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Network coding in wireless networks can not only introduce throughput benefits, but also improve the transmission reliability in a lossy wireless network, which.
2013 IEEE 24th International Symposium on Personal, Indoor and Mobile Radio Communications: Mobile and Wireless Networks

Network coding in convergecast of wireless sensor networks: friend or foe? Zhenzhou Tang∗† , Hongyu Wang† and Qian Hu∗ of Physics and Electronic Information Engineering, Wenzhou University, Wenzhou, China † School of Information and Communication Engineering, Dalian University of Technology, Dalian, China Email: [email protected], [email protected], [email protected] ∗ College

Abstract—Convergecast is probably the most common communication style in wireless sensor networks (WSNs). And network coding (NC) is a promising concept to improve throughput or reliability of convergecast. Most of the existing works have mainly focused on exploiting these benefits without considering its potential adverse effect. In this paper, we argue that network coding may not always benefit convergecast. This viewpoint is discussed within four scenarios: The networkcoding-aided (NC-aided) and the none-network-coding (noneNC) convergecast schemes with or without automatic repeat request (ARQ) mechanisms. The most concerned performance metrics, including packet collection rate, energy consumption and end-to-end delay, are investigated. Theoretical analyses and simulation results show that the way network coding operates, i.e., conscious overhearing and the prerequisite of successfully decoding, could naturally diminish its advantages in convergecast. And NC-aided convergecast schemes may even be inferior to none-NC ones when the wireless link delivery ratio is high enough. The conclusion drawn in this paper casts a new light on how to effectively apply network coding to practical WSNs.

I. I NTRODUCTION Network coding, initially introduced by Ahlswede et al., has been proved that it is able to improve the throughput of wired networks [1]. Network coding suggests the fundamental idea of mixing the passing packets in an intermediate node, but not only replicating and forwarding them as those traditional routing protocols behave. And subsequent studies show that network coding is particularly well-suited for wireless networks due to the broadcast nature of their communications. Network coding in wireless networks can not only introduce throughput benefits, but also improve the transmission reliability in a lossy wireless network, which in turn reduce the number of retransmissions and energy consumption. Wireless network coding has been intensively studied in various networked scenarios such as multicast, broadcast and multi-flow unicast [2–4]. The attractive advantages of wireless network coding also boost the practical application of network coding in wireless sensor networks (WSNs). A WSN typically consists of devices which are capable of sensing environmental or physical quantities and communicate with each other over wireless links. They are generally powered by batteries which are difficult and costly to be recharged or replaced. These devices are scattered within the desired area, generate data by sensing the specified objects, and transport them to a

978-1-4577-1348-4/13/$31.00 ©2013 IEEE

Sink Nodes Sensor Node Figure 1. Convergecast in wireless sensor networks: Sensor devices generate data by sensing the specified objects, and transport them to a common sink.

common sink, as shown in Fig.1. Hence, the most common communication style in WSNs should be convergecast. Although plenty of far-reaching theories and practical solutions on applying NC to WSNs have been proposed in recent years, which have demonstrated that NC is beneficial for WSNs in multicast/broadcast or unicast scenarios [5– 7], it is harder to apply NC to convergecast. Differing from multicast or unicast, the typical traffic patterns where the NC benefits are generated, such as the well-known pattern shown in Fig.2, do not typically occur during convergecasting. And most of the existing solutions for NC-aided convergecast have mainly focused on exploiting some kind of benefits without considering its potential adverse effect. Hong have proposed the Cascading Data Collection (CDC) mechanism to reliably gather data from sensor nodes [8]. CDC can achieve high energy efficiency, while its performance on end-to-end delay has not been presented. Since the original packets cannot be recovered until the sink has received enough number of coded packets, it is believed that CDC most probably suffers long end-to-end delay. Samarasinghe have also proposed a NC-aided convergecast solution in [9], and have practically applied it to a realistic WSN. And they have showed two key limitations of NC, i.e., strongly increased delay and high overhead due to limited lack of adaptability [10]. Keller have presented SenseCode, a NC-aided collection protocol for WSNs [11]. Compared to the best existing alternative, SenseCode improves reliability, however, at the cost of consuming more energy. So, a natural question is: Is network coding a friend or foe to convergecast in WSNs? The answer is significant for applying NC to practical WSN applications. Therefore, in this paper, we mainly focus on the role NC plays in con-

