NETCOMPRESS: COUPLING NETWORK CODING AND COMPRESSED SENSING FOR EFFICIENT DATA COMMUNICATION IN WIRELESS SENSOR NETWORKS Nam Nguyen, Douglas L. Jones

Sudha Krishnamurthy

School of Electrical and Computer Engineering University of Illinois, Urbana-Champaign

United Technologies Research Center East Hartford, CT

ABSTRACT Measurements from sensor networks consisting of thousands of nodes are often correlated, since nearby sensors observe the same phenomenon. Using Compressed Sensing, that data can be reconstructed with a high probability from a small collection of random linear combinations of those measurements. This opens a new approach to simultaneously extract, transmit and distribute information in wireless sensor networks. Efficient communication schemes well matched to compressive sensing are, nonetheless, needed to realize the full benefits of this approach. We present a simple, practical scheme, called NetCompress, using a novel form of Network Coding. It preserves the reconstruction conditions required for Compressed Sensing and also overcomes the high link-failure rate in wireless sensor networks. NetCompress simultaneously transmits packets of sensor measurements and encodes them to form random projections for Compressed Sensing recovery. A recent result in Compressed Sensing guarantees that the data at all nodes can be accurately recovered with a high probability from a small number of projections, which is much less than the total number of nodes in the network. NetCompress demonstrates this result on both the TOSSIM simulation platform and a testbed comprising 20 micaz and tmote sensor nodes. Our experimental results show that the number of packets that is needed to reconstruct light intensity measurements with reasonable quality is just half the number of nodes in the network. Index Terms— Compressed Sensing, Network Coding, Wireless Sensor Networks. 1. INTRODUCTION With recent advances in semiconductor technology, wireless sensor networks (WSN) have emerged as a low-cost, ubiquitous and massive sensing platform to capture the physical world for many applications such as military surveillance [1], infrastructure maintenance [2], habitat monitoring [3], and scientific exploration [4]. As a sensor node can be miniaturized into a cubic centimeter package with sensing, processing, and wireless communication units, WSNs can be deployed anywhere in buildings for monitoring energy consumption, along roads for traffic condition update, or on battlefields for military surveillance. Information now becomes abundantly available, but the challenge is how to efficiently process, transmit and The authors acknowledge the partial support of the Multiscale Systems Center, one of five research centers funded under the Focus Center Research Program, a Semiconductor Research Corporation program. This work was also done in part when the first author was an intern at Deutsche Telekom Labs. We are grateful to the management at Deutsche Telekom Labs for supporting this project and the internship.

collect that information from a dense network of hundreds to thousands of nodes. Measurements from a sensor network are either spatially or temporally correlated, since many sensors observe the same phenomenon. Therefore, it is desirable to exploit this correlation, in order to save energy when relaying those measurements to a central processing node or a mobile collector. Compressed Sensing (CS) has recently become a powerful new tool for processing data that is correlated. It basically reveals that a data vector with correlated entries, which effectively can be transformed into a sparse vector under some transforming basis, may be recovered from a small number of random projections onto another basis that is incoherent with the transforming basis [5, 6]. This approach is directly applicable for sensor-network scenarios if the correlated data vector is considered as a collection of all measurements in the network at a certain time. The spatial correlation of the measurements is reflected in the data vector. Then, random projections of the data vector can be considered as the random ways in which those measurements are linearly combined. The power of CS lies in the fact that only a small number of data packets need to be received to reconstruct all of the data from the network. In fact, this approach for collecting data from WSNs has been formulated into a framework provided by Duarte et al [7]. However, the authors did not provide a practical communication scheme to realize this framework. In this paper, we fill this gap by introducing a practical scheme for encoding data at each of the sensor nodes using Network Coding and couple that with Compressed Sensing to achieve efficient communication in wireless sensor networks. Besides having correlated measurements, WSNs also bear two other characteristics, namely the broadcast nature of wireless transmission and the dynamic nature of network links. As sensor nodes are typically deployed in remote, unattended or even harsh conditions, network connectivities in a WSN are extremely ad-hoc due to moving obstacles, link failures, and the discontinuous operating schedule of nodes in order to save energy. Therefore, the challenge in designing a communication scheme for WSNs is how to accommodate both the dynamic nature and exploit the broadcast nature of WSNs. Network Coding has long been considered as a promising tool to solve this challenge in wireless networks and also leverage the multicast network capacity. The main concept behind Network Coding is that instead of just buffering and forwarding data packets, intermediate nodes aggregate input packets using simple algebraic operations, before forwarding the packets to the neighboring nodes. In particular, intermediate nodes using a linear random network coding scheme produce outputs by linearly combining inputs with random coefficients. This operation is similar to the random projection operation in Compressed Sensing. Coupled with the broadcast na-

