The broadcasting attribute of the wireless communication channel poses severe security vulnerabilities since any adversary node in the range of reception is able to listen as well as to disrupt the ongoing communication. This dissertation considers the problem of security from two different perspectives: The information-theoretic approach at the physical-layer to avert eavesdropping and centralized and decentralized detection algorithms to detect the presence of a jammer. In the first part, we apply the available tools in information-theoretic security to study the achievable secrecy rate region of the following channel models: the discrete memoryless broadcast channel with two confidential messages for each of the two users, the discrete memoryless interference channel with two confidential messages, and the discrete memoryless untrusted relay channel with decode-and-forward (DF) relays (DMURC). For the first two scenarios, we extend the existing results on the weak secrecy to the strong secrecy criterion. Owing to its definition, the strong secrecy has a practical interpretation, whereas weak secrecy provides asymptotic results. In the third scenario, we apply a precoder and a post-decoder in addition to the common channel coding required to provide secrecy, to deal with the dishonest nature of the relays. An achievable secrecy rate region for DMURC is established. We revisit the untrusted relay scenario with some different assumptions: with Gaussian channel and both DF and amplify-and-forward (AF) relaying. The objective, however, is to develop a secure scheme that allows for weaker secrecy than Shannon’s perfect secrecy but with a higher transmission rate. We propose a new measure for secrecy, referred to as a-secrecy (0 = a = 1), where a = 1 represents the perfect secrecy, whereas a = 0 denotes no secrecy at all. We suggest using a cross-layer design where at the physical layer the information-theoretic security is applied and some higher layer scheme, e.g. secure network coding, allows to obtain any point in the transmission rate and a-secrecy trade-off. The analysis of performance achievable by the scheme leads to a mixed-integer optimization problem. Moreover, we study the problem asymptotically to gain some insights. Active security attacks are the main focus of the second part of this thesis. We study the problem of joint jamming detection and spectrum sensing. The problem arises in the cognitive radio scenario, where the secondary users (SU)s sensing the channel to detect the primary users (PU)s. We model the problem as a multiple-hypothesis testing problem where the observations from the SUs experience spatial channel correlation. The optimal test statistic is derived according to Neyman-Pearson lemma. We derive the exact probability distribution of the test statistic in terms of Meijer’s G-functions. We consider a practical application where the SUs’ power efficiency is analyzed. This leads to a non-convex optimization problem that addresses the power efficiency and detection performance trade-off. The detection performance in the exact form is too complex to be handled analytically, therefore, we consider the asymptotic regime. Two heuristics are proposed to tackle the optimization problem; one based on the projected gradient method and the other one is motivated by the KKT conditions. All of the algorithms mentioned above are designed for a centralized system. Taking into account the susceptibility of centralized systems to the Byzantine attacks, we study the decentralization of eigenvalue-based detection algorithms in the last chapter of this thesis. We use generic consensus algorithm as a building block in decentralizing an eigenvalue estimator algorithm. The algorithm estimates all eigenvalues of a covariance matrix, which is available only partly to each node. We further modify the algorithm for two special practical scenarios, including the channel probing for admission control problem.
