Fountain Code based Adaptive Multi-hop Reliable Data Transfer for Underwater Acoustic Networks

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1 Fountain Code based Adaptive Multi-hop Reliable Data Transfer for Underwater Acoustic Networs Zhong Zhou 1, Haining Mo 1, Yibo Zhu 1, Zheng Peng 1, Jie Huang 2 and Jun-Hong Cui 1 {zhongzhou, haining.mo, yibo.zhu, zhengpeng, jhuang, jcui}@engr.uconn.edu 1 Computer Science & Engineering Department, University of Connecticut, Storrs, CT Electrical & Computer Engineering Department, University of Connecticut, Storrs, CT Abstract In this paper, we investigate multi-hop reliable data transfer for underwater acoustic networs. We propose a new protocol, called FOuntain Code based Adaptive multi-hop Reliable data transfer (FOCAR. FOCAR is essentially a hybrid ARQ scheme which integrates Fountain codes with hop-by-hop retransmission-upon-failure. It considers the half duplex nature of the underwater acoustic modems and adapts the bloc size of each hop to optimize the end-to-end delay for the multi-hop networ scenario. Extensive simulation results show that FOCAR can achieve high reliability with low end-to-end delay and high energy efficiency. I. INTRODUCTION As an emerging area, underwater acoustic networ has attracted rapidly growing interests in last several years [1], [2], [3]. The unique characteristics of underwater acoustic communication have posed significant challenges for the protocol design on each layer of the networs. In this paper, we tacle a challenging yet unsolved problem, multi-hop reliable data transfer, for underwater acoustic networs. Generally, underwater networs are characterized by long propagation delays, error-prone channel and low available bandwidth. In addition, current underwater acoustic modems are half-duplex and the state transition delay between transmitting and receiving is significant (ranging from hundreds of milliseconds to several seconds [4], [5]. These features mae conventional methods for reliable data transfer undesirable for underwater acoustic networs. First, end-to-end approaches are inefficient since a transmission failure on any one hop leads to a retransmission from the source to the sin over multiple hops, which significantly increases the average end-to-end delay. Second, even with hop by hop methods, one retransmission can largely degrade overall system performance given the large propagation and state transition delay. Finally, although some pioneering studies, such as [6], have investigated hybrid ARQ schemes for reliable data transfer in underwater acoustic networs, they have not taen into consideration the large state transition delay within the acoustic modems. These schemes do not optimize for the multi-hop scenario, where one hop with poor lin quality can become the bottlenec lin in the whole system and starve subsequent hops with good lin qualities. Inspired by the thoughts and ideas discussed above, in this paper, we propose a new scheme, called FOuntain Code based Adaptive multi-hop Reliable data transfer (FOCAR for underwater acoustic networs. FOCAR is a hybrid scheme which integrates coding with retransmission-upon-failure. Fountain codes are used due to their strong error correction capability and rateless property. The integration with a selective repeat based retransmission scheme can greatly reduce the delay within one hop. In addition, FOCAR proposes an optimization framewor to imize the end-to-end delay over multiple hops. Further, FOCAR considers the impact of the large state transition delay within current acoustic modems, which has been neglected by prior research wor. The rest of this paper is organized as follows. In Section II, we first review some bacground nowledge and related wor. Then in Section III, we describe FOCAR in detail. After that, we present simulation results in Section IV. We finally conclude our paper in Section V. II. RELATED WORK Reliable data transfer has been extensively investigated for terrestrial wireless networs. In [7], Wan et al. proposed PSFQ protocol, which employs a hop-by-hop ARQ lie approach with fast data rate for retransmission. In [8], a protocol, ESRT was investigated. Due to the distinctions between underwater acoustic networs and terrestrial radio networs, these protocols are unsuitable for the underwater environment. Recently, efficient reliable data transfer for underwater acoustic networs has received significant research interests. The authors in [9] analyze three inds of stop-and-wait protocols for underwater acoustic networs and shows that the performance of the basic stop-and-wait