Network Coding in Underwater Sensor Networks

Transcription

1 in Underwater Sensor Networks Claude Manville, Abdulaziz Miyajan, Ayman Alharbi, Haining Mo, Michael Zuba and Jun-Hong Cui Computer Science & Engineering Department, University of Connecticut, Storrs, CT, USA {claude.manville, abdulaziz.miyajan, ayman.alharbi, haining.mo, michael.zuba, Abstract In this paper, we expand upon previous work in the application of network coding to Underwater Sensor Networks (UWSN). Network coding allows information from multiple packets to be encoded into a single packet and decoded upon receiving sufficient linearly independent encoded packets, improving throughput and providing redundancy for error recovery. Encoding and decoding algorithms for network coding are reviewed, and an algorithm capable of implementing network coding on an UWSN with arbitrary block size, packet length, and symbol size is presented. The network coding algorithms are implemented on real UWSN nodes utilizing our hardware and software platforms and tested using our UWSN testbed. Initial results indicate improved throughput with less overhead than other error-recovery techniques. I. INTRODUCTION AND MOTIVATION In recent years, underwater sensor networking has become an active field of research with applications ranging from environmental monitoring to underwater surveillance. Acoustic networking of aqueous sensors provides a broad range of possibilities for large-scale automated data collection. However, before the full realization of such potential, the implementation of fast and efficient Underwater Sensor Networks (UWSN) presents many challenges [1] [4]. The naturally lossy nature of underwater acoustic channels introduces significant barriers to the effective transmission of network traffic. High error rates and long propagation delays suffered by any acoustic underwater network require intelligent and efficient means of error-recovery. A number of approaches exist to mitigate the effects of high error rates, though many incur high overhead costs. Forward Error Correction (FEC) introduces redundancy at the sender to compensate for the assumed loss of packets. The effectiveness of an FEC scheme depends highly on the use of an appropriate amount of redundancy. Without enough redundancy the network will continue to suffer losses; too much redundancy wastes valuable battery power. The difficulty of accurately estimating error rates, and therefore the necessary redundancy, renders FEC less than ideal for UWSNs [1]. Automatic Repeat Request (ARQ) waits for the receiver to detect a loss and transmit a message back to the sender requesting retransmission of the lost packet. This approach does not require that the error rate be known ahead of time, but it significantly increases the delay for successful packet transmission and introduces additional traffic to the network. One technique with great promise for error recovery and improved data throughput is network coding, first proposed in [5]. In network coding, a node may encode several packets together before sending the information. This approach Fig. 1: Example of network coding on a butterfly network [5] allows for the maximum information flow through a network s resources while requiring minimal overhead when compared to other error-recovery techniques [6]. Figure 1 demonstrates how network coding can improve the throughput of a network by transmitting information encoded from multiple packets simultaneously [5]. Without network coding, the paths leaving the two center relay nodes can carry either packet A or B, but not both, therefore one of the destination nodes is able to receive only one of the two desired packets. Network coding can encode the information from both A and B at the relays, allowing both destination nodes to receive enough information to decode both packets. The same principle can be used to introduce redundancy into a network as a means of error-recovery. Previous work [7] contributed a promising theoretical proof of concept for network coding in underwater sensor networks. This paper contributes to this end by implementing a broader and more general network coding scheme and evaluating it on a real world system. The rest of this paper is organized as follows: Section II discusses previous work in the area. Section III introduces the mathematical theory and general algorithms used in the implementation of network coding. Section IV details the scheme implemented to test networking coding as part of a physical UWSN, and Section V presents and analyzes the empirical results. Finally, Section VI concludes the paper and considers future work.

