Degraded Broadcast Channel with Side Information, Confidential Messages and Noiseless Feedback

In this paper, first, we investigate the model of degraded broadcast channel with side information and confidential messages. This work is from Steinberg's work on the degraded broadcast channel with causal and noncausal side information, and Csisz$\acute{a}$r-K\"{o}rner's work on broadcast channel with confidential messages. Inner and outer bounds on the capacity-equivocation regions are provided for the noncausal and causal cases. Superposition coding and double-binning technique are used in the corresponding achievability proofs. Then, we investigate the degraded broadcast channel with side information, confidential messages and noiseless feedback. The noiseless feedback is from the non-degraded receiver to the channel encoder. Inner and outer bounds on the capacity-equivocation region are provided for the noncausal case, and the capacity-equivocation region is determined for the causal case. Compared with the model without feedback, we find that the noiseless feedback helps to enlarge the inner bounds for both causal and noncausal cases. In the achievability proof of the feedback model, the noiseless feedback is used as a secret key shared by the non-degraded receiver and the transmitter, and therefore, the code construction for the feedback model is a combination of superposition coding, Gel'fand-Pinsker's binning, block Markov coding and Ahlswede-Cai's secret key on the feedback system.Comment: Part of this paper has been accepted by ISIT2012, and this paper is submitted to IEEE Transactions on Information Theor

Lecture Notes on Network Information Theory

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/

A Unified Approach for Network Information Theory

In this paper, we take a unified approach for network information theory and prove a coding theorem, which can recover most of the achievability results in network information theory that are based on random coding. The final single-letter expression has a very simple form, which was made possible by many novel elements such as a unified framework that represents various network problems in a simple and unified way, a unified coding strategy that consists of a few basic ingredients but can emulate many known coding techniques if needed, and new proof techniques beyond the use of standard covering and packing lemmas. For example, in our framework, sources, channels, states and side information are treated in a unified way and various constraints such as cost and distortion constraints are unified as a single joint-typicality constraint. Our theorem can be useful in proving many new achievability results easily and in some cases gives simpler rate expressions than those obtained using conventional approaches. Furthermore, our unified coding can strictly outperform existing schemes. For example, we obtain a generalized decode-compress-amplify-and-forward bound as a simple corollary of our main theorem and show it strictly outperforms previously known coding schemes. Using our unified framework, we formally define and characterize three types of network duality based on channel input-output reversal and network flow reversal combined with packing-covering duality.Comment: 52 pages, 7 figures, submitted to IEEE Transactions on Information theory, a shorter version will appear in Proc. IEEE ISIT 201