protocols can be significantly improved by transmitting pacets in group and selective acnowledgment. In [10], fountain code is employed to facilitate the reliability and efficiency of broadcasting in underwater acoustic networs. A mathematical model on the performance of fountain codes for broadcasting is given in this paper. In [11], a fountain code based reliable data transport and storage protocol for underwater acoustic networs is proposed. A concatenated fountain coding mechaniss employed. While sensing-zone fountain code is utilized to enable reliable data transport, a second layer of fountain code is used to guarantee uniform storage reliability. In [6], a hop-by-hop hybrid ARQ scheme, called SDRT, was proposed for underwater acoustic networs. In SDRT, the sender first divides pacets into multiple blocs. It then encodes each bloc using a simple version of Tornado codes and transmits pacets fast inside a window. After that, it slows down data transmission, waiting for the response from the receiver. If the sender does not get a positive ACK from the receiver, it will send one and only one coded pacet to the receiver after it times out. No negative ACK is used in SDRT. When the underwater acoustic channel is in deep fading, such a single pacet retransmission scheme is ignorant of the current channel condition and thus very inefficient. In addition, SDRT and most existing researches ignore the large state transition delay of the underwater acoustic modems, which

2 2 has significant impacts on multi-hop reliable data transfer in underwater acoustic networs. III. PROTOCOL DESCRIPTION In this section, we first introduce Fountain Codes and present the networ model. Then, we describe our FOCAR protocol in detail. A. Fountain Codes Fountain codes are record-breaing codes for channels with erasures (e.g., pacet losses in a communication networ. It has enabled a revolutionary way of non-flow-based data delivery over unreliable networs, pioneered by the invention of LT codes [12] and Raptor codes [13]. The basic idea of a Digital Fountain code is as follows. The encoder is a fountain that produces an endless supply of water drops (encoded pacets. Suppose the original source file has a size of K pacets, and each drop contains l encoded pacet. A receiver that wishes to receive the encoded file holds a bucet to collect drops until the number of drops in the bucet is K (which is a little larger than K, and then it can recover the original file. Fountain codes are rateless in the sense that the number of encoded pacets that can be generated from a source message is potentially limitless. In addition, the number of encoded pacets generated can be detered on the fly. Furthermore, another attractive feature of fountain codes is that they are nown to have efficient encoding and decoding algorithms [12], [13]. In this paper, we choose Fountain codes for the coding process of FOCAR. On the one hand, Fountain codes have very efficient encoding and decoding algorithms with linear complexity [12], [13], which could help to reduce the overall end-to-end delay. On the other hand, the amount of redundancy can be detered on the fly, which will greatly facilitate the implementation of selective repeat, directly contributing to low end-to-end delays and high energy efficiency. B. Networ Model The target multi-hop underwater acoustic networ is illustrated in Fig. 1. From a source to a destination, there exists a multi-hop path. How to obtain the path is discussed in Section III-F. On the path, the ith node is defined as node i, its next hop as node i + 1, and its previous hop as node i 1. Each node is equipped with only one half-duplex underwater acoustic modem, where the state transition delay between the sending and receiving states is not negligible any more [4], [5]. And during the modem state transition, the node can neither send nor receive any data. Further, on each node, there is a First In First Out (FIFO queue to store all pacets. Any pacet cog from the upper layer or from the upper stream node will first be fed into this queue. When it is time for transmission, the node fetches pacets frots queue head and sends them out. C. Protocol Overview As mentioned earlier, FOCAR is essentially a hybrid ARQ scheme, smartly integrating Fountain codes and retransmission-upon-failure to improve the system reliability and efficiency. FOCAR includes two essential components: per-hop reliable data transfer and multi-hop optimization. The per-hop reliable data transfer wors as follows: Referring to Fig. 1, on node i, after it receives pacets from node source