ture of wireless transmissions, Network Coding can introduce diversity and redundancy in the network to adapt to the dynamic changes in network topology. This is our motivation behind combining Network Coding and Compressed Sensing in WSNs. So far Network Coding has been mainly employed in wireless networks to enable downlink communication, i.e. delivering data from one point to one or more points in the network. However, communication in WSNs is predomominantly an uplink communication, where data from all the nodes are forwarded to a central processing node or a mobile collector. In this paper, we propose a practical scheme, called NetCompress, for both transmitting and reconstructing measurements in WSNs. Linear random network coding is used to relay information across the network and also to simultaneously perform in-network compression on those correlated measurements by forming random projections for recovery using Compressed Sensing. In doing this, NetCompress combines the best features of both techniques and demonstrates a number of advantages. It • exploits the broadcast nature of wireless transmission to increase diversity. • adapts to the dynamic nature of wireless sensor networks. • exploits the correlation between sensor measurements to minimize the number of received packets required for decoding, thereby reducing the communication overhead. In the remainder of this paper, we present the details of NetCompress, the packet format, and the encoding algorithm. We also evaluate the performance of NetCompress through both simulation and experiments on a real testbed. A key contribution is the implementation of NetCompress on a real system using 20 microcontrollerdriven sensor motes. We demonstrate a significant reduction in the number of packets required for data reconstruction with reasonably high quality. This makes NetCompress a competitively efficient data communication scheme in WSNs. 2. BACKGROUND AND PROBLEM FORMULATION Consider a data vector x = [x1 , . . . , xn ]T representing a spatial snapshot of a sensor network of size n, where xi of vector x is a measurement of sensor i. Since all the sensors in a neighborhood observe the same event or sequence of events, their data are highly correlated [8]. Vector x is then compressible. In other words, there is a transformation basis Ψ so that x can be approximately represented by a sparse vector u: x ≈ Ψu (1) where the number of non-zero elements in u is k << n. In this section, we will explain how the Compressed Sensing technique can be applied in WSN to recover this compressible data vector x from a small number of random projections and how the Network Coding technique can lead to a new encoding scheme to produce those random projections during in-network transmission. 2.1. Compressed Sensing An important result in Compressed Sensing is that if we project vector x in (1) onto an m × n random matrix Φ and produce a new measurement vector y = Φx = ΦΨu (2) then x can be accurately reconstructed with high probability from the vector y which has a much shorter length m = O(k log n) << n [5, 6]. In fact, for m < n, Equation (2) is an inverse problem with