2 2 II. RELATED WORKS Ahlswede et al. [5] show that for multicast to multiple sinks, the upper bound on throughput, as determined by the max-flow min-cut theorem [8] [9], cannot be obtained with traditional routing. They then proceed to prove that maximum throughput is possible through the use of network coding. Li et al. [6] prove that the max flow bound on information transmission can be achieved with multicast in a network using linear coding, allowing for computationally realistic implementations of network coding. Ho et al. [10] further reduce the computational complexity of network coding by using a randomized approach to the construction of linear coding schemes. They show that an independent, random linear code design at each node achieves the max-flow rate with probability approaching one with a tight lower bound as the finite field size increases with respect to the number of sinks. They present a distributed algorithm with runtime logarithmic in the size of the finite field. Chou et al. [11] present a practical, distributed, asynchronous implementation of network coding without the need for centralized knowledge of the graph topology. They show that their scheme is able to achieve near maximum throughput while remaining robust to topological and capacity changes resulting from node joins and leaves, node or link failures and congestion. Wu et al. [12] compare network coding to routing solutions through simulation over the network graphs of six internet service providers. Their results indicate that the improvement in throughput gained through network coding is marginal for the simulated networks, however the approach presents additional benefits in management, robustness, and reduced resource consumption. Jaggi et al. [13] present polynomial time algorithms to design linear multicast network codes proven to achieve maximum throughput. They further show that not only is the maximum throughput without coding significantly smaller, but finding that maximum-rate routing is NP-hard. Network coding has since proven useful for many applications, including wireless networking [14], distributed storage systems [15], peer to peer file distribution, network security and tomography, and of course sensor networks [16]. Recent research in joint channel-network coding has seen network coding move into the physical layer [17]. As it pertains to UWSNs, Guo et al. [7] analyze the benefits that network coding can provide for UWSN, and devise a network coding scheme specifically for UWSN. They present simulation results that demonstrate the value of network coding as a means of error recovery. This paper expands upon previous work by implementing a more general network coding scheme for UWSN capable of utilizing arbitrary symbol size, packet length, and block size, and producing empirical data through testing on a physical system. III. ALGORITHM DESCRIPTION The general algorithms for implementing linear network coding are as follows. A. Encoding We start by assuming that a number of original packets M 1,..., M n are generated by one or more sources. We associate with each packet a sequence of coefficients g 1,..., g n in the finite field GF (2 s ) by applying the following formula [16]: X = n (g i Mk) i (1) For the encoded information to be decoded, it is necessary that the encoded packets be linearly independent. This presents an issue in the computational complexity of deciding the linear combinations that each node should perform. Random network coding solves this issue by having each node in the network select coefficients independently and uniformly at random over the field GF (2 s ) [10]. With random network coding there exists a probability of selecting linearly dependent combinations; however, it has been shown that this probability decreases with increasing finite field size [13], and simulation results indicate that it becomes negligible in the case of GF (2 8 ) [12]. In testing, we choose an encoding symbol size of one byte (8 bits) since it is realistic and convenient, resulting in the use of GF (2 8 ) for the finite field arithmetic involved in all encoding and decoding calculations, though the algorithm is not limited to this choice. If a relay node r has received and stored a set of packets that have already been encoded (g 1,x 1 ),..., (g n,x n ), this relay node may generate a new recursively encoded packet (g,x ) by randomly picking a set of coefficients h 1,..., h m and computing the linear combination [16]: m X = (g i X i ) (2) The corresponding encoding vector g can be computed as follows: g i = m (h j g j i ) (3) j=1 B. Decoding The destination node receives the set (g 1,X 1 ),..., (g m,x m ). In order to recover the original packets, it must solve the system [16]: n X j = (g j i M i ) (4) Which has m equations and n unknowns. All M packets can be recovered when m n; meaning the number of received packets must be at least the number of original packets used in the encoding. Since the original transmission