The broadcasting attribute of the wireless communication channel poses severe security vulnerabilities since any adversary node in the range of reception is able to listen as well as to disrupt the ongoing communication. This dissertation considers the problem of security from two different perspectives: The information-theoretic approach at the physical-layer to avert eavesdropping and centralized and decentralized detection algorithms to detect the presence of a jammer. In the first part, we apply the available tools in information-theoretic security to study the achievable secrecy rate region of the following channel models: the discrete memoryless broadcast channel with two confidential messages for each of the two users, the discrete memoryless interference channel with two confidential messages, and the discrete memoryless untrusted relay channel with decode-and-forward (DF) relays (DMURC). For the first two scenarios, we extend the existing results on the weak secrecy to the strong secrecy criterion. Owing to its definition, the strong secrecy has a practical interpretation, whereas weak secrecy provides asymptotic results. In the third scenario, we apply a precoder and a post-decoder in addition to the common channel coding required to provide secrecy, to deal with the dishonest nature of the relays. An achievable secrecy rate region for DMURC is established. We revisit the untrusted relay scenario with some different assumptions: with Gaussian channel and both DF and amplify-and-forward (AF) relaying. The objective, however, is to develop a secure scheme that allows for weaker secrecy than Shannon’s perfect secrecy but with a higher transmission rate. We propose a new measure for secrecy, referred to as a-secrecy (0 = a = 1), where a = 1 represents the perfect secrecy, whereas a = 0 denotes no secrecy at all. We suggest using a cross-layer design where at the physical layer the information-theoretic security is applied and some higher layer scheme, e.g. secure network coding, allows to obtain any point in the transmission rate and a-secrecy trade-off. The analysis of performance achievable by the scheme leads to a mixed-integer optimization problem. Moreover, we study the problem asymptotically to gain some insights. Active security attacks are the main focus of the second part of this thesis. We study the problem of joint jamming detection and spectrum sensing. The problem arises in the cognitive radio scenario, where the secondary users (SU)s sensing the channel to detect the primary users (PU)s. We model the problem as a multiple-hypothesis testing problem where the observations from the SUs experience spatial channel correlation. The optimal test statistic is derived according to Neyman-Pearson lemma. We derive the exact probability distribution of the test statistic in terms of Meijer’s G-functions. We consider a practical application where the SUs’ power efficiency is analyzed. This leads to a non-convex optimization problem that addresses the power efficiency and detection performance trade-off. The detection performance in the exact form is too complex to be handled analytically, therefore, we consider the asymptotic regime. Two heuristics are proposed to tackle the optimization problem; one based on the projected gradient method and the other one is motivated by the KKT conditions. All of the algorithms mentioned above are designed for a centralized system. Taking into account the susceptibility of centralized systems to the Byzantine attacks, we study the decentralization of eigenvalue-based detection algorithms in the last chapter of this thesis. We use generic consensus algorithm as a building block in decentralizing an eigenvalue estimator algorithm. The algorithm estimates all eigenvalues of a covariance matrix, which is available only partly to each node. We further modify the algorithm for two special practical scenarios, including the channel probing for admission control problem.
This dissertation studies the fundamental rate limits of wireless communication systems through which confidential messages can be transmitted without being intercepted by an adversary. It is assumed that the adversary is subject to noise and interference, as are the legitimate nodes in the system. The security guarantees offered are irrespective of the computational power of the adversary.
Three themes are developed in parallel throughout the dissertation. The first theme explores the relationship between cooperation and secrecy. In wireless networks, cooperation from intermediate relay nodes are essential for facilitating long range communications. This dissertation considers a series of network models where the information from a source to a destination needs to be kept confidential from intermediate relays. Four different network models with untrusted relay nodes are considered: the three-node relay channel, the two-hop link, the two-way relay channel and the multi-hop line network. These models are studied for relays that are honest but curious. That is, the relay nodes are legitimate nodes with lower security clearance, that willingly carry out the designated relay schemes. Secrecy capacity lower and upper bounds for each channel model are found and cases where secrecy capacity can be found are identified. Next the two-hop link is studied where the relay turns malicious in that it can manipulate the signals being relayed and carry out a Byzantine attack. In this case, two requirements must be satisfied simultaneously: The message must be kept confidential from the relay node, and, any modification carried out by the relay node must be detected reliably by the legitimate parties. The dissertation shows that both requirements can be fulfilled for this model with arbitrarily small overhead.
The next two themes developed in this dissertation serve as the technical foundation for the first theme. One establishes the foundation for providing secrecy using structured codes. Traditionally, the achievability proofs for information theoretic secrecy rely on Shannon’s random codebook generation argument in which the codebook does not exhibit structure. In this dissertation, it is shown that by imposing structure requirements in random codebook generation, higher rates for secure communication can be achieved than known results obtained using the conventional approach. This dissertation develops the necessary tool and general methodology for computing the secrecy rate when a nested lattice structure is used in codebook generation. Two results are presented that rely on this foundation. First, it is proved that, for a class of Gaussian channel models with interference and secrecy constraints, structured codes outperform Gaussian signaling at medium to high SNR. Second, this tool is used to develop a strong secrecy scheme for the two-hop link with an untrusted relay, which in turn is the centerpiece of the Byzantine detection scheme developed in this dissertation.