an infinite number of solutions. However, Candes and Tao showed in [5] that if the product matrix ΦΨ satisfies the Restricted Isometry Property (RIP) condition and the vector u is sparse, then u and effectively x can be recovered by solving an `1 -minimization problem. Furthermore, Candes and Tao point out that the random matrix Φ, taking the form of an i.i.d Gaussian or Bernoulli/Rademacher (±1) can universally meet the RIP condition. Apply this finding to WSNs, we can recover all measurements in the network if we collect enough (m) packets to form the vector y, whose entries are the sums of the products of sensor measurements with some random numbers. However, the question of how to efficiently form and deliver those m packets or random projections to a central processing unit is still open. In fact, Rabbat et.al. in [9] are the first to introduce a practical implementation of random projections for compression and distribution in a multi-hop wireless sensor network. In that paper, the communication scheme uses a simple gossip algorithm to gradually flood the network with all random projections. Although the scheme is resilient to changing network topology and unreliable transmission links, it requires a large amount of communication and takes time to converge. Using another approach, [10] proposed an energy-efficient scheme with a sparse random matrix Φ. In the scheme, each node is responsible for producing and storing one sparse random projection. First, a node generates a sparse random coefficient vector. Based on the coefficient vector, it can request measurements from a sensor corresponding to a non-zero coefficient in its coefficient vector. Although the scheme seems to reduce the amount of communications by generating only sparse random projections, it does so with an assumption of an underlying routing layer in the network. However, forming and maintaining routes in a dynamic network, like WSN, involves significant overhead and results in delay. 2.2. Linear Network Coding Network coding has recently received much attention from the networking community as a new, efficient solution for data communication in broadcast networks, such as multicast and wireless networks. Conventionally, in a multi-hop network, a node routes a packet to the destination through a sequence of intermediate nodes by simply copying and forwarding it to the next-hop node. Using Network Coding, a node aggregates several received packets into a single packet and then forwards it through one or more outgoing links. Previous work showed that Network Coding increases the network throughput, and linear network coding is sufficient to achieve capacity in the multicast network [11, 12, 13]. Although demonstrating clear throughput gain, Network Coding only became practical when Ho et al. [14, 15] theoretically showed that the linear encoding function can be designed using random coefficients. After that, Chou et.al. in [16] proposed an encoding scheme for downlink transmission in a wireless network. In that scheme, a source injects N data packets into the network. At an intermediate node, when two or more packets arrive, the node generates the same number of random coefficients, multiplies them one-by-one with the input packets, then sums up all products to form a new output packet. The coefficients, which constitute the linear combination in the output packet, are updated and stored in the output packet’s header. Therefore, the header size is proportional to N . When a sink wants to decode the data from the source, it collects at least N different packets and uses a Gaussian elimination process to get the N original data packets. (Note that all the numbers are in a finite field and all additions and multiplications are finite-field operations.) The above explanation described how Network Coding can ef-

ficiently form and deliver random projections to a central processing unit for reconstruction using Compressed Sensing. In fact, Katti et.al. also introduce the concept of combining Network Coding and Compressed Sensing [17]. However, there is still one more challenge hindering practical implementation, that is not addressed in their work. In the Network Coding scheme, the size of the header is proportional to the number of packets injected into the network. For downlink communication, one can set this number to a relatively small value. However, in WSNs, where the communication is predominantly uplink, this number is the number of nodes in the network, which can be on the order of hundreds or thousands. The header is therefore too long for a practical implementation. Since this problem was not addressed by previous work, it stops short of being realizable on all platforms. In the next section, we present the design of our NetCompress scheme and describe how we address this header explosion problem. 3. NETCOMPRESS DESIGN In this section, we adapt Network Coding to incorporate Compressed Sensing in WSNs. On the one hand, Network Coding can be regarded as a mechanism at the transport layer to relay information across the network. On the other hand, Network Coding serves as an encoding algorithm at the application layer to produce random projections for Compressed Sensing. Therefore, the first task is to modify the network coding scheme, so that it not only meets the Compressed Sensing RIP condition for random projections, but also addresses the header explosion problem during uplink communication in WSNs. We then present the packet format and finally, outline the encoding algorithm implemented on each sensor node. 3.1. Modifications to Network Coding Random linear network coding is the right choice to generate random projections for Compressed Sensing. However, there are two options for random coefficients: 1) i.i.d Gaussian or 2) i.i.d Bernoulli/Rademacher (±1) random variables. We select the Bernoulli/Rademacher option for two reasons. First, it is simple to implement by just randomly adding or subtracting packets together. Second, there is a remarkable result in [8] claiming that a sparse random matrix Φ, containing entries  1  +1 with probability 2s 0 with probability 1 − 1s Φij =  1 −1 with probability 2s

Fig. 1. Packet format for compressed sensing via network coding.