3 3 is likely to be heard by multiple relay nodes and retransmitted, redundancy is a natural consequence and the likelihood that the destination node will receive enough encoded information to decode the original block of packets increases. Also, the sender of the encoded packets can transmit more than m encodings of the original sequence of packets to introduce additional redundancy. When an encoded packet is received, the receiver builds a decoding matrix by inserting the new packet s encoding vector into the last row. By using Gaussian elimination, the decoding matrix is then transformed to triangular form. When the matrix is of rank equal to the number of original packets, it is possible to recover the encoded information. Before solving the matrix, however, the receiver must guarantee there are not any zeros in the diagonals of the matrix. If there exists a zero diagonal, it is necessary to pivot that row with those beneath it in decreasing order and reorder all of the corresponding values to the altered rows [11]. Once Gaussian elimination produces the correct coefficient values, they are applied to each subsequent symbol in the information vector until the original message is fully decoded. The same coefficient values are then used to decode the information vectors for every other packet that contributed an encoding vector to the decoding matrix. Once this process is complete, the messages from the original packets M 1,..., M n are all obtained and may be passed along up the network stack. IV. IMPLEMENTATION The network coding encoding and decoding algorithms were implemented on the University of Connecticut Underwater Sensor Network (UWSN) laboratory s underwater network protocol stack framework Aqua-Net [18]. A network coding scheme was developed and data was collected by utilizing Teledyne Benthos acoustic modems in multiple laboratory tests. The network coding scheme involves three separate node roles. The first role is that of a source node, the second is a Source A/B/C/D relay node, and the third is the destination node. In our test, the source node creates packets containing a series of characters designed to fill the desired packet length, along with numerical data increased at a fixed increment with each packet sent. The outbound packets are stored in order to build a block of packets for encoding. The number of packets in a block can be set to any value; for the tests presented in this paper we chose a block size of four packets. Upon receiving a full block bound for one destination node, the source node uses the previously defined randomized linear encoding algorithm to encode the packets payloads into four separate information vectors and corresponding encoding vectors. The source node then broadcasts the encoded packets sequentially, placing the destination in the MAC layer header, the encoding vector and block ID in the network layer header, and the encoded information vector in the packet s payload. The only additional packet data our scheme requires is the encoding vector, of length equal to the block size, and packet block identification information. This data easily fits inside the existing network layer header and so does not produce any overhead. The redundancy is provided through the broadcast nature of the information transmission. Compared with other error recovery techniques that require entire additional packets to be introduced to the network traffic, our network coding scheme provides a significant reduction in overhead. For the purposes of testing, the packets sent by a source node are ensured, through the topological definition of the network, to be receivable only by relay nodes and not by the destination node to guarantee the packets will pass through a relay. The source node also cannot receive packets from any other node, and relay nodes cannot receive packets from one another. These effects can be produced by adding the sourcedestination pair to the network header and having nodes ignore packets identical to any recently received. A relay node, upon receiving a packet from the source node bound for the destination node, simulates packet loss on an unreliable channel by randomly dropping the packet with a configurable probability. At startup, each node is given a packet drop probability from zero to 100 as an argument. E 1 /E 2 /E 3 /E 4 E 1 /E 2 /E 3 /E 4 R1 R2 E 1 /E 2 /E 3 /E 4 E 1 /E 2 /E 3 /E 4 Destination A/B/C/D Fig. 2: Diagram of test setup. The example data flow shown demonstrates a case where both relay nodes drop half of the packets they receive and the destination node is able to recover all of the original data sent by the source node. Fig. 3: Experiment setup. Four Teledyne Benthos modems, two ATM-920 (tall, back) and two UDB Deck Box.

4 Throughput (bps) Throughput (bps) Packet Length (Bytes) (a) Throughput vs. Packet Length Packet Loss Rate (%) (b) Throughput vs. Packet Loss Rate Fig. 4: Effect of packet length and packet loss rate on network throughput. Each time a node receives a packet for which it is not the destination, it will produce a (pseudo) random number from 1 to 100. If the randomly generated number is greater than the specified packet drop probability, then the node will relay the packet, otherwise it will drop it. Finally, a destination node receiving the packets from a relay node will build a block of packets based on the block ID found in the network layer header in a fashion similar to that of the source node. It will first check if it has already received an identical packet and if so ignore it. If the packet received is novel, it is added to the decoding block. When a destination node has received sufficient packets for a given block to build a matrix of rank equal to the block size, the destination node uses the previously defined decoding algorithm to decode all of the packets in the block at once and send the decoded original messages up the stack. With these three node roles in place, our test setup was configured as in Figure 2. The two relay nodes between the source and destination nodes in the diamond topology provide complete data redundancy. For our test environment we set fixed delays on the relay nodes to control for collisions and focus on the effect of the simulated packet loss rate, though collisions can also be effectively countered using random relay delays [19]. With a block size of four, the destination node must receive four linearly independent encoded packets to decode the four original messages, otherwise it will not be able to recover