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Figure 2. The typical pattern for which network coding is known to provide benefits: Nodes A and C exchange packets p1 and p2 via their common neighbor B. B receives p1 and p2 , and then XORs them and broadcasts the coded packet (p1 ⊕ p2 ). Node A can recover p2 by reXOR-ing p1 ⊕ p2 with its own packet p1 , and so does node C

vergecast of WSNs. We discuss about this problem within scenarios with or without ARQ mechanism respectively. The most essential difference between these scenarios is whether the success of packet delivery is guaranteed or not. For the former scenario, data collection rate and energy consumption are the most concerned performance metrics. While for the latter, energy efficiency and end-to-end delay are the most common performance requirements since the success of packet delivery has been guaranteed by ARQ mechanisms. Accordingly, two NC-aided convergecast schemes are proposed in this paper. Theoretical analyses on concerned performance metrics are carried out and simulation are conducted. The rest of this paper is organized as follows. Section 2 presents the system models. In Section 3, we consider the scenario of NC-aided convergecast without ARQ and offer analyses on packet collection rate and energy consumption. In Section 4, we investigate the NC-aided convergecast with ARQ, followed by Section 5 giving the conclusions. II. S YSTEM MODELS AND SIMULATION SCENARIOS A. Network models In this paper, We assume that a converge tree (T) has been created by existing traditional data collection protocols or routing protocols, such as CTP [12]. The T is a directed tree and the sink node is just its root. Fig.1 shows a convergetree. Then, we give the definition of the converge-structure, which have been introduced in [13]. Definition 1: An n-order converge-structure CSn is a three-layer subtree of the T composed of n leaves Si (i = 1, 2, . . . , n), n interior nodes Ci (i = 1, 2, . . . , n), and a root D, as shown in Fig.3. A CSn possesses the following characteristics: 1) Ci only has one child Si . 2) Ci (i = 2, 3, . . . , n − 1) can overhear the communications of Si−1 and Si+1 . While C1 and Cn can only overhear the communications of S2 and Sn−1 respectively. A CSn is the most basic structure to perform a complete process of linear network coding. The original packets are

S2 (a) CSn

(b) CS2

Figure 3. Converge-structures. The nodes and solid lines with arrows form a subtree of converge-tree. The dashed lines represent the overhearing links.

generated by Si (i = 1, 2, . . . , n). Ci (i = 1, 2, . . . , n) receives and overhears those original packets and mixes them into a coded packet, which is sent to the decoder D. It should be noted that these CSn are abstracted from the T, and the probability of forming CSn is considerably high during convergecasting, especially for low order CSn in a dense network. In this paper, we simply investigate NC-aided convergecast in a CSn , but not an entire T. The reason is that the performance of NC-aided convergecast in a complete T is influenced by some other factors than NC itself. For example, the method of how to recognize CSn from T impose a significant effect on the overall performance. B. Network coding operation In our previous work, we have investigated the feasibility of acquiring network coding benefits in convergecast, and argued that the reliability benefits can be obtained by applying linear network coding in the ubiquitous CSn [13]. In a CSn , Ci may receive at most three original packets from Si−1 , Si and Si+1 and mix them as follows: Xk =

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gki Mi

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where Mi (i = 1, 2, 3) are the original packets, gki are the coefficients randomly selected from a q-order Galois field GF(q), and Xk is the coded packet. Totally n coded packets are generated by n coders and are forwarded to D, where they are decoded by means of Gaussian Elimination only if D has received n coded packets [14]. C. Simulation scenarios In this paper, plenty of simulations are conducted to verify our analyses. All the simulations run on the Network Simulator II (NS2). The topologies are shown in Fig.4. Since our primary objective is to evaluate network coding benefits, we simply assign the converge-tree manually as shown in Fig.3. Each source node generates 100 CBR packets destined to D. And the packet size is defined as 1000 bits. In the simulations, no mobility is assumed.