or 32-bit slots. The data field stores the random projection values. For example, the packet in Figure 1 displays the linear combination of 3 nodes: 4, 6, and 11 with coefficients of 1, -1, 1, respectively. Then the data value of 0.249 is equal to (measurement of node 4) (measurement of node 6) + (measurement of node 11). 3.3. Encoding process The encoding process is divided into two stages: the merging stage to form the sparse random projections, and the forwarding stage to transmit those projections to a collector or a collecting zone. During the merging stage, the nodes start broadcasting their respective measurements according to their own schedule. The nodes that are awake receive packets broadcast from neighbouring nodes and merge them together. Two packets can be merged into a single packet, if they do not share any node ID in their header. Two packets are not mergeable, if after merging, the header exceeds the length. Figure 2 shows some examples of mergeable and non-mergeable packets. A saturated packet is a packet with no more free slots in the header and hence, not amenable to further aggregation. On the other hand, unsaturated packets have header space to accommodate further aggregation and hence, nodes will broadcast unsaturated packets, whereas saturated packets will be stored and simply forwarded.

with s as a parameter for sparseness of the projection, still yields good reconstruction. This significantly reduces the amount of communication among network nodes to form random projections as nodes require less data to be exchanged. This result also leads to a solution that addresses the header explosion problem. Instead of keeping track of coefficients of all the nodes in the header, we only reserve in the header l = ns slots for the non-zero coefficient values and the corresponding node IDs. 3.2. Packet Format The modification of Network Coding in the previous section is realized in the design of a packet format, as illustrated in Figure 1. The header field has two sections, the first one containing l 2-bit slots for the Bernoulli coefficient values (0,1 or -1), and the second section containing l 8-bit slots for the node IDs. Depending on the application specification, the data field can contain one or more 16-bit

Fig. 2. Examples of merging 2 packets: (A) Mergeable (B) Nonmergeable: share the same element node 4 (C) Non-mergeable: header overflows. During the forwarding stage, saturated packets are stored and ready for delivery. In some applications, like ocean exploration and forest monitoring, a mobile collector will visit boundary nodes to

gather data for processing. In that case, the NetCompress scheme offers the flexibility of collecting just enough saturated packets to meet the desired level of reconstruction. Algorithm 1 summarizes the implementation of the encoding process in a sensor node. Each node has two buffers, one for saturated packets and another for unsaturated packets. Packets also have a time-to-live (TTL) field, which acts as a count-down hop counter. When a packet is created, its TTL is set to a certain fixed value (for example, TTL = 20 in our experiment). The TTL is decremented at each hop and if the TTL reaches zero before delivery, then that packet is discarded.

n Compression gain gc = m : The ratio of the total number of measurements (which is also the number of nodes in the network) to the number of packets used for reconstruction. This is effectively the ratio of the length of the vector x to the length of the vector y in Equation (2). Reconstruction SNR: The Signal-to-Noise-Ratio of the original sensor network measurements and the reconstruction error. If x is the original measurement vector and x ˆ is the reconstructed vector then kxk SNR = 20 log . kˆ x − xk

Algorithm 1 : Encoding Algorithm

4.1. Simulation setup and results

1: Each node sleeps and wakes up periodically; 2: When a node is awake, it first spends a portion of its time in LISTEN mode and then switches to COMPRESS mode, before going back to sleep again; 3: if node i is awake and is in LISTEN mode then 4: if node i receives a packet p then 5: if receive buffer is full or TTL of p has expired then 6: Drop packet p; 7: else 8: if p is a full packet then 9: Add packet p to full-buffer; 10: else 11: Add packet p to compress-buffer; 12: end if 13: end if 14: end if 15: end if 16: if node i is awake and is in COMPRESS mode then 17: Remove the dupblicate packets in compress-buffer (packets with identical content, except TTL); 18: repeat 19: Merge packets in compress-buffer; 20: until no more packets to merge in compress-buffer 21: Move full packets from compress-buffer to full-buffer; 22: Remove duplicate packets in full-buffer; 23: Broadcast the not-full packets in compress-buffer; 24: end if 25: Return to sleep state

We use TOSSIM, a discrete event simulator for TinyOS sensor network [19], as a simulation platform. Sensor nodes are arranged in a 2D square grid and have a transmission range of one hop. A collector is placed near one edge to collect packets from at most three nearby nodes. We run two sets of simulation, each on different types of sensing data.