The third theme is methods of proving strong secrecy. Information theoretic secrecy results often rely on the weak secrecy constraint which provides only asymptotic guarantees with respect to the information rate leaked to the adversary. As this would likely be insufficient in a practical system, a non-asymptotic, strong secrecy guarantee must be sought. More often than not, weak secrecy rates can be strengthened to strong secrecy rates in a straightforward manner, leading back to the justification of proving weak secrecy only. This dissertation challenges this conventional wisdom and identifies two cases where this approach does not follow. In both cases, direct strong secrecy proofs are established. These are: the two-hop link with a Byzantine relay, and models with arbitrarily varying eavesdropper channel considered in the last chapter of this dissertation.
The latter model is motivated by the need to bring the theory of providing unconditional secrecy guarantees closer to practice. In particular, the dissertation addresses the case where the channel that the adversary (eavesdropper) experiences is completely unknown to the legitimate parties. To do so, a multiple input-multiple output (MIMO) wiretap channel is considered where the eavesdropper’s channel is arbitrarily varying. A coding theorem is derived for with this setting. The secrecy rate obtained from this coding theorem is tight in terms of secure degree of freedom, which is a high SNR characterization of the secrecy capacity. In addition, the secure degree of freedom regions for the MIMO multiple access (MAC) wiretap channel and the MIMO broadcast wiretap channel are derived when the legitimate nodes have the same number of antennas, identifying the high SNR characterization of the fundamental transmission limits for these models.
Inherent openness of the wireless medium imposes stronger challenges on the security of wireless communications. Information-theoretic security addresses these challenges at the physical layer by using tools from wireless communication theory, signal processing and information theory. In information-theoretic security, physical layer communication is intelligently designed to exploit the characteristics of the wireless medium, such as fading, interference, cooperation, and multi-dimensional signaling, in order to provide or improve security. In this dissertation, we study the security of several fundamental wireless network configurations from an information-theoretic perspective. First, we study the Gaussian multiple-input multiple-output (MIMO) wiretap channel. In this channel, the transmitter sends a common message to both the legitimate user and the eavesdropper. In addition to the common message, a private message is sent only to the legitimate user, which needs to be kept hidden as much as possible from the eavesdropper. We obtain the entire capacity-equivocation region for this channel model. In particular, we show the sufficiency of jointly Gaussian auxiliary random variables and channel input to evaluate the existing single-letter description of the capacity-equivocation region due to Csiszar-Korner. Next, we study the secure broadcasting problem, where a transmitter wants to have secure communication with multiple legitimate users in the presence of an external eavesdropper. We study several special cases of the secure broadcasting problem. First, we consider the degraded multi-receiver wiretap channel, and establish its secrecy capacity region. Second, we consider the parallel less noisy multi-receiver wiretap channel, and obtain its common message secrecy capacity and sum secrecy capacity. Third, we consider the parallel degraded multi-receiver wiretap channel for the two-user and two-sub-channel case, and obtain its entire secrecy capacity region. Finally, we consider a parallel channel model with two sub-channels, where the transmitter can use only one of the subchannels at any time, and characterize its secrecy capacity region. Then, we study the two-user Gaussian MIMO broadcast channel with common and confidential messages. In this channel model, the transmitter sends a common message to both users, and a confidential message to each user which needs to be kept perfectly secret from the other user. We obtain the entire capacity region of this channel. We also explore the connections between this channel model and its non-confidential counterpart, i.e., the Gaussian MIMO broadcast channel with common and private message. Next, we consider the Gaussian MIMO multi-receiver wiretap channel and obtain its secrecy capacity region for the most general case. We first show that even for the single-input single-output (SISO) case, existing converse techniques fall short of proving the secrecy capacity region, to emphasize the need for a new proof technique, which we develop by using the relationships between the Fisher information and the differential entropy. Using this new proof technique, we obtain the secrecy capacity region of the degraded MIMO channel. We then establish the secrecy capacity region of the general MIMO channel by using the channel enhancement technique in conjunction with the capacity result we obtained for the degraded MIMO channel. For the general MIMO channel, we show that dirty-paper coding (DPC) combined with stochastic encoding attains the entire secrecy capacity region. Then, we study the multi-receiver wiretap channel for a more general scenario, where, in addition to confidential messages, the transmitter sends public messages to the legitimate users, on which there are no secrecy constraints. First, we consider the degraded discrete memoryless channel, and obtain inner and outer