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Four convergecast schemes have been implemented in this paper, i.e. the NC-aided and the none-NC schemes with and without ARQ. All the schemes are based on a simple Time Division Multiple Access (TDMA) Medium Access Control (MAC) protocol. For simplicity, TDMA schedules with global time synchronization are employed. In detail, the first n slots of a TDMA frame are allocated to the source nodes, the next n slots are allocated to the coders, and the last slot is assigned for the decoder. For the schemes without ARQ, senders do nothing more after transmissions. And for the none-NC convergecast schemes with ARQ, the most common link-level stop-andwait ARQ is adopted. While for those NC-aided ones with ARQ, two different ARQ mechanisms are adopted. On the one hand, for communications between Si and Ci (Ci is the unique parent of Si in T), Si will not start to send another packet unless the current one has been successfully acknowledged. However, unlike the general ARQ that only Ci is allowed to give the acknowledgement to Si , in the NCaided convergecast scheme, Ci−1 and Ci+1 are also allowed. Specifically, after having received an original packet from Si , all the Ci−1 , Ci and Ci+1 should acknowledge it one by one. And Si discards the duplicated ACK frames once it has already got one. On the other hand, the process of Gaussian Elimination starts after the decoder has received a coded packet successfully. If all or some of the original packets are successfully recovered, the decoder replies with a particular acknowledgement (DACK, Decoder ACK) which carries the IDs of the recovered packets. If a coder fails to get a DACK in time, it re-codes the original packets and sends it to the decoder again. For simplicity, we assume that all the ACK frames can always be received successfully. It is reasonable because an ACK frame is so short that the probability of failure is low enough. In our simulations, any node has four operational modes: transmitting, receiving, idle, and sleep, consuming Pt = 24.75 mW, Pr = 13.5 mW, Pi = 13.5 mW, and Ps = 15 μW, respectively [15]. And the data rate is 250 kbps.



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Figure 5. The ratios of collection rate between the NC-aided and the none-NC convergecast schemes in a CSn (n = 2, 3, 4) without ARQ.

to recover all the original ones. Packet collection rate and energy consumption are discussed, since they are the most concerned metrics. A. Collection rate We have investigated the probability that D can recover all the original packets in [13]. However, there are cases that although D cannot recover all the original packets, but it can recover some of them. Fig.5 shows the ratios of the collection rates between the NC-aided and the noneNC convergecast schemes in a CSn (n = 2, 3, 4) without ARQ, where it can be observed that when the link delivery ratio is low, the NC-aided scheme considerably outperforms the traditional one due to the redundant links introduced by overhearing. Moreover, the gain is proportional to n and inversely proportional to the link delivery ratio. However, things changes when the link quality gets better. The traditional none-NC convergecast scheme collects more packets than the NC-aided one does. The reason is that, although the redundant links between the sources and coders help collect more original packets (this benefit is inversely proportional to the link delivery ratio, as we have discussed in [13]), however, the losses of coded packets result in the recovery failure of n original ones directly, i.e., packet loss penalty. And this side effect of NC trends to play a major role in total packet loss when the link quality is high. B. Energy consumption The total energy consumption (E) in the NC-aided convergecast is E = Ets + Etc + Erc + Erd + Ei + Es where Ets = εdt Nt

In these scenarios, no ACK mechanism is adopted. Original and coded packets may be lost due to link failures which causes that the decoder cannot collect enough coded packet

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Figure 7. The ratios of energy consumption between the NC-aided and the none-NC convergecast schemes in a CSn (n = 2, 3, 4) with ARQ.