3.4. Decoding process At the collector side, the original measurements are reconstructed from the received packets using any standard `1 -minimization package, such as the `1magic package [18]. 4. SIMULATION AND EXPERIMENTAL RESULTS As the main goal of our work is to provide a practical scheme for data transmission and reconstruction in WSNs, we implemented and validated the NetCompress scheme using both simulation and a real testbed. We first define some system parameters that we use for performance evaluation. Duty cycle: The percentage of time that a sensor node is awake. In both simulations and experiments, we set a duty cycle of 30%, so that each node is awake for 3 seconds during every 10-second period. In each cycle, we randomize the starting time of the awake period to create a highly dynamic network. Aggregation limit l: The maximum number of packets that can be aggregated into a single packet. It is effectively the header size of a packet. It also determine the sparseness of the random projection s = nl . We use l = 8 for our implementation.

Fig. 3. Process of extracting ocean temperature from image. (a) Image of surface ocean temperature off of Florida, USA coast. (b) Selection of a region to extract data. (c) Sampling of the image with a 9-by-9 grid of sensor measurements. (d) Aggregation of all the sampled data into a single image. The first simulation is run on a 9-by-9 network with sensing data extracted from an image of surface ocean temperature (available from the Ocean Remote Sensing Group at John Hopkins University [20]). Figure 3 shows the process of extracting the temperature data from the image. First, we selected a region of the image to extract the data. We then sampled the region with a 9-by-9 grid. The grid is considered as the sensor network in which each pixel corresponds to a sensor measurement of the local ocean temperature. The 2D spectra of the ocean temperature map, as shown in Figure 4(B), has only three main spikes. Therefore, the data vector is compressible and NetCompress can be used to achieve some compression gain. Figure 4 shows the reconstruction of the temperature image using

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Fig. 5. Reconstruction of 8-by-8 light intensity image with 32 packets. (A) Original light intensity image. (B) Spectrum of the original image via Discrete Cosine Transform. (C) Reconstructed light intensity image. (D) Spectrum of the reconstructed image via Discrete Cosine Transform.

m = 45 packets. Note that the spectrum of both the original and reconstructed maps in (B) and (D) are almost the same, with identically placed three main spikes. Comparing the two images in spatial domain (A and C), we can see some distortions at some pixels but the overall trend is still preserved during reconstruction. In particular, the scheme achieves a compression gain of 1.8 at a reconstruction SNR of 26.72dB. The second simulation runs on an 8-by-8 network with real sensing data extracted from light measurements recorded by our sensor nodes. The measured light intensity is shown on Figure 5(A). Using Discrete Cosine Transform, we get the 2D spectrum of the light intensity with three major spikes as shown in Figure 5(B). Again, the light intensity data is compressible and NetCompress can be effective. Figure 5 shows the result of reconstruction with 32 packets. In this case, the scheme achieves a compression gain of 2.0 at a reconstruction SNR of 28.26 dB.

scheme. At the end of the process, the orginal light measurement stored in each node was extracted to compare with the reconstructed data from the collector. This experiment tested both the communication and compression aspects of the scheme. Figure 6 displays the results of the experiment. The spectrum of the original light intensity measurements in (B) indicates that the signal is compressible. (C) and (D) show the reconstructed measurements and the spectrum recovered from 8 received packets. The scheme achieves a compression gain of 2.5 at a reconstruction SNR of 30.2dB.

4.2. Experimental setup and results NetCompress was also fully deployed on a test-bed of 20 sensor nodes. The sensor nodes were arranged in a linear topology, with 15 centimeter spacing between each pair of nodes, to capture light intensity. The communication range was set at about 25 to 35 centimeters for all the nodes. However, this range occasionally varies either three times longer or even shorter. This introduced more randomness into the topology of the network. A collector was placed near Node 10 in the middle of the linear topology. Based on the communication range, the collector was expected to be able to collect packets from Node 9, 10 and 11. A light source was set up to shine the light from one end of the array (near Node 1). Initially, a control packet was transmitted to signal all the nodes to capture the light intensity and store in the memory. After that, the nodes started to communicate and exchange packets, following the NetCompress