bounds for the capacity region. These inner and outer bounds match for certain cases, providing the capacity region. Second, we obtain an inner bound for the general discrete memoryless channel by using Marton's inner bound. Third, we consider the degraded Gaussian MIMO channel, and show that jointly Gaussian auxiliary random variables and channel input are sufficient to exhaust the inner and outer bounds. Finally, we provide an inner bound for the capacity region of the general Gaussian MIMO channel. Next, we focus on the multiple access wiretap (MAC-WT) channel whose capacity region is unknown. We consider a special class of MAC-WT channels which we call the weak eavesdropper class, where each user's link to the legitimate receiver is stronger than its link to the eavesdropper. For this class of channels, we develop an outer bound for the secrecy capacity region, which partially matches the achievable region in an n-letter form. We evaluate a looser version of our outer bound for the Gaussian case, and show that our outer bound is within 0.5 bits/channel use of the achievable rates along the individual secrecy rates for all weak eavesdropper Gaussian MAC-WT. Then, we investigate the effects of user cooperation on the secrecy of broadcast channels by considering the cooperative relay broadcast channel (CRBC). We propose an achievable scheme that combines Marton's coding scheme for broadcast channels and Cover and El Gamal's compress-and-forward (CAF) scheme for relay channels. For the Gaussian CRBC, we show that both users can have positive secrecy rates, which is not possible for scalar Gaussian broadcast channels without cooperation. We further investigate the effects of user cooperation on secrecy by considering the multiple access channel with generalized feedback (MAC-GF), which can be viewed as the MAC-dual of the CRBC. We propose a CAF-based achievable secrecy rate region for the MAC-GF. Specializing our results to a Gaussian MAC-GF, we present numerical results which demonstrate that cooperation can improve secrecy for the MAC-GF. Next, we study the two-user one-eavesdropper discrete memoryless compound wiretap channel, and provide the best known lower bound for the secrecy capacity of this compound channel. We evaluate this achievable secrecy rate for the Gaussian MIMO case by using DPC. We show that this achievable secrecy rate achieves at least half of the secrecy capacity of this Gaussian MIMO compound wiretap channel, and also attains the secrecy capacity when the eavesdropper is degraded with respect to one of the two users. Then, we study the degraded compound multi-receiver wiretap channel (DCMRWC), which, in addition to a group of eavesdroppers, has two groups of users, namely the stronger group and the weaker group. We study two different communication scenarios for this channel. In the first scenario, there is only one eavesdropper, and the transmitter sends a confidential message to each group of legitimate users while keeping both messages secret from the eavesdropper. In the second scenario, we study the DCMRWC with layered messages without any restriction on the number of eavesdroppers. For both scenarios, we obtain the secrecy capacity region for the discrete memoryless channel, the parallel channel, and the Gaussian parallel channel. For the Gaussian MIMO channel, we obtain the secrecy capacity region when there is only one user in the second group. Next, we study the two-user fading broadcast channel and obtain its ergodic secrecy capacity region. We show that, thanks to fading, both users can have simultaneous secure communication with the transmitter, although this is not possible in the scalar non-fading Gaussian broadcast channel where only one user can have secure communication. This simultaneous secrecy of both users is achieved by an opportunistic communication scheme, in which, at each time instant, the transmitter communicates with the user having a better channel gain. Then, we study the secure lossy transmission of a vector Gaussian source to a legitimate user in the presence of an eavesdropper, where both the legitimate user and the eavesdropper have vector Gaussian side information. We obtain an outer bound for the rate, equivocation and distortion region. Moreover, we obtain the maximum equivocation at the eavesdropper when there is no constraint on the transmission rate. By using this maximum equivocation result, we show two facts. First, for this problem, in general, Wyner-Ziv scheme is suboptimal, although, it is optimal in the absence of an eavesdropper. And, second, even when there is no transmission rate constraint, an uncoded transmission scheme is suboptimal; the presence of an eavesdropper necessitates the use of a coded scheme to attain the maximum equivocation. Finally, we revisit the secure lossy source coding problem. In all works on this problem, either the equivocation of the source at the eavesdropper or the equivocation of the legitimate user's reconstruction of the source at the eavesdropper is used to measure secrecy. We first propose the relative equivocation of the source at the eavesdropper with respect to the legitimate user as a new secrecy measure. We argue that this new secrecy measure is the one that corresponds to the natural generalization of the equivocation in a wiretap channel to the context of secure lossy source coding. Under this new secrecy measure, we provide a single-letter description of the rate, relative equivocation and distortion region, as well as its specializations to degraded and reversely degraded cases. We investigate the relationships between the optimal scheme that attains this region and the Wyner-Ziv scheme.
