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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