Node i-1 Node i Node i+1 Destination Fig. 1. Illustration of the networ model i 1, it will first group pacets into one bloc ( is defined as the data bloc size of node i. Then it will code the pacets in each bloc into M pacets with Fountain codes (M is defined as the coded pacet bloc size. Note that for the ease of design, M is the same for every node. After that, node i sends the M coded pacets to node i + 1 and switches to receiving status. If node i + 1 can correctly decode the original data pacets (it has received equal to or more than coded pacets, it will send a positive ACK to node i. Otherwise, node i + 1 will send a negative ACK (indicating the number of unrecovered pacets to node i. The sender, node i, based on the negative ACK information, will transmit more coded pacets to the receiver node i + 1. If node i + 1 can receive pacets out of all the coded pacets sent out by node i in this retransmission, all the original data pacets can be recovered. From the above description, we can see that appropriately setting is very critical: if is large, the coding rate will be reduced, which results in more retransmissions on node i; on the other hand, if is small, the queueing delay on node i will be increased, which also degrades the system performance. This brings us to the second component of FOCAR: multi-hop optimization. In order to optimize the data bloc size on every node, FOCAR first collects the pacet error rate information of every hop from the source to the destination. Then, it solves an approximate convex optimization problem (detailed in Section III-E to get the optimal solutions. After that, it will distribute the optimal solution to every node. How to couple this multi-hop optimization with routing in a distributed way is discussed in Section III-F. Next, we will first analyze the per-hop reliable data transfer. Then we will present the multi-hop optimization. After that, we will discuss the distributed implementation of FOCAR. D. Per-hop Reliable Data Transfer Obviously, to reduce the number of retransmissions, we need to mae sure that every transmission of the coded pacets within one hop can be successfully decoded with a high probability. With Fountain codes, we can safely assume that if the receiver can correctly receive pacets from the M coded pacets, it can correctly recover the original data pacets [12], [13]. If we denote the unsuccessful decoding probability for one transmission as δ (note that δ is a system design parameter, we can have =0 (p e i M (1 p e i δ, (1 where p e is the pacet error rate of the acoustic channel from node i to node i+1. This equation also applies during the retransmission process. When the sender receives a negative

3 3 ACK from the receiver, which includes the number of coded pacets that are needed for correct decoding, it sets in Eq.(1 to and calculates the number of coded pacets for its next retransmission. With Eq. (1, we now that the receiver can correctly recover the original data pacets at least with probability after every transmission or retransmission. Intuitively, to reduce the retransmission delay, δ usually taes a very small value. Thus, the average transmission delay d i for data pacets to be correctly transmitted from node i to node i + 1 can be derived as d i = [( + 2δ( δ 1 ( +...], (2 where is the average time for one-time transmission which includes the transmission time, the signal propagation delay and the transition delay of the acoustic modem between the sending and receiving status. For the ease of analysis, we assume to be the same for every node. Then the average number of the coded pacets, m c i, needed for the successful transmission of data pacets can be written as M M(1 p e m c i i = 1 p e M(1 p e (3 i < i E. Multi-hop Optimization On a multi-hop path, recall that each node has a FIFO queue to store the received pacets from the upper layer or the upstream node. For a node on the path, say node i, when there are more than data pacets in its queue, if it is in the sending status and its next hop, node i + 1, is in the receiving status, then node i will try to code first pacets into M pacets and send them to its next hop. Since the underwater acoustic modem wors in half-duplex mode, any node can be in either sending or receiving status. Let s set the probability that node i sits in the sending status to be p s i. Then it is clear that ps i should be a function of optimal bloc size : a smaller means a larger coding rate and thus means a worse channel condition; to compensate for this, node i should be assigned a larger sending probability if the channel