263 research outputs found

    Nonparametric Anomaly Detection and Secure Communication

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    Two major security challenges in information systems are detection of anomalous data patterns that reflect malicious intrusions into data storage systems and protection of data from malicious eavesdropping during data transmissions. The first problem typically involves design of statistical tests to identify data variations, and the second problem generally involves design of communication schemes to transmit data securely in the presence of malicious eavesdroppers. The main theme of this thesis is to exploit information theoretic and statistical tools to address the above two security issues in order to provide information theoretically provable security, i.e., anomaly detection with vanishing probability of error and guaranteed secure communication with vanishing leakage rate at eavesdroppers. First, the anomaly detection problem is investigated, in which typical and anomalous patterns (i.e., distributions that generate data) are unknown \emph{a priori}. Two types of problems are investigated. The first problem considers detection of the existence of anomalous geometric structures over networks, and the second problem considers the detection of a set of anomalous data streams out of a large number of data streams. In both problems, anomalous data are assumed to be generated by a distribution qq, which is different from a distribution pp generating typical samples. For both problems, kernel-based tests are proposed, which are based on maximum mean discrepancy (MMD) that measures the distance between mean embeddings of distributions into a reproducing kernel Hilbert space. These tests are nonparametric without exploiting the information about pp and qq and are universally applicable to arbitrary pp and qq. Furthermore, these tests are shown to be statistically consistent under certain conditions on the parameters of the problems. These conditions are further shown to be necessary or nearly necessary, which implies that the MMD-based tests are order level optimal or nearly order level optimal. Numerical results are provided to demonstrate the performance of the proposed tests. The secure communication problem is then investigated, for which the focus is on degraded broadcast channels. In such channels, one transmitter sends messages to multiple receivers, the channel quality of which can be ordered. Two specific models are studied. In the first model, layered decoding and layered secrecy are required, i.e., each receiver decodes one more message than the receiver with one level worse channel quality, and this message should be kept secure from all receivers with worse channel qualities. In the second model, secrecy only outside a bounded range is required, i.e., each message is required to be kept secure from the receiver with two-level worse channel quality. Communication schemes for both models are designed and the corresponding achievable rate regions (i.e., inner bounds on the capacity region) are characterized. Furthermore, outer bounds on the capacity region are developed, which match the inner bounds, and hence the secrecy capacity regions are established for both models

    Lecture Notes on Network Information Theory

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    These lecture notes have been converted to a book titled Network Information Theory published recently by Cambridge University Press. This book provides a significantly expanded exposition of the material in the lecture notes as well as problems and bibliographic notes at the end of each chapter. The authors are currently preparing a set of slides based on the book that will be posted in the second half of 2012. More information about the book can be found at http://www.cambridge.org/9781107008731/. The previous (and obsolete) version of the lecture notes can be found at http://arxiv.org/abs/1001.3404v4/

