In communications, the multiuser Gaussian channel model is commonly used to capture fundamental features of a wireless channel. Over the past couple of decades, study of multiuser Gaussian networks has been an active area of research for many scientists. However, due to the complexity of the Gaussian model, except for the simplest networks such as the one-to-many Gaussian broadcast channel and the many-to-one Gaussian multiple access channel, the capacity region of most Gaussian networks is still unknown. For example, even the capacity of a three node Gaussian relay network, in which a point to point communication is assisted by one helper (relay), has been open for more than 30 years.To make further progress, we present a linear finite-field deterministic channel model which is analytically simpler than the Gaussian model but still captures two key wireless channels: broadcast and superposition. The noiseless nature of this model allows us to focus on the interaction between signals transmitted from different nodes of the network rather than background noise of the links.Then, we consider a model for a wireless relay network with nodes connected by such 1 deterministic channels, and present an exact characterization of the end-to-end capacity when there is a single source and a single destination and an arbitrary number of relay nodes. This result is a natural generalization of the celebrated max-flow min-cut theorem for wireline networks. We also characterize the multicast capacity of linear finite-field deterministic relay networks when one source is multicasting the same information to multiple destinations, with the help of arbitrary number of relays.Next, we use the insights obtained from the analysis of the deterministic model and present an achievable rate for general Gaussian relay networks. We show that the achievable rate is within a constant number of bits from the information-theoretic cut-set upper bound on the capacity of these networks. This constant depends on the number of nodes in the network, but not the values of the channel gains. Therefore, we uniformly characterize the capacity of Gaussian relay networks within a constant number of bits, for all channel parameters. For example, we approximate the unknown capacity of the three node Gaussian relay channel within one bit/sec/Hz.Finally, we illustrate that the proposed deterministic approach is a general tool and can be applied to other problems in wireless network information theory. In particular we demonstrate its application to make progress in two other problems: two-way relay channel and relaying with side information.

The vast majority of today's critical infrastructure is supported by numerous feedback control loops and an attack on these control loops can have disastrous consequences. This is a major concern since modern control systems are becoming large and decentralized and thus more vulnerable to attacks. This paper is concerned with the estimation and control of linear systems when some of the sensors or actuators are corrupted by an attacker.In the first part we look at the estimation problem where we characterize the resilience of a system to attacks and study the possibility of increasing its resilience by a change of parameters. We then propose an efficient algorithm to estimate the state despite the attacks and we characterize its performance. Our approach is inspired from the areas of error-correction over the reals and compressed sensing.In the second part we consider the problem of designing output-feedback controllers that stabilize the system despite attacks. We show that a principle of separation between estimation and control holds and that the design of resilient output feedback controllers can be reduced to the design of resilient state estimators.for example the sensors communicate their measurements to the controllers, the controllers use 2 this information to compute the control input, and the control input is then sent to the actuators so that it can be physically implemented. In order for this communication to take place, a communication network is usually deployed across the plant to be controlled. Although wired networks have been traditionally used for this purpose, an increasing number of control systems now use wireless networks since they are easier to deploy and to maintain. In addition, these networks are sometimes connected to the corporate intranet, and in some cases even to the Internet. Consequently, modern control systems are becoming more open to the cyber-world, and as such, are more vulnerable to attacks that can cause faults and failures in the physical process even though launched in the cyber-domain. This realization led to the emergence of new security challenges that are distinct from traditional cyber security as highlighted in [1], [2]. Real-world attacks on control systems have in fact occurred in the past decade and have in some cases caused significant damage to the targeted physical processes. Perhaps one of the most popular examples is the attack on Maroochy Shire Council's sewage control system in Queensland, Australia that happened in January 2000 [3], [4]. In this incident, an attacker managed to hack into some controllers that activate and deactivate valves and, by doing so, caused flooding of the grounds of a hotel, a park, and a river with a million liters of sewage [3]. Another well publicized example of an attack launched on physical systems is the very recent StuxNet virus that targeted Siemens' supervisory control and data acquisition systems which are used in many industrial processes [5]. Other cases of attacks have been reported in the past years, and we refer ...