quality between node i and node i+1 is worse. Hence, p s i should be a monotonically decreasing function of. To simplify our analysis, we choose p s i = e M. Since must be smaller than M, p s i lies in (0, 1. Now, the average service rate u i for pacets on node i thus can be derived as u i = p s i p r i+1 = e mi +1 M (1 e M (4 If the input traffic follows a Poisson process, the whole system can be modeled as a Jacson networ since the service time of every node follows exponential distributions approximately. The average queueing delay of a pacet, q i, on node i thus can be derived as: q i = λ u 2 i u i λ (5 where λ is the parameter of the input Poisson process. Now the total delay of a pacet on node i, which includes both queueing delay and transmission delay can be denoted as τ i = q i + (6 Based on the above, we can formulate an optimization problem to imize the average end-to-end delay for a data pacet as follows: q i + i (1,2,...n =0 (p e i M (1 p e i δ 0 M, (7 where n is the number of hops on the studied path. The variables to be optimized in Eq.(7 are the data bloc size for every node. The first constraint specifies that the optimal value of should mae sure that every transmission of M coded pacets can be correctly decoded with high probability. And the second constraint specifies that should be larger than 0 and smaller than the maximal allowable number of coded pacets, M. Since /( does not change with, we can neglect /(1 δ. Combining Eq.(4, Eq.(5 with Eq.(7, we can get i (1..n [e M (1 e +1 M =0 λ 1 δ ] 2 e (p e i M (1 p e i δ M (1 e +1 M (1 δλ 0 M. (8 Again we neglect (/ and tae logarithm on every item. Also we apply the Chernoff s upper bound to the first constraint. Then Eq. (8 can be written as i (1,2,...n logλ log + M log(1 e +1 M log(e e ( (Mp e i 2 2p e i M +1 M (1 e M λ δ 0 M. (9 It should be noted that Eq.(9 is an integer programg problem since can only tae integer values, which is hard to solve efficiently. However, if we relax to tae continuous values, Eq.(9 is a continuous convex optimization problem because the Hessian matrix of both its objective function and its constraints is semi-definitive, which can be efficiently solved by the interior point method [14]. F. Integration with Routing FOCAR can be easily integrated with an on-demand routing protocol (such as AODV lie approach for the distributed implementation. During the routing process of the on-demand routing protocol, the source node can flood a Route Request message to the destination. Any intermediate node who receives this Route Request for the first time will forward it.

4 4 In FOCAR, an intermediate node will insert measured pacet error rate of its acoustic lin in its relayed Route Request message. When the destination node receives an Route Request message which includes the pacet error rates of all the upstream lins, it will first do the multi-hop optimization as in Section III-E to get the optimized data bloc size for every preceding node. Then it will send the optimal solution to every preceding node in its Route Reply message reversely along the path of the corresponding Route Request message. In this way, FOCAR does not need to start a new networ traffic to gather pacet error rates or to distribute optimal data bloc sizes and thus incurs very small communication overhead. Even in highly dynamic environments where channel lin qualities fluctuate frequently, FOCAR is able to gather pacet error rates and distribute optimal solutions in a timely way via routing update messages. IV. PERFORMANCE EVALUATION In this section, we evaluate the performance of FOCAR via simulations. As the baseline, we also implement SDRT [6], which was introduced in Section II, and compare it with FOCAR. A. Simulation Settings We simulate a multi-hop underwater acoustic networ, where multiple nodes are randomly deployed. Unless specified otherwise, the networ parameters are defined as follows: the pacet error rate of every acoustic channel is uniformly distributed between 0.2 and 0.5; the maximum bloc size (or the coded pacet bloc size M is set to be 10; the average number of hops from the source to the destination is 6; and the input traffic on the source node follows a Poisson process with parameter Further, the pacet length is set to be 125 bytes, the bit rate of every node is set to be 1 bps, and the acoustic modem state transition delay is set to be 3 seconds. Two metrics are used to measure the performance: average end-to-end delay and energy efficiency. The former is defined as the average end-to-end delay of a pacet transmitted from the source to the destination. The