    Physical-Layer Security in Wireless Communication Systems

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    The use of wireless networks has grown significantly in contemporary times, and continues to develop further. The broadcast nature of wireless communications, however, makes them particularly vulnerable to eavesdropping. Unlike traditional solutions, which usually handle security at the application layer, the primary concern of this dissertation is to analyze and develop solutions based on coding techniques at the physical-layer. First, in chapter 22, we consider a scenario where a source node wishes to broadcast two confidential messages to two receivers, while a wire-tapper also receives the transmitted signal. This model is motivated by wireless communications, where individual secure messages are broadcast over open media and can be received by any illegitimate receiver. The secrecy level is measured by the equivocation rate at the eavesdropper. We first study the general (non-degraded) broadcast channel with an eavesdropper, and present an inner bound on the secrecy capacity region for this model. This inner bound is based on a combination of random binning, and the Gelfand-Pinsker binning. We further study the situation in which the channels are degraded. For the degraded broadcast channel with an eavesdropper, we present the secrecy capacity region. Our achievable coding scheme is based on Cover's superposition scheme and random binning. We refer to this scheme as the Secret Superposition Scheme. Our converse proof is based on a combination of the converse proof of the conventional degraded broadcast channel and Csiszar Lemma. We then assume that the channels are Additive White Gaussian Noise and show that the Secret Superposition Scheme with Gaussian codebook is optimal. The converse proof is based on Costa's entropy power inequality. Finally, we use a broadcast strategy for the slowly fading wire-tap channel when only the eavesdropper's channel is fixed and known at the transmitter. We derive the optimum power allocation for the coding layers, which maximizes the total average rate. Second, in chapter 33 , we consider the Multiple-Input-Multiple-Output (MIMO) scenario of a broadcast channel where a wiretapper also receives the transmitted signal via another MIMO channel. First, we assume that the channels are degraded and the wiretapper has the worst channel. We establish the capacity region of this scenario. Our achievability scheme is the Secret Superposition Coding. For the outerbound, we use notion of the enhanced channels to show that the secret superposition of Gaussian codes is optimal. We show that we only need to enhance the channels of the legitimate receivers, and the channel of the eavesdropper remains unchanged. We then extend the result of the degraded case to a non-degraded case. We show that the secret superposition of Gaussian codes, along with successive decoding, cannot work when the channels are not degraded. We develop a Secret Dirty Paper Coding scheme and show that it is optimal for this channel. We then present a corollary generalizing the capacity region of the two receivers case to the case of multiple receivers. Finally, we investigate a scenario which frequently occurs in the practice of wireless networks. In this scenario, the transmitter and the eavesdropper have multiple antennae, while both intended receivers have a single antenna (representing resource limited mobile units). We characterize the secrecy capacity region in terms of generalized eigenvalues of the receivers' channels and the eavesdropper's channel. We refer to this configuration as the MISOME case. We then present a corollary generalizing the results of the two receivers case to multiple receivers. In the high SNR regime, we show that the capacity region is a convex closure of rectangular regions. Finally, in chapter 44, we consider a KK-user secure Gaussian Multiple-Access-Channel with an external eavesdropper. We establish an achievable rate region for the secure discrete memoryless MAC. Thereafter, we prove the secrecy sum capacity of the degraded Gaussian MIMO MAC using Gaussian codebooks. For the non-degraded Gaussian MIMO MAC, we propose an algorithm inspired by the interference alignment technique to achieve the largest possible total Secure-Degrees-of-Freedom . When all the terminals are equipped with a single antenna, Gaussian codebooks have shown to be inefficient in providing a positive S-DoF. Instead, we propose a novel secure coding scheme to achieve a positive S-DoF in the single antenna MAC. This scheme converts the single-antenna system into a multiple-dimension system with fractional dimensions. The achievability scheme is based on the alignment of signals into a small sub-space at the eavesdropper, and the simultaneous separation of the signals at the intended receiver. We use tools from the field of Diophantine Approximation in number theory to analyze the probability of error in the coding scheme. We prove that the total S-DoF of K−1K\frac{K-1}{K} can be achieved for almost all channel gains. For the other channel gains, we propose a multi-layer coding scheme to achieve a positive S-DoF. As a function of channel gains, therefore, the achievable S-DoF is discontinued

    Information-Theoretically Secure Communication Under Channel Uncertainty

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    Secure communication under channel uncertainty is an important and challenging problem in physical-layer security and cryptography. In this dissertation, we take a fundamental information-theoretic view at three concrete settings and use them to shed insight into efficient secure communication techniques for different scenarios under channel uncertainty. First, 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 uncertainty 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. Second, 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. Finally, 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

    Coding for Cryptographic Security Enhancement using Stopping Sets

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    In this paper we discuss the ability of channel codes to enhance cryptographic secrecy. Toward that end, we present the secrecy metric of degrees of freedom in an attacker's knowledge of the cryptogram, which is similar to equivocation. Using this notion of secrecy, we show how a specific practical channel coding system can be used to hide information about the ciphertext, thus increasing the difficulty of cryptographic attacks. The system setup is the wiretap channel model where transmitted data traverse through independent packet erasure channels with public feedback for authenticated ARQ (Automatic Repeat reQuest). The code design relies on puncturing nonsystematic low-density parity-check codes with the intent of inflicting an eavesdropper with stopping sets in the decoder. Furthermore, the design amplifies errors when stopping sets occur such that a receiver must guess all the channel-erased bits correctly to avoid an expected error rate of one half in the ciphertext. We extend previous results on the coding scheme by giving design criteria that reduces the effectiveness of a maximum-likelihood attack to that of a message-passing attack. We further extend security analysis to models with multiple receivers and collaborative attackers. Cryptographic security is enhanced in all these cases by exploiting properties of the physical-layer. The enhancement is accurately presented as a function of the degrees of freedom in the eavesdropper's knowledge of the ciphertext, and is even shown to be present when eavesdroppers have better channel quality than legitimate receivers.Comment: 13 pages, 8 figure