Caching of popular content during off-peak hours is a strategy to reduce network loads during peak hours. Recent work has shown significant benefits of designing such caching strategies not only to deliver part of the content locally, but also to provide coded multicasting opportunities even among users with different demands. Exploiting both of these gains was shown to be approximately optimal for caching systems with a single layer of caches.Motivated by practical scenarios, we consider in this work a hierarchical content delivery network with two layers of caches. We propose a new caching scheme that combines two basic approaches. The first approach provides coded multicasting opportunities within each layer; the second approach provides coded multicasting opportunities across multiple layers. By striking the right balance between these two approaches, we show that the proposed scheme achieves the optimal communication rates to within a constant multiplicative and additive gap. We further show that there is no tension between the rates in each of the two layers up to the aforementioned gap. Thus, both layers can simultaneously operate at approximately the minimum rate. I. INTRODUCTIONThe demand for high-definition video streaming services such as YouTube and Netflix is driving the rapid growth of Internet traffic. In order to mitigate the effect of this increased load on the underlying communication infrastructure, content delivery networks deploy storage memories or caches throughout the network. These caches can be populated with some of the content during off-peak traffic hours. This cached content can then be used to reduce the network load during peak traffic hours when users make the most requests.Content caching has a rich history, see for example [1] and references therein. More recently, it has been studied in the context of video-on-demand systems for which efficient content placement schemes have been proposed in [2], [3] among others. The impact of different content popularities on the performance of caching schemes has been investigated for example in [4]- [6]. A common feature among the caching schemes studied in the literature is that those parts of a requested file that are available at nearby caches are served locally, whereas the remaining files parts are served via orthogonal transmissions from an origin server hosting all the files.Recently, [7], [8] proposed a new caching approach, called coded caching, that exploits cache memories not only to deliver part of the content locally, but also to create coded multicasting opportunities among users with different demands. It is shown there that the reduction in rate due to these coded multicasting opportunities is significant and can be on the order of the number of users in the network. The setting considered in [7], [8] consists of a single layer of caches between the origin server and the end users. The server communicates directly with all the caches via a shared link, and the objective is to minimize the required transmission rate ...

The maximum entropy noise under a lag autocorrelation constraint is known by Burg's theorem to be the th order Gauss-Markov process satisfying these constraints. The question is, what is the worst additive noise for a communication channel given these constraints? Is it the maximum entropy noise? The problem becomes one of extremizing the mutual information over all noise processes with covariances satisfying the correlation constraints. For high signal powers, the worst additive noise is Gauss-Markov of order as expected. But for low powers, the worst additive noise is Gaussian with a covariance matrix in a convex set which depends on the signal power.

In this paper, we examine multicarrier transmission over time-varying channels. We first develop a model for such a transmission scheme and focus particularly on multiple-input multiple output (MIMO) orthogonal frequency division multiplexing (OFDM). Using this method, we analyze the impact of time variation within a transmission block (time variation could arise both from Doppler spread of the channel and from synchronization errors). To mitigate the effects of such time variations, we propose a time-domain approach. We design ICI-mitigating block linear filters, and we examine how they are modified in the context of space-time block-coded transmissions. Our approach reduces to the familiar single-tap frequency-domain equalizer when the channel is block time invariant. Channel estimation in rapidly time-varying scenarios becomes critical, and we propose a scheme for estimating channel parameters varying within a transmission block. Along with the channel estimation scheme, we also examine the issue of pilot tone placement and show that in time-varying channels, it may be better to group pilot tones together into clumps that are equispaced onto the FFT grid; this placement technique is in contrast to the common wisdom for time-invariant channels. Finally, we provide numerical results illustrating the performance of these schemes, both for uncoded and space-time block-coded systems.