Wireless networks are fundamentally limited by the intensity of the received signals and by their interference. Since both of these quantities depend on the spatial location of the nodes, ...mathematical techniques have been developed in the last decade to provide communication-theoretic results accounting for the networks geometrical configuration. Often, the location of the nodes in the network can be modeled as random, following for example a Poisson point process. In this case, different techniques based on stochastic geometry and the theory of random geometric graphs -including point process theory, percolation theory, and probabilistic combinatorics-have led to results on the connectivity, the capacity, the outage probability, and other fundamental limits of wireless networks. This tutorial article surveys some of these techniques, discusses their application to model wireless networks, and presents some of the main results that have appeared in the literature. It also serves as an introduction to the field for the other papers in this special issue.
Plants have evolved intracellular immune receptors to detect pathogen proteins known as effectors. How these immune receptors detect effectors remains poorly understood. Here we describe the ...structural basis for direct recognition of AVR-Pik, an effector from the rice blast pathogen, by the rice intracellular NLR immune receptor Pik. AVR-PikD binds a dimer of the Pikp-1 HMA integrated domain with nanomolar affinity. The crystal structure of the Pikp-HMA/AVR-PikD complex enabled design of mutations to alter protein interaction in yeast and in vitro, and perturb effector-mediated response both in a rice cultivar containing Pikp and upon expression of AVR-PikD and Pikp in the model plant Nicotiana benthamiana. These data reveal the molecular details of a recognition event, mediated by a novel integrated domain in an NLR, which initiates a plant immune response and resistance to rice blast disease. Such studies underpin novel opportunities for engineering disease resistance to plant pathogens in staple food crops.
An achievable bit rate per source-destination pair in a wireless network of n randomly located nodes is determined adopting the scaling limit approach of statistical physics. It is shown that ...randomly scattered nodes can achieve, with high probability, the same 1/radicn transmission rate of arbitrarily located nodes. This contrasts with previous results suggesting that a 1/radicnlogn reduced rate is the price to pay for the randomness due to the location of the nodes. The network operation strategy to achieve the result corresponds to the transition region between order and disorder of an underlying percolation model. If nodes are allowed to transmit over large distances, then paths of connected nodes that cross the entire network area can be easily found, but these generate excessive interference. If nodes transmit over short distances, then such crossing paths do not exist. Percolation theory ensures that crossing paths form in the transition region between these two extreme scenarios. Nodes along these paths are used as a backbone, relaying data for other nodes, and can transport the total amount of information generated by all the sources. A lower bound on the achievable bit rate is then obtained by performing pairwise coding and decoding at each hop along the paths, and using a time division multiple access scheme
It is shown that the capacity scaling of wireless networks is subject to a fundamental limitation which is independent of power attenuation and fading models. It is a degrees of freedom limitation ...which is due to the laws of physics. By distributing uniformly an order of n users wishing to establish pairwise independent communications at fixed wavelength inside a two-dimensional domain of size of the order of n , there are an order of n communication requests originating from the central half of the domain to its outer half. Physics dictates that the number of independent information channels across these two regions is only of the order of radicn , so the per-user information capacity must follow an inverse square-root of n law. This result shows that information-theoretic limits of wireless communication problems can be rigorously obtained without relying on stochastic fading channel models, but studying their physical geometric structure.
Motivated by navigation and tracking applications within sensor networks, we consider the problem of performing Kalman filtering with intermittent observations. When data travel along unreliable ...communication channels in a large, wireless, multihop sensor network, the effect of communication delays and loss of information in the control loop cannot be neglected. We address this problem starting from the discrete Kalman filtering formulation, and modeling the arrival of the observation as a random process. We study the statistical convergence properties of the estimation error covariance, showing the existence of a critical value for the arrival rate of the observations, beyond which a transition to an unbounded state error covariance occurs. We also give upper and lower bounds on this expected state error covariance.
A data rate theorem for stabilization of a linear, discrete-time, dynamical system with arbitrarily large disturbances, over a rate-limited, time-varying communication channel is presented. Necessary ...and sufficient conditions for stabilization are derived, their implications and relationships with related results in the literature are discussed. The proof techniques rely on both information-theoretic and control-theoretic tools.
This paper studies the problem of secure communication over a wiretap channel p(y,z|x) with a secure feedback link of rate R f , where X is the channel input, and Y and Z are channel outputs observed ...by the legitimate receiver and the eavesdropper, respectively. It is shown that the secrecy capacity, the maximum data rate of reliable communication while the intended message is not revealed to the eavesdropper, is upper bounded as C s (R f ) les maxmin/p(x) {I(X;Y), I(X;Y |Z) + R f }. The proof of the bound crucially depends on a recursive argument which is used to obtain the single-letter characterization. This upper bound is shown to be tight for the class of physically degraded wiretap channels. A capacity-achieving coding scheme is presented for this case, in which the receiver securely feeds back fresh randomness with rate R f , generated independent of the received channel output symbols. The transmitter then uses this shared randomness as a secret key on top of Wyner's coding scheme for wiretap channels without feedback. Hence, when a feedback link is available, the receiver should allocate all resources to convey a new key rather than sending back the channel output.
This paper considers a random access system where each sender is in one of two possible states, active or not active, and the states are only known to the common receiver. Active senders encode data ...into independent information streams, a subset of which is decoded depending on the collective interference. An information-theoretic formulation of the problem is presented and the set of achievable rates is characterized with a guaranteed gap to optimality. Inner and outer bounds on the capacity region of a two-sender system are tight in the case of a binary-expansion deterministic channel and differ by less than one bit in the case of a Gaussian channel. In systems with an arbitrary number of senders, the symmetric scenario of equal access probabilities and received power constraints is studied and the system throughput, i.e., the maximum achievable expected sum rate, is characterized. It is shown that a simple coding scheme where active senders transmit a single message is optimum for a binary-expansion deterministic channel and achieves within one bit of the optimum in the case of a Gaussian channel. Finally, a comparison with the slotted ALOHA protocol is provided, showing that encoding rate adaptation at the transmitters achieves constant (rather than zero) throughput as the number of users tends to infinity.
A variation of Landau's eigenvalue theorem describing the phase transition of the eigenvalues of a time-frequency limiting, self adjoint operator is presented. The total number of degrees of freedom ...of square-integrable, multidimensional, bandlimited functions is defined in terms of Kolmogorov's n -width and computed in some limiting regimes, where the original theorem cannot be directly applied. Results are used to characterize up to order the total amount of information that can be transported in time and space by multiple-scattered electromagnetic waves, rigorously addressing a question originally posed in the early works of Toraldo di Francia and Gabor. Applications in the context of wireless communication and electromagnetic sensing are discussed.
The throughput of wireless networks is known to scale poorly when the number of users grows. The rate at which an arbitrary pair of nodes can communicate must decrease to zero as the number of users ...tends to infinity, under various assumptions. One of them is the requirement that the network is fully connected: the computed rate must hold for any pair of nodes of the network. We show that this requirement can be responsible for the lack of throughput scalability. We consider a two-dimensional (2-D) network of extending area with only one active source-destination pair at any given time, and all remaining nodes acting only as possible relays. Allowing an arbitrary small fraction of the nodes to be disconnected, we show that the per-node throughput remains constant as the network size increases. As a converse bound, we show that communications occurring at a fixed nonzero rate imply a fraction of the nodes to be disconnected. Our results are of information theoretic flavor, as they hold without assumptions on the communication strategies employed by the network nodes.
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