained by E(N ) = n=1 npn . The number of paths from the source node S to reach the destination node D is m. The value of E(N ) depends on the delivery probability p and the number of NC-WSN packets k. Therefore, the throughput gain of NC-WSN is: T =m· =m·
4k p 2k p
+ E(N )
2k p
+
∞
n=k
=m·
4k p
2k p 4k p
+
∞
n=k
npn
np(1 − p)n−1 · p(1 − p)n−1
(7)
where T represents the throughput gain for NC-WSN when there are two nodes in the network and the number of packets in the current batch is k.
4 Simulation Experiments 4.1 Simulation Model and Performance Metrics We implement the proposed NC-WSN by modifying and developing the traditional multipath routing module. We compare it with traditional multipath routing CHAMP [14], and LAMR [15] according to the packet delivery ratio and coding gain. To conduct the simulation studies, we have used randomly generated networks on which the algorithms were executed [20]. The simulated environment consists of 100 wireless nodes forming an WSN, about over a square (1,000 m × 1,000 m) flat space for 600 s of simulated time [18]. Network coding scheme are using the linear network coding scheme [19]. The coefficient field is G F = 28 , which can be efficiently implemented in a 8-bit. Table 1 demonstrates part of the important parameters and settings in the simulation.
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Table 1 Simulation parameters Number of nodes
100
Terrain range
1,000 m × 1,000 m
Transmission range
250 m
Average node degree
3–5
Simulation time
600 s
Channel bandwidth
1–3 Mbps
Links delay
20–200 ms
Traffic type
Constant bit rate (CBR)
Node pause time
0–2 s
Examined routing protocol
CHAMP [14], LAMR [15]
We will compare the performance of three multipath routing methods under the same movement models and communication models. We evaluate the performance according to the following metrics: Packet delivery ratio: the packet delivery ratio is the ratio of the correctly delivered data packets, and is obtained as follows. Packet delivery ratio = [No. of packets delivered] / [No. of packets sent] The number of delivered data packets is the summation of total numbers of delivered data packets received by each node. The number of sent data packets is the total number of sent data packets of each node. The packet delivery ratio shows the transmission efficiency of the network with the given protocol. Packet loss ratio: the ratio of the data packets originated by the sources fails to deliver to the destination. Average end-to-end delay of data packets: This includes all possible delays caused by buffering during route discovery latency, queuing at the interface queue, retransmission delays at the MAC, propagation and transfer times. 4.2 Simulation Results We make use of ns-2 [21], which has support for simulating a multihop wireless environment completed with physical, data link, and medium access control (MAC) layer models on ns-2. The Distributed Coordination Function (DCF) of IEEE 802.11 for wireless LANs is used as the MAC layer protocols. Figure 3 plots the throughput gain T , as a function of delivery probability p. It shows that when p decreases, the throughput gain for NC-WSN decreases correspondingly, but it is always higher than the throughput gain for CHAMP and LAMR. Moreover, when the channel is lossier, i.e., when p is smaller, NC-WSN outperforms CHAMP and LAMR much more significantly. Figure 4 compares the packet delivery ratio of the NC-WSN algorithm with CHAMP and LAMR. The delivery ratio presents the ratio of the number of packets received by multipath receivers versus the number of data packets supposed to be received. The corresponding value shows the effectiveness of the protocol in handling the traffic and delivering the data to the intended multipath receivers. For all kinds of traffic load, all schemes performance is affected by the increasing traffic load. The proposed NC-WSN has the better packet delivery ratio
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Fig. 3 Comparison of throughput gain
Fig. 4 Comparison of packet delivery rate
Fig. 5 Packet loss rate with varying mobility
than that of CHAMP and LAMR, because both are using a traditional multipath structure, which can bring the network coding-based multipath route for the packets to deliver. Packet loss mechanisms are much more complicated in WSNs because wireless links are subject to transmission errors and the network topology changes dynamically. Figure 5 shows
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Fig. 6 Comparison of average end-to-end delay
the relationship between the number of nodes and the loss ratio of the typical protocols which indicates the reliable degree of each protocol. It is not hard to see that the multipath routing based on network coding is smaller than the multipath network coding because the former is more suit to make use of WSNs. However, with the number of nodes increasing, the three protocols have a greater loss ratio especially for NC-RMR. In these scenarios, LAMR fails to converge at number of nodes bigger than 50. With 50 nodes, LAMR’s average packet loss ratio comes to 40 % nearby, although upon examination of the data we found that variability was extremely large, with packet loss ratio ranging from 25 to 50 %. There is a large reduction in the average end-to-end delay of NC-MR compared with CHAMP and LAMR as shown in Fig. 6. This is because NC-MR that extends the single path CHAMP and LAMR to compute multiple loop-free and link-disjoint paths, this mechanism eliminates route discovery by availability of alternate routes on route failures. As shown in Fig. 6, NC-MR has (almost) the lowest average end-to-end delay of all four methods. At low speed, the difference of delay is small, compared to higher speeds; all four methods have a higher end-to-end delay. Since as speed increases, more route requests are needed thus, delay increase with speed in all methods.
5 Conclusion This paper discusses multpath routing problem, which may deal with the network coding model for researching the wireless sensor network (WSN) multpath routing problem. It presents proposes a Network Coding Multipath Routing algorithm in WSN (NC-WSN). It is typically proposed in order to increase the reliability of data transmission, and by applying network coding, which allows packet encoding at a relay node. Simulation results show that, with the proposed network coding in wireless sensor network multipath routing protocol (NC-WSN), throughput gain, packet delivery ratio, packet loss rate and Average end-to-end delay of data packets can be improved in most of cases. In the future, we hope to develop an optimization multipath routing in coded WSNs. We also wish to integrate the relay nodes encode the packets to improve the performance of WSN. Acknowledgments This work was supported by the Young and Middle-aged Elitists’ Scientific and Technological Innovation Team Project of the Institutions of Higher Education in Hubei Province (T200902), Natural
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Science Foundation of Hubei Province of China (2013CFB035, 2013CFB309), Key Scientific Research Project of Hubei Education Department (D20121903, Q20121906, Q20111610, B20129205), Key Project of Hubei Province Education Science During the 12th Five-Year (2012A042).
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Author Biographies Baolin Sun was born in 1963, Hubei, P. R. China. He is currently a professor of computer science and technology of Hubei University of Economics, China, and and one of Editorial Board Guest Members of World Sci-Tech R&D, Editorial Board of Advances in Information Sciences and Service Sciences (AISS), International Journal of Advancements in Computing Technology (IJACT), Advances in Network and Communication (ANC), one of the KGCM, WMSCI, ICCIT, INC, NISS, NCM, ICIS program committee members, and also an International Standard Draft organizing members of ISO/IEC JTC1/SC6. He was awarded the Province Special Prize by the Hubei Province Government in 2007. His research interests include multipath routing, parallel and distributed computing, network optimization and ad hoc networks. He has published over 100 journal and conference papers and has author of four books in the above areas.
Chao Gui was born in 1964, Hubei, P. R. China. He is currently a professor of computer science and technology of Hubei University of Economics, China. His research interests include wireless communication, performance analysis and analytical modeling. He has published over 30 research papers.
Ying Song was born in 1975, Hubei, P. R. China. She is currently an associate professor of computer science and technology of Hubei University of Economics, China. Her research interests include wireless communication, mesh networks and network protocol. She has published over 10 research papers.
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99 Hua Chen was born in 1977, Hubei, P. R. China. She is currently an associate professor of mathematics and computer science of Wuhan Textile University, China. Her research interests include algorithm, wireless communication, performance analysis, and network model. She has published over 20 research papers.
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