latter is measured by the average number of coded pacets transmitted along all hops which are needed for the successful end-to-end transmission of one data pacet. B. Simulation Results 1 Impact of Hop Count: In this set of simulations, we change the average number of hops between the source and the destination from 2 to 12 with a step size 2. We run the simulation for 500 rounds and generate 100 pacets in each round. The results on average end-to-end delay and energy efficiency are plotted in Fig. 2 and Fig. 3 respectively. From Fig. 2, we can observe that the average end-toend delay of FOCAR is shorter than that of SDRT. And as the number of hops increases, the delay of FOCAR grows slower than that of SDRT. SDRT does not consider multi-hop optimization. If there is a bad lin with a high pacet error rate on the path from the source to the destination, it will become the bottlenec and pacets will be queued on this lin, which results in high queuing delays. With the increase of the number of hops, the chance of the existence of such a bad lin becomes larger. FOCAR is specially optimized for multi-hop networ scenarios. It optimizes the data bloc size on every node as well as its sending probability p s i, which is defined as a function of. In this way, a bad acoustic channel will be assigned a small bloc size providing it a high coding rate and a high sending probability, which contributes to a larger chance of successful transmission. Thus, FOCAR has a better performance in average end-to-end delay. Fig. 3 shows the comparison of FOCAR with SDRT on the performance of energy efficiency. From this figure, we can see that the energy efficiency of FOCAR is slightly worse but comparable to that of SDRT. We believe this is mainly due to their different pacet retransmission mechanisms. In SDRT, whenever a bloc of pacets fails to be decoded, only one more pacet is retransmitted. After the receiver receives this new coded pacet, if it can correctly recover the original pacets, it will send an ACK and no more pacets are needed. If not, another coded pacet will be sent from the sender. Such a single-pacet retransmission strategy may achieve highest energy efficiency since in most cases, the sender just needs to send the exact number of coded pacets needed for successful decoding. However, this approach can incur a lot of retransmissions on a hop with bad lin quality since the single retransmitted coded pacet can easily get lost. In FOCAR, however, with Fountain codes and negative ACK mechanism, the receiver estimates and ass for multiple pacets for one single retransmission. As a result, the sender may send out more coded pacets than actually needed by the receiver to recover all original pacets. However, Fountain codes can guarantee the number of extra unnecessary coded pacets is very small. Moreover, this strategy can greatly reduce the number of retransmissions. To summarize, compared with SDRT, FOCAR achieves a much better balance between end-to-end delay and energy efficiency. It could guarantee high reliability with low endto-end delay and high energy efficiency. 2 Impact of Traffic Rate λ: In this set of simulations, we investigate the impact of the input traffic rate λ. Fig. 4 and Fig. 5 plot the results on average end-to-end delay and energy efficiency respectively. As illustrated in Fig. 4, with the increase of the input traffic rate λ, the average end-to-end delay of FOCAR stays stable. This is because the input traffic rate is considered in the optimization of FOCAR, which limits their impacts on the delay. On the other hand, in SDRT, the average end-to-end delay for a pacet grows significantly with λ. This is because that a large λ causes significant growth in queueing delay of a pacet on every node. On energy efficiency, from Fig. 5, we can observe that the performance of FOCAR does not vary much when λ increases. For SDRT, the energy efficiency also stays nearly unchanged when λ grows. Since the input traffic rate will not affect the pacet error rate of the channel, the number of coded pacets which are needed for a successful transmission of a data pacet will not change for both FOCAR and SDRT. We have also conducted simulations to evaluate the various parameters for FOCAR, such as the maximum bloc size M, pacet error rate P ER and required unsuccessful decoding probability δ. The simulation results show that FOCAR outperforms SDRT on average end-to-end delay while holding comparable energy efficiency. Due to space limitation, these results are not included in this paper. Interested reader can refer to our technical report [15].