4.3. Reconstruction quality In this part, we investigate how the quality of reconstruction, measured in terms of reconstruction SNR, varies with the compression gain. We re-run the simulation with the 8-by-8 network reported in Figure 5 with the light measurements, but vary the number of packets used for recovery. As can be seen in Figure 7, the SNR decreases as the compression gain increases. The SNR drops significantly when the compression gain passes the 2.1 point. If the gain stays below 2.1, we achieve a reasonably high SNR (≥ 28dB). Interestingly, when the compression gain is at around 1.2, the SNR stays flat indicating that the best reconstruction has been achieved. 5. CONCLUSIONS Communication in wireless sensor networks is mostly characterized by one or more sensor nodes forwarding the data they collect to a centralized collector. In most cases, the sensor measurements reported by neighboring nodes are correlated. The NetCompress scheme that we have presented combines the benefits of Compressed Sensing and Network Coding to achieve efficient data reconstruction and scalable communication in such networks characterized by uplink communication. While Compressed Sensing takes advantage of

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the data correlations to reconstruct data with a high probability using far fewer number of measurements than the number of nodes in the network, the network coding scheme in NetCompress leverages the broadcast nature of wireless transmissions and provides a way to efficiently aggregate and communicate that data by minimizing the communication overhead. The results we obtained from simulation and a real testbed implementation of NetCompress show that we are able to successfully reconstruct data with a reasonably high fidelity using only about half the number of measurements collected by the sensor nodes in a network. This demonstrates the scalability of the communication achieved by NetCompress, which is particularly useful in large sensor networks. 6. REFERENCES [1] T. He, S. Krishnamurthy, L. Luo, T. Yan, L. Gu, R. Stoleru, G. Zhou, Q. Cao, P. Vicaire, J.A. Stankovic, et al., “VigilNet: An integrated sensor network system for energy-efficient surveillance,” ACM Transactions on Sensor Networks (TOSN), vol. 2, no. 1, pp. 38, 2006.

[2] N. Xu, S. Rangwala, K.K. Chintalapudi, D. Ganesan, A. Broad, R. Govindan, and D. Estrin, “A wireless sensor network for structural monitoring,” in SenSys 04, pp. 13–24. [3] A. Mainwaring, D. Culler, J. Polastre, R. Szewczyk, and J. Anderson, “Wireless sensor networks for habitat monitoring,” in Proceedings of the 1st ACM International Workshop on Wireless Sensor Networks and Applications, 2002, pp. 88–97. [4] L. Selavo, A. Wood, Q. Cao, T. Sookoor, H. Liu, A. Srinivasan, Y. Wu, W. Kang, J. Stankovic, D. Young, et al., “Luster: wireless sensor network for environmental research,” in Proceedings of the 5th International Conference on Embedded Networked Sensor Systems, 2007, p. 116. [5] E.J. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Transactions on Information Theory, vol. 52, no. 2, pp. 489–509, 2006. [6] D.L. Donoho, “Compressed Sensing,” IEEE Transactions on Information Theory, vol. 52, no. 4, pp. 1289–1306, 2006. [7] M.F. Duarte, M.B. Wakin, D. Baron, and R.G. Baraniuk, “Universal distributed sensing via random projections,” IPSN 06, pp. 177–185, 2006. [8] S.S. Pradhan, J. Kusuma, and K. Ramchandran, “Distributed compression in a dense microsensor network,” Signal Processing Magazine, IEEE, vol. 19, no. 2, pp. 51–60, 2002. [9] M. Rabbat, J. Haupt, A. Singh, and R. Nowak, “Decentralized compression and predistribution via randomized gossiping,” IPSN 06, pp. 51–59, 2006. [10] W. Wang, M. Garofalakis, and K. Ramchandran, “Distributed sparse random projections for refinable approximation,” IPSN 07, pp. 331–339, 2007. [11] R. Ahlswede, N. Cai, S.Y.R. Li, and R.W. Yeung, “Network information flow,” IEEE Transactions on Information Theory, vol. 46, no. 4, pp. 1204–1216, 2000. [12] S.Y.R. Li and R.W.N. Cai, “Linear network coding,” IEEE Transactions on Information Theory, vol. 49, no. 2, pp. 371– 381, 2003. [13] R. Koetter and M. Medard, “An algebraic approach to network coding,” IEEE/ACM Transactions on Networking, vol. 11, no. 5, pp. 782–795, 2003. [14] T. Ho, R. Koetter, M. Medard, D.R. Karger, and M. Effros, “The benefits of coding over routing in a randomized setting,” ISIT 03, 2003. [15] T. Ho, M. Medard, R. Koetter, D.R. Karger, M. Effros, J. Shi, and B. Leong, “A random linear network coding approach to multicast,” IEEE Transactions on Information Theory, vol. 52, no. 10, pp. 4413–4430, 2006. [16] P.A. Chou, Y. Wu, and K. Jain, “Practical network coding,” Allerton Conference on Communication, Control, and Computing, 2003. [17] S. Katti, S. Shintre, S. Jaggi, and M. Medard, “Real Network Codes,” Allerton Conference on Communication, Control, and Computing, 2007. [18] “http://www.acm.caltech.edu/l1magic/,” . [19] P. Levis and N. Lee, “TOSSIM: A Simulator for TinyOS Networks,” Computer Science Division, University of California Berkeley, California, vol. 17, 2003. [20] “http://fermi.jhuapl.edu/avhrr/gallery/index.html,” .