The current research on physical layer security is far from implementations in practical networks, arguably due to impractical assumptions in the literature and the limited applicability of physical layer security. Aiming to reduce the gap between theory and practice, this thesis focuses on wireless physical layer security towards practical assumptions and requirements. In the first half of the thesis, we reduce the dependence of physical layer security on impractical assumptions. The secrecy enhancements and analysis based on impractical assumptions cannot lead to any true guarantee of secrecy in practical networks. The current study of physical layer security was often based on the idealized assumption of perfect channel knowledge on both legitimate users and eavesdroppers. We study the impact of channel estimation errors on secure transmission designs. We investigate the practical scenarios where both the transmitter and the receiver have imperfect channel state information (CSI). Our results show how the optimal transmission design and the achievable throughput vary with the amount of knowledge on the eavesdropper's channel. Apart from the assumption of perfect CSI, the analysis of physical layer security often ideally assumed the number of eavesdropper antennas to be known. We develop an innovative approach to study secure communication systems without knowing the number of eavesdropper antennas by introducing the concept of spatial constraint into physical layer security. That is, the eavesdropper is assumed to have a limited spatial region to place (possibly an infinite number of) antennas. We show that a non-zero secrecy rate is achievable with the help of a friendly jammer, even if the eavesdropper places an infinite number of antennas in its spatial region. In the second half of the thesis, we improve the applicability of physical layer security. The current physical layer security techniques to achieve confidential broadcasting were limited to application in single-cell systems. The primary challenge to achieve confidential broadcasting in the multi-cell network is to deal with not only the inter-cell but also the intra-cell information leakage and interference. To tackle this challenge, we design linear precoders performing confidential broadcasting in multi-cell networks. We optimize the precoder designs to maximize the secrecy sum rate with based on the large-system analysis. Finally, we improve the applicability of physical layer security from a fundamental aspect. The analysis of physical layer security based on the existing secrecy metric was often not applicable in practical networks. We propose new metrics for evaluating the secrecy of transmissions over fading channels to address the practical limitations of using existing secrecy metrics for such evaluations. The first metric establishes a link between the concept of secrecy outage and the eavesdropper's ability to decode confidential messages. The second metric provides an error-probability-based secrecy metric which is often used for the practical implementation of secure wireless systems. The third metric characterizes how much or how fast the confidential information is leaked to the eavesdropper. We show that the proposed secrecy metrics enable one to appropriately design secure communication systems with different views on how secrecy is measured.
The study of the physical layer has offered a new perspective to the problem of communication security. This led to the development of a vast set of ideas and techniques rooted in information theory which can be employed in practice to provide unbreakable security. The information-theoretic approach relies mainly on the physical nature of the communication medium. In a wireless medium, the unique features of the wireless communication channel, such as its fading and broadcast nature, can be exploited to achieve higher secure information rates. In this dissertation, we study the secure transmission problem in wireless channels from an information-theoretic perspective. We first consider the fading multiple access wiretap channel. We give two new achievable schemes that use the time-varying (fading) nature of the channel to align the interference from different users at the eavesdropper perfectly in a one-dimensional space while creating a higher-dimensional space for the interfering signals at the legitimate receiver hence allowing for better chance of recovery. While we achieve this alignment through signal scaling at the transmitters in our first scheme (scaling based alignment), we let nature provide this alignment through the ergodicity of the channel coefficients in the second scheme (ergodic secret alignment). For each scheme, we show that the achievable secrecy rates scale logarithmically with the signal-to-noise ratio (SNR). Next, we study the security gains that can be achieved in a wireless network by employing cooperation among the nodes which is possible due to the broadcast nature of the wireless channel. We investigate the role of passive (also known as deaf) cooperation in improving the achievable secrecy rates in a Gaussian multiple relay network with an external eavesdropper. We distinguish between two modes of deaf cooperation, namely, cooperative jamming (CJ) and noise forwarding (NF). We derive the conditions in which each mode of deaf cooperation achieves secrecy rates that are higher than the secrecy capacity of the original Gaussian wiretap channel. As a result, we show that a deaf helper cannot be a useful cooperative jammer and noise forwarder at the same time. We derive the optimal power control policy for each mode. We consider the deaf helper selection problem where a fixed-size set of deaf helpers (possibly operating in different modes) are to be selected from the set of available relays so that the achievable secrecy rate is maximized. We propose a simple and efficient suboptimal strategy for selection which is shown to be optimal when only one helper is selected. Furthermore, we study the role of a multi-antenna deaf helper. Unlike the single antenna case, we show that, in general, it is useful to split the helper's power between cooperative jamming and noise forwarding. Hence, we propose a deaf cooperation strategy for this model and derive its optimal power control policy. We also show, for specific class of relay-eavesdropper channels, that a simple cooperative jamming strategy yields a secrecy rate that approaches the secrecy capacity as the helper's power is increased. Finally, we consider the role of active cooperation for secrecy in the multiple relay networks. We propose several relaying strategies for secure communication and derive the achievable secrecy rate for each strategy. In our strategies the relays decode the source signal and then forward it to the destination either in a single-hop or a multi-hop fashion. Each relay scales its transmitted signal in a way that ensures that signal components from different relays are canceled out at the eavesdropper.