    Construction of lattices for communications and security

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    In this thesis, we propose a new class of lattices based on polar codes, namely polar lattices. Polar lattices enjoy explicit construction and provable goodness for the additive white Gaussian noise (AWGN) channel, \textit{i.e.}, they are \emph{AWGN-good} lattices, in the sense that the error probability (for infinite lattice coding) vanishes for any fixed volume-to-noise ratio (VNR) greater than 2πe2\pi e. Our construction is based on the multilevel approach of Forney \textit{et al.}, where on each level we construct a capacity-achieving polar code. We show the component polar codes are naturally nested, thereby fulfilling the requirement of the multilevel lattice construction. We present a more precise analysis of the VNR of the resultant lattice, which is upper-bounded in terms of the flatness factor and the capacity losses of the component codes. The proposed polar lattices are efficiently decodable by using multi-stage decoding. Design examples are presented to demonstrate the superior performance of polar lattices. However, there is no infinite lattice coding in the practical applications. We need to apply the power constraint on the polar lattices which generates the polar lattice codes. We prove polar lattice codes can achieve the capacity \frac{1}{2}\log(1+\SNR) of the power-constrained AWGN channel with a novel shaping scheme. The main idea is that by implementing the lattice Gaussian distribution over the AWGN-good polar lattices, the maximum error-free transmission rate of the resultant coding scheme can be arbitrarily close to the capacity \frac{1}{2}\log(1+\SNR). The shaping technique is based on discrete lattice Gaussian distribution, which leads to a binary asymmetric channel at each level for the multilevel lattice codes. Then it is straightforward to employ multilevel asymmetric polar codes which is a combination of polar lossless source coding and polar channel coding. The construction of polar codes for an asymmetric channel can be converted to that for a related symmetric channel, and it turns out that this symmetric channel is equivalent to an minimum mean-square error (MMSE) scaled Λ/Λ′\Lambda/\Lambda' channel in lattice coding in terms of polarization, which eventually simplifies our coding design. Finally, we investigate the application of polar lattices in physical layer security. Polar lattice codes are proved to be able to achieve the strong secrecy capacity of the Mod-Λ\Lambda AWGN wiretap channel. The Mod-Λ\Lambda assumption was due to the fact that a practical shaping scheme aiming to achieve the optimum shaping gain was missing. In this thesis, we use our shaping scheme and extend polar lattice coding to the Gaussian wiretap channel. By employing the polar coding technique for asymmetric channels, we manage to construct an AWGN-good lattice and a secrecy-good lattice with optimal shaping simultaneously. Then we prove the resultant wiretap coding scheme can achieve the strong secrecy capacity for the Gaussian wiretap channel.Open Acces

    Rate-splitting multiple access for non-terrestrial communication and sensing networks

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    Rate-splitting multiple access (RSMA) has emerged as a powerful and flexible non-orthogonal transmission, multiple access (MA) and interference management scheme for future wireless networks. This thesis is concerned with the application of RSMA to non-terrestrial communication and sensing networks. Various scenarios and algorithms are presented and evaluated. First, we investigate a novel multigroup/multibeam multicast beamforming strategy based on RSMA in both terrestrial multigroup multicast and multibeam satellite systems with imperfect channel state information at the transmitter (CSIT). The max-min fairness (MMF)-degree of freedom (DoF) of RSMA is derived and shown to provide gains compared with the conventional strategy. The MMF beamforming optimization problem is formulated and solved using the weighted minimum mean square error (WMMSE) algorithm. Physical layer design and link-level simulations are also investigated. RSMA is demonstrated to be very promising for multigroup multicast and multibeam satellite systems taking into account CSIT uncertainty and practical challenges in multibeam satellite systems. Next, we extend the scope of research from multibeam satellite systems to satellite- terrestrial integrated networks (STINs). Two RSMA-based STIN schemes are investigated, namely the coordinated scheme relying on CSI sharing and the co- operative scheme relying on CSI and data sharing. Joint beamforming algorithms are proposed based on the successive convex approximation (SCA) approach to optimize the beamforming to achieve MMF amongst all users. The effectiveness and robustness of the proposed RSMA schemes for STINs are demonstrated. Finally, we consider RSMA for a multi-antenna integrated sensing and communications (ISAC) system, which simultaneously serves multiple communication users and estimates the parameters of a moving target. Simulation results demonstrate that RSMA is beneficial to both terrestrial and multibeam satellite ISAC systems by evaluating the trade-off between communication MMF rate and sensing Cramer-Rao bound (CRB).Open Acces

    Finite-Block-Length Analysis in Classical and Quantum Information Theory

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    Coding technology is used in several information processing tasks. In particular, when noise during transmission disturbs communications, coding technology is employed to protect the information. However, there are two types of coding technology: coding in classical information theory and coding in quantum information theory. Although the physical media used to transmit information ultimately obey quantum mechanics, we need to choose the type of coding depending on the kind of information device, classical or quantum, that is being used. In both branches of information theory, there are many elegant theoretical results under the ideal assumption that an infinitely large system is available. In a realistic situation, we need to account for finite size effects. The present paper reviews finite size effects in classical and quantum information theory with respect to various topics, including applied aspects
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