any of them. This means that if one of the encoded packets is dropped by both relay nodes, then all of the packets in that block will be lost. However, if every packet in a block is passed along by either one or both of the relay nodes, then the entire block can be recovered. Figure 2 shows a case in which half of the packets are dropped, yet all of the original data is recovered after only two hops. In large networks with unpredictable link reliability such as those in UWSNs, network coding provides dynamic error-recovery. Multicast networks with multiple sinks can benefit even more from the encoding process, though we do not test for that effect here. Figure 3 shows the physical laboratory test setup using Teledyne Benthos modems. V. PERFORMANCE RESULTS AND ANALYSIS With the test environment set up, we ran multiple tests to analyze the system s throughput and error recovery rates. Each test was compared with the baseline performance of the existing Aqua-Net static routing protocol. In the static routing protocol, routes are predefined for source-destination pairs. At each hop, a single next hop destination is determined until the packet arrives at its destination. Since only one route is used, only one relay node receives the packet bound for the destination node. Therefore no dropped data can be recovered and the rate of packet loss is equal to the rate at which relay nodes drop packets. First, the relay packet drop probability was fixed to 20% and the packet length was varied to determine the effect on throughput. The test was set to run for an extended time period. The source node maintained logs on the data sent, the relay nodes maintained data on the packets dropped and relayed, while the destination node kept track of how many blocks were missed. The destination node was also able to ensure that the decoded data matched the data sent since the source node produced packets with messages following a predictable pattern. Since none of the packet lengths tested were long enough to require splitting across multiple packets, the results follow the expected linear increase and are shown in Figure 4(a). The throughput obtained with network coding rises slightly faster than that of static routing due to its capacity for error recovery. Next, the packet length was fixed at 200 bytes and the relay packet drop probability was varied to measure its effect on the network throughput directly. Since the test setup drops packets randomly with a certain probability, it was not possible to guarantee a specific packet drop rate without running a test indefinitely. Therefore, the tests were allowed to run long enough for the percent of packets dropped to converge to a reasonable level roughly half an hour in our tests.

5 5 The process was repeated with enough distinct packet drop probabilities to produce sufficiently varied data to establish a trend. As can be seen in Figure 4(b), the throughput with network coding drops off more slowly than with static routing as it recovers lost packets. Finally we present the collected data in Figure 5 to show the percent of packets recovered as a function of the packet loss rate. Since static routing cannot receive any packet dropped by the relay node, its packet recovery rate falls linearly with the packet loss rate, while network coding is able to delay its drop in recovery rate. With lower packet loss rates below 10%, the network coding scheme maintained enough redundancy to recover every packet sent. The packet recovery rate does decrease with increasing packet loss rate, but remains above the baseline static routing rate. Note that encoding the packets in blocks means that either every packet in a block is recoverable, or none of them are. Therefore the packet recovery is quantized to the size of a block; an effect which can be seen in the steep drops in packet recovery rate. VI. CONCLUSIONS AND FUTURE WORK In this paper, we propose an application of network coding principles on an underwater acoustic sensor network. For the encoding of information, we implement an algorithm to encode with arbitrary block size, packet length, and symbol size. We correspondingly implement a decoding algorithm accounting for equally arbitrary parameters. We implement network coding on real underwater acoustic network nodes and test using real UWSN equipment. Real world testing demonstrates the ability of network coding to compensate for the naturally lossy channels of underwater environments and perform effective error recovery. The chosen test setup demonstrates the full functionality of the network coding scheme developed and implemented, if not necessarily providing an ideal scenario for utilizing the full potential of network coding. Choosing a block size of four packets demonstrates our implementation s ability to perform network coding, and still follows the same overall trend of packet recovery rate, even though a block size of one (no encoding) would have reduced the quantization of packet loss. This work focused solely on network coding as a means of error recovery. Future work will aim to realize the full potential of network coding by deploying it in a multicast scenario. With multiple destination nodes, we can test the practical capacity for information encoding to increase network throughput in UWSN. A thorough network coding implementation can increase both the data throughput and reliability of underwater acoustic sensor networks. REFERENCES [1] Jun-Hong Cui, Jiejun Kong, Mario Gerla, and Shengli Zhou. Challenges: building scalable mobile underwater wireless sensor networks for aquatic applications. IEEE Network, Special Issue on Wireless Sensor Networking, 20(3):12 18, May [2] J. Heidemann, Y Li, A. 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