Wireless communication networks are widely deployed today and the networks are used in many applications which require that the data transmitted be secure. Due to the open nature of wireless systems, it is important to have a fundamental understanding of coding schemes that allow for simultaneously secure and reliable transmission. The information theoretic approach is able to give us this fundamental insight into the nature of the coding schemes required for security. The security issue is approached by focusing on the confidentiality of message transmission and reception at the physical layer. The goal is to design coding and signal processing schemes that provide security, in the information theoretic sense. In so doing, we are able to prove the simultaneously secure and reliable transmission rates for different network building blocks. The multi-receiver broadcast channel is an important network building block, where the rate region for the channel without security constraints is still unknown. In the thesis this channel is investigated with security constraints, and the secure and reliable rates are derived for the proposed coding scheme using a random coding argument. Cooperative relaying is next applied to the wiretap channel, the fundamental physical layer model for the communication security problem, and signal processing techniques are used to show that the secure rate can be improved in situations where the secure rate was small due to the eavesdropper enjoying a more favorable channel condition compared to the legitimate receiver. Finally, structured lattice codes are used in the wiretap channel instead of unstructured random codes, used in the vast majority of the work so far. We show that lattice coding and decoding can achieve the secrecy rate of the Gaussian wiretap channel; this is an important step towards realizing practical, explicit codes for the wiretap channel.
Wireless communication networks are widely deployed today and the networks are used in many applications which require that the data transmitted be secure. Due to the open nature of wireless systems, it is important to have a fundamental understanding of coding schemes that allow for simultaneously secure and reliable transmission. The information theoretic approach is able to give us this fundamental insight into the nature of the coding schemes required for security. The security issue is approached by focusing on the confidentiality of message transmission and reception at the physical layer. The goal is to design coding and signal processing schemes that provide security, in the information theoretic sense. In so doing, we are able to prove the simultaneously secure and reliable transmission rates for different network building blocks. The multi-receiver broadcast channel is an important network building block, where the rate region for the channel without security constraints is still unknown. In the thesis this channel is investigated with security constraints, and the secure and reliable rates are derived for the proposed coding scheme using a random coding argument. Cooperative relaying is next applied to the wiretap channel, the fundamental physical layer model for the communication security problem, and signal processing techniques are used to show that the secure rate can be improved in situations where the secure rate was small due to the eavesdropper enjoying a more favorable channel condition compared to the legitimate receiver. Finally, structured lattice codes are used in the wiretap channel instead of unstructured random codes, used in the vast majority of the work so far. We show that lattice coding and decoding can achieve the secrecy rate of the Gaussian wiretap channel; this is an important step towards realizing practical, explicit codes for the wiretap channel.
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.
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.
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 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.
Secure communication under channel uncertainty is an important and challenging problem in physical-layer security and cryptography. In this dissertation, we take a \nfundamental information-theoretic view at three concrete settings and use them to shed insight into efficient secure communication techniques for different scenarios under channel uncertainty. \n \nFirst, a multi-input multi-output (MIMO) Gaussian broadcast channel with two receivers and two messages: a common message intended for both receivers (i.e., channel \nuncertainty for decoding the common message at the receivers) and a confidential message intended for one of the receivers but needing to be kept asymptotically perfectly secret from the other is considered. A matrix characterization of the secrecy capacity region is established via a channel-enhancement argument and an extremal entropy inequality previously established for characterizing the capacity region of a degraded compound MIMO Gaussian broadcast channel. \n \nSecond, a multilevel security wiretap channel where there is one possible realization for the legitimate receiver channel but multiple possible realizations for the eavesdropper channel (i.e., channel uncertainty at the eavesdropper) is considered. A coding scheme is designed such that the number of secure bits delivered to the legitimate receiver depends on the actual realization of the eavesdropper channel. More specifically, when the eavesdropper channel realization is weak, all bits delivered to the legitimate receiver need to be secure. In addition, when the eavesdropper channel realization is strong, a prescribed part of the bits needs to remain secure. We call such codes security embedding codes, referring to the fact that high-security bits are now embedded into the low-security ones. We show that the key to achieving efficient security embedding is to jointly encode the low-security and high-security bits. In particular, the low-security bits can be used as (part of) the transmitter randomness to protect the high-security ones. \n \nFinally, motivated by the recent interest in building secure, robust and efficient distributed information storage systems, the problem of secure symmetrical multilevel diversity coding (S-SMDC) is considered. This is a setting where there are channel uncertainties at both the legitimate receiver and the eavesdropper. The problem of encoding individual sources is first studied. A precise characterization of the entire admissible rate region is established via a connection to the problem of secure coding over a three-layer wiretap network and utilizing some basic polyhedral structure of the admissible rate region. Building on this result, it is then shown that the simple coding strategy of separately encoding individual sources at the encoders can achieve the minimum sum rate for the general S-SMDC problem.
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.