5 5 Fig. 2. Average End-to-End Delay with Varying Number of Hops Fig. 4. Average End-to-End Delay with Varying λ Fig. 3. Energy Efficiency with Varying Number of Hops Fig. 5. Energy Efficiency with Varying λ V. CONCLUSIONS AND FUTURE WORK In this paper, we studied the reliable data transfer for multihop underwater acoustic networs and proposed a new protocol, called Fountain code based adaptive multi-hop reliable data transfer (FOCAR. FOCAR smartly integrates Fountain codes with hop-by-hop retransmission-upon-failure. Further, it taes the half duplex nature of underwater acoustic modems into consideration and is especially optimized for multi-hop networ scenarios. We formulate an optimization framewor to maximize the system performance over multiple hops, and solve the problem by appropriate relaxation. Extensive simulation results show that FOCAR can achieve high reliability with low end-to-end delays and high energy efficiency. Further Wor. We plan to pursue future wor in two directions. 1 In current FOCAR, we assume the average time for one-time transmission is the same for all hops (as the modem status transition delay is doating along the path. It would be interesting to investigate the case that propagation delays are more doating, which will introduce significant complexity to the multi-hop optimization problem. 2 We would lie to explore the real implementation of FOCAR, especially focusing on the coding structure and dynamic channel conditions. Along this path, various underwater testbeds developed at the University of Connecticut will be leveraged. REFERENCES [1] M. Chitre, S. Shahabudeen, and M. Stojanovic, Underwater acoustic communicatin and networs: Recent advances and future challenges, Marine Technology Society Journal, no. 1, pp , [2] J.-H. Cui, J. Kong, M. Gerla, and S. Zhou, Challenges: building scalable mobile underwater wireless sensor networs for aquatic applications, IEEE Networ, Special Issue on Wireless Sensor Networing, vol. 20, pp , May [3] L. Liu, S. Zhou, and J.-H. Cui, Prospects and problems of wireless communication for underwater sensor networs, Wireless Communications & Mobile Computing, vol. 8, pp , [4] L. Freitag, M. Grund, S. singh, J. Partan, P. Kosi, and K. Ball, The WHIO micro-modem: An acoustic communications and navigation system for multiple platforms, in Proceedings of MTS/IEEE OCEANS, vol. 2, pp , June [5] Benthos acoustic modem: [6] P. Xie and J.-H. Cui, An fec-based reliable data transport protocol for underwater sensor networs, in Proceedings of 16th International Conference on Computer Communications and Networs (ICCCN, pp , Aug [7] C.-Y. Wan, A. T. Campbell, and L. Krishnamurthy, PSFQ: A reliable transport protocol for wireless sensor networs, in Proceedings of IEEE WSNA, Sept [8] Y. Sanarasubramainam, O. B. Aan, and I. F. Ayildiz, ESRT: Eventto-sin reliable transport in wireless sensor networs, in Proceedings of ACM Mobihoc, June [9] M. Stojanovic, Optimization of a data lin protocol for an underwater acoustic channel, in Proceedings of MTS/IEEE OCEANS, June [10] P. Casari, M. Rossi, and M. Zorzi, Fountain codes and their application to broadcasting in underwater networs: Performance modeling and relevant tradeoffs, in Proceedings of of ACM WUWNet, Sept [11] R. Cao and L. Yang, Reliable transport and storage protocol with fountain codes for underwater acoustic sensor networs, in WUWNET, (Woods Hole, MA, US, [12] M. Luby, LT codes, in Proceedings of the Annual IEEE Symposium on Foundations of Computer Science, pp , Nov [13] A. Shorollahi, Raptor codes, IEEE Transactions on Information Theory, vol. 52, pp , Jul [14] S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge University Press, [15] Z. Zhou, H. Mo, Y. Zhu, Z. Peng, J. Huang, and J.-H. Cui, Fountain Code based Adaptive Multi-hop Reliable Data Transfer for Underwater Acoustic Networs, in UCONN CSE Technical Report: UbiNet-TR10-02, July 2010.

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