Fundamentals of Large Sensor Networks: Connectivity, Capacity, Clocks and Computation

Sensor networks potentially feature large numbers of nodes that can sense their environment over time, communicate with each other over a wireless network, and process information. They differ from data networks in that the network as a whole may be designed for a specific application. We study the theoretical foundations of such large scale sensor networks, addressing four fundamental issues- connectivity, capacity, clocks and function computation. To begin with, a sensor network must be connected so that information can indeed be exchanged between nodes. The connectivity graph of an ad-hoc network is modeled as a random graph and the critical range for asymptotic connectivity is determined, as well as the critical number of neighbors that a node needs to connect to. Next, given connectivity, we address the issue of how much data can be transported over the sensor network. We present fundamental bounds on capacity under several models, as well as architectural implications for how wireless communication should be organized. Temporal information is important both for the applications of sensor networks as well as their operation.We present fundamental bounds on the synchronizability of clocks in networks, and also present and analyze algorithms for clock synchronization. Finally we turn to the issue of gathering relevant information, that sensor networks are designed to do. One needs to study optimal strategies for in-network aggregation of data, in order to reliably compute a composite function of sensor measurements, as well as the complexity of doing so. We address the issue of how such computation can be performed efficiently in a sensor network and the algorithms for doing so, for some classes of functions.Comment: 10 pages, 3 figures, Submitted to the Proceedings of the IEE

Cooperative Compute-and-Forward

We examine the benefits of user cooperation under compute-and-forward. Much like in network coding, receivers in a compute-and-forward network recover finite-field linear combinations of transmitters' messages. Recovery is enabled by linear codes: transmitters map messages to a linear codebook, and receivers attempt to decode the incoming superposition of signals to an integer combination of codewords. However, the achievable computation rates are low if channel gains do not correspond to a suitable linear combination. In response to this challenge, we propose a cooperative approach to compute-and-forward. We devise a lattice-coding approach to block Markov encoding with which we construct a decode-and-forward style computation strategy. Transmitters broadcast lattice codewords, decode each other's messages, and then cooperatively transmit resolution information to aid receivers in decoding the integer combinations. Using our strategy, we show that cooperation offers a significant improvement both in the achievable computation rate and in the diversity-multiplexing tradeoff.Comment: submitted to IEEE Transactions on Information Theor

Reliable Physical Layer Network Coding

When two or more users in a wireless network transmit simultaneously, their electromagnetic signals are linearly superimposed on the channel. As a result, a receiver that is interested in one of these signals sees the others as unwanted interference. This property of the wireless medium is typically viewed as a hindrance to reliable communication over a network. However, using a recently developed coding strategy, interference can in fact be harnessed for network coding. In a wired network, (linear) network coding refers to each intermediate node taking its received packets, computing a linear combination over a finite field, and forwarding the outcome towards the destinations. Then, given an appropriate set of linear combinations, a destination can solve for its desired packets. For certain topologies, this strategy can attain significantly higher throughputs over routing-based strategies. Reliable physical layer network coding takes this idea one step further: using judiciously chosen linear error-correcting codes, intermediate nodes in a wireless network can directly recover linear combinations of the packets from the observed noisy superpositions of transmitted signals. Starting with some simple examples, this survey explores the core ideas behind this new technique and the possibilities it offers for communication over interference-limited wireless networks.Comment: 19 pages, 14 figures, survey paper to appear in Proceedings of the IEE

Principles of Physical Layer Security in Multiuser Wireless Networks: A Survey

This paper provides a comprehensive review of the domain of physical layer security in multiuser wireless networks. The essential premise of physical-layer security is to enable the exchange of confidential messages over a wireless medium in the presence of unauthorized eavesdroppers without relying on higher-layer encryption. This can be achieved primarily in two ways: without the need for a secret key by intelligently designing transmit coding strategies, or by exploiting the wireless communication medium to develop secret keys over public channels. The survey begins with an overview of the foundations dating back to the pioneering work of Shannon and Wyner on information-theoretic security. We then describe the evolution of secure transmission strategies from point-to-point channels to multiple-antenna systems, followed by generalizations to multiuser broadcast, multiple-access, interference, and relay networks. Secret-key generation and establishment protocols based on physical layer mechanisms are subsequently covered. Approaches for secrecy based on channel coding design are then examined, along with a description of inter-disciplinary approaches based on game theory and stochastic geometry. The associated problem of physical-layer message authentication is also introduced briefly. The survey concludes with observations on potential research directions in this area.Comment: 23 pages, 10 figures, 303 refs. arXiv admin note: text overlap with arXiv:1303.1609 by other authors. IEEE Communications Surveys and Tutorials, 201