This dissertation studies the security of wireless interference networks from an information-theoretic point of view. In this setting, several transmitter-receiver pairs wish to have secure communication against the eavesdropper(s). The central goal of this dissertation is to develop a framework based on information-theoretic principles to determine the complete solutions for the signaling schemes in different wireless interference networks with large transmit powers, and derive the corresponding fundamental limits in terms of the secure degrees of freedom (s.d.o.f.). Next, we study one-hop wireless networks by considering four fundamental wireless network structures: Gaussian wiretap channel with helpers, Gaussian broadcast channel (BC) with confidential messages, Gaussian interference channel (IC) with confidential messages, and Gaussian multiple access (MAC) wiretap channel. The secrecy capacity of the canonical Gaussian wiretap channel does not scale with the transmit power, and hence, the s.d.o.f. of the Gaussian wiretap channel with no helpers is zero. We show that the exact s.d.o.f. of the Gaussian wiretap channel with a helper is 1/2. Our achievable scheme is based on real interference alignment and cooperative jamming, which renders the message signal and the cooperative jamming signal separable at the legitimate receiver, but aligns them perfectly at the eavesdropper preventing any reliable decoding of the message signal. Our converse is based on two key lemmas. The first lemma quantifies the secrecy penalty by showing that the net effect of an eavesdropper on the system is that it eliminates one of the independent channel inputs. The second lemma quantifies the role of a helper by developing a direct relationship between the cooperative jamming signal of a helper and the message rate. We extend this result to the case of M helpers, and show that the exact s.d.o.f. in this case is M/(M+1). We then generalize this approach to more general network structures with multiple messages. We show that the sum s.d.o.f. of the Gaussian BC with confidential messages and M helpers is 1, the sum s.d.o.f. of the two-user IC with confidential messages is 2/3, the sum s.d.o.f. of the two-user IC with confidential messages and M helpers is 1, and the sum s.d.o.f. of the K-user MAC wiretap channel is K(K-1)/(K(K-1)+1). Then, we study the sum s.d.o.f. of multi-receiver networks. In this dissertation, we determine the exact sum s.d.o.f. of the K-user Gaussian IC. We consider three different secrecy constraints: 1) K-user IC with one external eavesdropper (IC-EE), 2) K-user IC with confidential messages (IC-CM), and 3) K-user IC with confidential messages and one external eavesdropper (IC-CM-EE). We show that for all of these three cases, the exact sum secure d.o.f. is K(K-1)/(2K-1). We show converses for IC-EE and IC-CM, which imply a converse for IC-CM-EE. We show achievability for IC-CM-EE, which implies achievability for IC-EE and IC-CM. We develop the converses by relating the channel inputs of interfering users to the reliable rates of the interfered users, and by quantifying the secrecy penalty in terms of the eavesdroppers' observations. Our achievability uses structured signaling, structured cooperative jamming, channel prefixing, and asymptotic real interference alignment. While the traditional interference alignment provides some amount of secrecy by mixing unintended signals in a smaller sub-space at every receiver, in order to attain the optimum sum s.d.o.f., we incorporate structured cooperative jamming into the achievable scheme, and intricately design the structure of all of the transmitted signals jointly. Next, we study the entire s.d.o.f. regions of multi-user network structures. In this dissertation, we determine the entire s.d.o.f. regions of the K-user MAC wiretap channel and the K-user IC with secrecy constraints. The converse for the MAC follows from a middle step in the converse of the sum s.d.o.f. The converse for the IC includes constraints both due to secrecy as well as due to interference. Although the portion of the region close to the optimum sum s.d.o.f. point is governed by the upper bounds due to secrecy constraints, the other portions of the region are governed by the upper bounds due to interference constraints. Different from the