IV. C ONVERGECAST WITH ARQ In most practical applications of WSNs, ARQ should be employed to ensure the packet delivery. In these scenarios, all the original packets can be collected by D with the help of the ARQ mechanisms mentioned above. Therefore, instead of the collection rate, we care much more about the performance metrics such as energy consumption and endto-end delay. A. Energy consumption

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Explanation Link delivery ratio The order of a CSn Number of packets Transmitting energy consumption per data packet or ACK Receiving energy consumption per data packet or ACK Energy consumed by idle listening and sleeping Transmitting energy consumption of Si , Ci and D Receiving (including overhearing) energy consumption of Si , Ci and D The average number of transmissions of Si The average number of transmissions for data packets or ACK of Ci The average number of transmissions for ACK of D The average number of receptions for data packets or ACK of Ci

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Figure 6. The ratios of energy consumption per successfully received packet between the NC-aided and the none-NC convergecast schemes in a CSn (n = 2, 3, 4) without ARQ.

Erc All the mentioned variables are listed in Table I. We have ignored Ei and Es , since they are far less than energy consumed by transmitting and receiving (In TDMA based MAC protocol, Ei can be reduced to a very low level). While that in none-NC scheme is

Ers = εar N = + εat Nra c 2 × 2 + 3(n − 2) = εdr Nt s + εat rNtd c n Erd = εdr nNtd c εdr Nrd c

(12) (13)

While those in none-NC scheme are Eˆts = εdt Nˆt s = εdt (N/r) Eˆtc = εdt Nˆtd c + εat Nˆta c = εdt (N/r) + εat N Eˆd = εa nN

ˆ ≈ Eˆts + Eˆtc + Eˆrc + Eˆrd = εdt (N +rN )+εdr (N +nrN ) (7) E

t

The theoretical and simulational results on the ratios of energy consumption per successfully received packet between the NC-aided and the none-NC convergecast schemes in a CSn (n = 2, 3, 4) without ARQ are shown in Fig. 6, where it can be observed that the NC-aided schemes are more energy-saving than none-NC ones only when r is low enough. While in most cases, none-NC ones consume less energy. And the contrast is even more obvious in a high order CSn .

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Eˆrs = εar N Eˆrc = εdr Nˆrd c + εat Nˆra c = εdr (N/r) + εat N Eˆd = εd n(N/r) r

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From (8) - (19), we can find that NC has a two-fold impact on energy consumption. On one hand, NC reduces Ets with the help of redundant links, but on the other, NC increases Erc due to overhearing. This leads to results shown in Fig.7 ˆ while when r gets better, E > E. ˆ that when r is low, E < E,

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Figure 8. The ratios of end-to-end delay (in slots) between the NC-aided and the none-NC convergecast schemes in a CSn (n = 2, 3, 4) with ARQ.

B. End-to-end delay Fig. 8 illustrates the simulational results of the ratios of end-to-end delay (in slots) between the NC-aided and the none-NC convergecast schemes in a CSn (n = 2, 3, 4). Clearly, in the case of poor wireless link quality, NC is able to reduce the delay by means of its reliability benefits. In these cases, retransmission is the chief reason of the delay. However, when the link quality gets better, noneNC schemes outperform NC-aided ones. The reason is that, with the delivery ratio improves, the delay caused by retransmissions decreases rapidly and tends to play a minor role of the total delay. And meanwhile the inevitable waiting period, which is introduced by the decoder for collecting enough coded packets to recover the original ones, significantly increases the end-to-end delay. V. C ONCLUSION In this paper, we discuss about whether network coding can always benefit convergecast in a WSN. We implement four various convergecast schemes, i.e., the NC-aided and the none-NC convergecast schemes with or without ARQ. By theoretical analysis and simulations, we reach the following conclusions: The NC-aided convergecast schemes surpass the none-NC ones in the case of low link delivery ratio. However, due to the considerable overhearing required by coders, the packet loss penalties and the prerequisite of successfully decoding, the NC-aided convergecast schemes fall behind none-NC ones almost in all respects if the link delivery ratio is high enough. In other words, NC is particularly fit for WSNs with awful link quality. And we also find that CS2 outperforms higher order CSn in most performance metrics only except the packet collection rate in low delivery ratio. Although CS2 introduces less redundant links, it suffers less side effects of NC. ACKNOWLEDGMENT This work is supported by the Zhejiang Provincial Natural Science Foundation of China (LQ12F02009).

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