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leads to a better data recovery, or equivalently, that the proposed ..... xj be estimations of xi and xj with an estimation noise ni and nj, respectively, i.e., xi = xi + ni.

Network Coding for Wireless Applications: A Brief Tutorial
Laboratory for Information and Decision Systems, Massachusetts Institute of ... Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of ...

On Delay Performance Gains From Network Coding
Massachusetts Institute of Technology. Cambridge, MA, 02139 ... use of network coding in wireless communication systems, gains in delay performance ...

Distributed Utility Maximization for Network Coding Based Multicasting ...
include for example prior works on Internet flow control [9] and cross-layer ...... wireless network using network coding have been formulated in [20], [21] ..... [3] T. Ho, R. Koetter, M. Médard, D. R. Karger, and M. Effros, “The benefits of codi

Opportunistic Noisy Network Coding for Fading Relay ... - IEEE Xplore
Nov 9, 2015 - Abstract—The parallel relay network is studied, in which a single source node sends a message to a single destination node with the help of N ...

On Achieving Optimal Throughput with Network Coding
problem of achieving optimal throughput in data networks, with single or multiple ...... degree already, which also has a low capacity, since the link bandwidth is ...

Adaptive Distributed Network-Channel Coding For ...
cooperative wireless communications system with multiple users transmitting independent ...... Cambridge: Cambridge University Press, 2005. [13] SAGE, “Open ...

Spatial-Modulated Physical-Layer Network Coding in ... - IEEE Xplore
Email: [email protected]. Abstract—We consider a spatial modulation (SM)-based physical-layer network coding (PNC) technique with convolu- tional codes ...

Network-Adaptive Video Coding and Transmission - (AMP) Lab ...
1. INTRODUCTION. The technology for delivering ubiquitous high bandwidth multimedia services, such as voice with video, will soon become a reality.

Multirate Media Streaming Using Network Coding
missions using layered source coding are generally used to deliver data streams to heterogeneous receivers. Network .... Illustration of network coding. that the ...

On Network Coding Based Multirate Video Streaming in ...
Department of Computer Science & Technology, University of Science & Technology of China ... Network Coding Scheme (LSNC) for layered video streaming. ...... Conference on Distributed Computing System (ICDCS) 2003, pp126-135.

Performance Modeling of Network Coding in Epidemic ...
or mobile opportunistic networks composed of moving vehi- .... coefficient matrix of such linear system. .... Torrent like P2P file sharing systems such as in [7].

Network Coding for Secret Key Agreement
and ei being an edge with sender selected as ui and receiver selected as ui+1. An outbranching from ...... key agreement,” June 2010. http://web.mit.edu/chungc/.