existing literature, in order to fully understand the characterization of the s.d.o.f. region of the IC, one has to study the 4-user case, i.e., the 2 or 3-user cases do not illustrate the generality of the problem. In order to prove the achievability, we use the polytope structure of the converse region. In both MAC and IC cases, we develop explicit schemes that achieve the extreme points of the polytope region given by the converse. Specifically, the extreme points of the MAC region are achieved by an m-user MAC wiretap channel with (K-m) helpers, i.e., by setting (K-m) users' secure rates to zero and utilizing them as pure (structured) cooperative jammers. The extreme points of the IC region are achieved by a (K-m)-user IC with confidential messages, m helpers, and N external eavesdroppers, for m>=1 and a finite N. As a byproduct of determining the entire s.d.o.f. regions of MAC and IC channels, we show that the sum s.d.o.f. is achieved only at one extreme point of the s.d.o.f. region, which is the symmetric-rate extreme point, for both MAC and IC channel models. Then, we determine the sum s.d.o.f. of two-unicast layered wireless networks. Without any secrecy constraints, the sum d.o.f. of this class of networks was shown to take only one of three possible values: 1, 3/2 and 2, for all network configurations. We consider the setting where, in addition to being reliably transmitted, each message is required to be kept information-theoretically secure from the unintended receiver. We show that the sum s.d.o.f. can only take one of five possible values: 0, 2/3, 1, 3/2,2, for all network configurations. To determine the sum s.d.o.f., we divide the class of two-unicast layered networks into several sub-classes, and propose an achievable scheme based on the specific structure of the networks in each sub-class. Our achievable schemes are based on real interference alignment, cooperative jamming, interference neutralization and cooperative jamming neutralization techniques. Next, we consider the Gaussian wiretap channel with M helpers, where no eavesdropper channel state information (CSI) is available at the legitimate entities. One of the key ingredients of our optimal achievable scheme with perfect CSI is to align cooperative jamming signals with the information symbols at the eavesdropper to limit the information leakage rate. This requires perfect eavesdropper CSI at the transmitters. We propose a new achievable scheme in which cooperative jamming signals span the entire space of the eavesdropper, but are not exactly aligned with the information symbols. We show that this scheme achieves the same s.d.o.f. of M/(M+1) but does not require any eavesdropper CSI; the transmitters blindly cooperative jam the eavesdropper. Then, we study the separability of the parallel MAC wiretap channel. Separability, when exists, is useful as it enables us to code separately over parallel channels, and still achieve the optimum overall performance. It is well-known that the parallel single-user channel, parallel MAC and parallel BC are all separable, however, the parallel IC is not separable in general. In this dissertation, we show that, while MAC is separable MAC wiretap channel is not separable in general. We prove this via a specific linear deterministic MAC wiretap channel. We then show that even the Gaussian MAC wiretap channel is inseparable in general. Finally, we show that, when the channel gains are drawn from continuous distributions, and when the s.d.o.f. region is considered, then the Gaussian MAC wiretap channel is almost surely separable. Finally, we study the two-user one-sided IC with confidential messages. In this IC, in addition to the usual selfishness of the users, the relationship between the users is adversarial in the sense of both receivers' desires to eavesdrop on the communication of the other pair. We develop a game-theoretic model for this setting. We start with a model where each pair's payoff is their own secrecy rate. We then propose a refinement for the payoff function by explicitly accounting for the desire of the receiver to eavesdrop on the other party's communication. This payoff function captures the adversarial relationship between the users better. We determine the Nash equilibria for the binary deterministic channel for both payoff functions.
The use of wireless networks has grown significantly in contemporary \ntimes, and continues to develop further. The broadcast nature of \nwireless communications, however, makes them particularly vulnerable \nto eavesdropping. Unlike traditional solutions, which usually handle \nsecurity at the application layer, the primary concern of this \ndissertation is to analyze and develop solutions based on coding \ntechniques at the physical-layer. \n \nFirst, in chapter 2, we consider a scenario where a source node \nwishes to broadcast two confidential messages to two receivers, \nwhile a wire-tapper also receives the transmitted signal. This model \nis motivated by wireless communications, where individual secure \nmessages are broadcast over open media and can be received by any \nillegitimate receiver. The secrecy level is measured by the \nequivocation rate at the eavesdropper. We first study the general \n(non-degraded) broadcast channel with an eavesdropper, and present \nan inner bound on the secrecy capacity region for this model. This \ninner bound is based on a combination of random binning, and the \nGelfand-Pinsker binning. We further study the situation in which the \nchannels are degraded. For the degraded broadcast channel with an \neavesdropper, we present the secrecy capacity region. Our achievable \ncoding scheme is based on Cover's superposition scheme and random \nbinning. We refer to this scheme as the Secret Superposition Scheme. \nOur converse proof is based on a combination of the converse proof \nof the conventional degraded broadcast channel and Csiszar Lemma. We \nthen assume that the channels are Additive White Gaussian Noise and \nshow that the Secret Superposition Scheme with Gaussian codebook is \noptimal. The converse proof is based on Costa's entropy power \ninequality. Finally, we use a broadcast strategy for the slowly \nfading wire-tap channel when only the eavesdropper's channel is \nfixed and known at the transmitter. We derive the optimum power \nallocation for the coding layers, which maximizes the total average \nrate. \n \n \nSecond, in chapter 3 , we consider the \nMultiple-Input-Multiple-Output (MIMO) scenario of a broadcast \nchannel where a wiretapper also receives the transmitted signal via \nanother MIMO channel. First, we assume that the channels are \ndegraded and the wiretapper has the worst channel. We establish the \ncapacity region of this scenario. Our achievability scheme is the \nSecret Superposition Coding. For the outerbound, we use notion of \nthe enhanced channels to show that the secret superposition of \nGaussian codes is optimal. We show that we only need to enhance the \nchannels of the legitimate receivers, and the channel of the \neavesdropper remains unchanged. We then extend the result of the \ndegraded case to a non-degraded case. We show that the secret \nsuperposition of Gaussian codes, along with successive decoding, \ncannot work when the channels are not degraded. We develop a Secret \nDirty Paper Coding scheme and show that it is optimal for this \nchannel. We then present a corollary generalizing the capacity \nregion of the two receivers case to the case of multiple receivers. \nFinally, we investigate a scenario which frequently occurs in the \npractice of wireless networks. In this scenario, the transmitter and \nthe eavesdropper have multiple antennae, while both intended \nreceivers have a single antenna (representing resource limited \nmobile units). We characterize the secrecy capacity region in terms \nof generalized eigenvalues of the receivers' channels and the \neavesdropper's channel. We refer to this configuration as the MISOME \ncase. We then present a corollary generalizing the results of the \ntwo receivers case to multiple receivers. In the high SNR regime, we \nshow that the capacity region is a convex closure of rectangular \nregions. \n \n \nFinally, in chapter 4, we consider a K-user secure Gaussian \nMultiple-Access-Channel with an external eavesdropper. We establish \nan achievable rate region for the secure discrete memoryless MAC. \nThereafter, we prove the secrecy sum capacity of the degraded \nGaussian MIMO MAC using Gaussian codebooks. For the non-degraded \nGaussian MIMO MAC, we propose an algorithm inspired by the \ninterference alignment technique to achieve the largest possible \ntotal Secure-Degrees-of-Freedom . When all the terminals are \nequipped with a single antenna, Gaussian codebooks have shown to be \ninefficient in providing a positive S-DoF. Instead, we propose a \nnovel secure coding scheme to achieve a positive S-DoF in the single \nantenna MAC. This scheme converts the single-antenna system into a \nmultiple-dimension system with fractional dimensions. The \nachievability scheme is based on the alignment of signals into a \nsmall sub-space at the eavesdropper, and the simultaneous separation \nof the signals at the intended receiver. We use tools from the field \nof Diophantine Approximation in number theory to analyze the \nprobability of error in the coding scheme. We prove that the total \nS-DoF of fracK−1K can be achieved for almost all channel \ngains. For the other channel gains, we propose a multi-layer coding \nscheme to achieve a positive S-DoF. As a function of channel gains, \ntherefore, the achievable S-DoF is discontinued.