CODING AND SCHEDULING IN ENERGY HARVESTING COMMUNICATION SYSTEMS

Wireless networks composed of energy harvesting devices will introduce several transformative changes in wireless networking: energy self-sufficient, energy self-sustaining, perpetual operation; and an ability to deploy wireless networks at hard-to-reach places such as remote rural areas, within the structures, and within the human body. Energy harvesting brings new dimensions to the wireless communication problem in the form of intermittency and randomness of available energy. In such systems, the communication mechanisms need to be designed by explicitly accounting for the energy harvesting constraints. In this dissertation, we investigate the effects of intermittency and randomness in the available energy for message transmission in energy harvesting communication systems. We use information theoretic and scheduling theoretic frameworks to determine the fundamental limits of communications with energy harvesting devices. We first investigate the information theoretic capacity of the single user Gaussian energy harvesting channel. In this problem, an energy harvesting transmitter with an unlimited sized battery communicates with a receiver over the classical AWGN channel. As energy arrives randomly and can be saved in the battery, codewords must obey cumulative stochastic energy constraints. We show that the capacity of the AWGN channel with such stochastic channel input constraints is equal to the capacity with an average power constraint equal to the average recharge rate. We provide two capacity achieving schemes: save-and-transmit and best-effort-transmit. In the save-and-transmit scheme, the transmitter collects energy in a saving phase of proper duration that guarantees that there will be no energy shortages during the transmission of code symbols. In the best-effort-transmit scheme, the transmission starts right away without an initial saving period, and the transmitter sends a code symbol if there is sufficient energy in the battery, and a zero symbol otherwise. Finally, we consider a system in which the average recharge rate is time-varying in a larger time scale and derive the optimal offline power policy that maximizes the average throughput, by using majorization theory. Next, we remove the battery from the model to understand the impact of stochasticity in the energy arrival on the communication rate. We consider the single user AWGN channel in the zero energy storage case. We observe that the energy arrival is a channel state and channel state information is available at the transmitter only. We determine the capacity in this case using Shannon strategies. We, then, extend the capacity analysis to an additive Gaussian multiple access channel where multiple users with energy harvesting transmitters of zero energy storage communicate with a single receiver. We investigate the achievable rate region under static and stochastic amplitude constraints on the users' channel inputs. Finally, we consider state amplification in a single user AWGN channel with an energy harvesting transmitter to analyze the trade-off between the objectives of decoding the message and estimating the energy arrival sequence. Next, we specialize in the finite battery regime in the energy harvesting channel. We focus on the case of side information available at the receiver side. We determine the capacity of an energy harvesting channel with an energy harvesting transmitter and battery state information available at the receiver side. This is an instance of a finite-state channel and the channel output feedback does not increase the capacity. We state the capacity as maximum directed mutual information from the input to the output and the battery state. We identify sufficient conditions for the channel to have stationary input distributions as optimal distributions. We also derive a single-letter capacity expression for this channel with battery state information at both sides and infinite-sized battery at the transmitter. Then, we determine the capacity when energy arrival side information is available at the receiver side. We first find an n-letter capacity expression and show that the optimal coding is based on only current battery state s_i. We, next, show that the capacity is expressed as maximum directed information between the input and the output and prove that the channel output feedback does not increase the capacity. Then, we consider security aspects of communication in energy harvesting systems. In particular, we focus on a wiretap channel with an energy harvesting transmitter where a legitimate pair of users wish to establish secure communication in the presence of an eavesdropper in a noisy channel. We characterize the rate-equivocation region of the Gaussian wiretap channel under static and stochastic amplitude constraints. First, we consider the Gaussian wiretap channel with a static amplitude constraint on the channel input. We prove that the entire rate-equivocation region of the Gaussian wiretap channel with an amplitude constraint is obtained by discrete input distributions with finite support. We also prove the optimality of discrete input distributions in the presence of an additional variance constraint. Next, we consider the Gaussian wiretap channel with an energy harvesting transmitter with zero energy storage. We prove that single-letter Shannon strategies span the entire rate-equivocation region and obtain numerically verifiable necessary and sufficient optimality conditions. In the remaining parts of this dissertation, we consider optimal transmission scheduling for energy harvesting transmitters. First, we consider the optimization of single user data transmission with an energy harvesting transmitter which has a limited battery capacity, communicating over a wireless fading channel. We consider two objectives: maximizing the throughput by a deadline, and minimizing the transmission completion time of the communication session. We optimize these objectives by controlling the time sequence of transmit powers subject to energy storage capacity and causality constraints. We, first, study optimal offline policies. We introduce a directional water-filling algorithm which provides a simple and concise interpretation of the necessary optimality conditions. We show the optimality of the directional water-filling algorithm for the throughput maximization problem. We solve the transmission completion time minimization problem by utilizing its equivalence to its throughput maximization counterpart. Next, we consider online policies. We use dynamic programming to solve for the optimal online policy that maximizes the average number of bits delivered by a deadline under stochastic fading and energy arrival processes with causal channel state feedback. We also propose near-optimal policies with reduced complexity, and numerically study their performances along with the performances of the offline and online optimal policies. Then, we consider a broadcast channel with an energy harvesting transmitter with a finite capacity battery and M receivers. We derive the optimal offline transmission policy that minimizes the time by which all of the data packets are delivered to their respective destinations. We obtain structural properties of the optimal transmission policy using a dual problem and determine the optimal total transmit power sequence by a directional water-filling algorithm. We show that there exist M-1 cut-off power levels such that each user is allocated the power between two corresponding consecutive cut-off power levels subject to the availability of the allocated total power level. Based on these properties, we propose an iterative algorithm that gives the globally optimal offline policy. Finally, we consider parallel and fading Gaussian broadcast channels with an energy harvesting transmitter. Under offline knowledge of energy arrival and channel fading variations, we characterize the transmission policies that achieve the boundary of the maximum departure region in a given interval. In the case of parallel broadcast channels, we show that the optimal total transmit power policy that achieves the boundary of the maximum departure region is the same as the optimal policy for the non-fading broadcast channel, which does not depend on the priorities of the users, and therefore is the same as the optimal policy for the non-fading scalar single user channel. The optimal total transmit power can be found by a directional water-filling algorithm while optimal splitting of the power among the parallel channels is performed in each epoch separately. In the case of fading broadcast channels, the optimal power allocation depends on the priorities of the users. We obtain a modified directional water-filling algorithm for fading broadcast channels to determine the optimal total transmit power allocation policy

Communication Sécurisée et Coopération dans les Réseaux sans Fil avec Interférences and of their Inverter

In this thesis, we conduct an information-theoretic study on two important aspects of wireless communications: the improvement of data throughput in interference-limited networks by means of cooperation between users and the strengthening of the security of transmissions with the help of feedback.In the first part of the thesis, we focus on the simplest model that encompasses interference and cooperation, the Interference Relay Channel (IRC). Our goal is to characterize within a fixed number of bits the capacity region of the Gaussian IRC, independent of any channel conditions. To do so, we derive a novel outer bound and two inner bounds. Specifically, the outer bound is obtained thanks to a nontrivial extension we propose of the injective semideterministic class of channels, originally derived by Telatar and Tse for the Interference Channel (IC).In the second part of the thesis, we investigate the Wiretap Channel with Generalized Feedback (WCGF) and our goal is to provide a general transmission strategy that encompasses the existing results for different feedback models found in the literature. To this end, we propose two different inner bounds on the capacity of the memoryless WCGF. We first derive an inner bound that is based on the use of joint source-channel coding, which introduces time dependencies between the feedback outputs and the channel inputs through different time blocks. We then introduce a second inner bound where the feedback link is used to generate a key that encrypts the message partially or completely.Dans cette thèse, nous menons une étude dans le cadre de la théorie de l'information sur deux questions importantes de la communication sans fil : l'amélioration du débit de données dans les réseaux avec interférence grâce à la coopération entre utilisateurs et le renforcement de la sécurité des transmissions à l'aide d'un signal de rétroaction.Dans la première partie de la thèse, nous nous concentrons sur le modèle le plus simple qui intègre à la fois l'interférence et la coopération, le canal à relais et interférence ou IRC (Interference Relay Channel). Notre objectif est de caractériser dans un nombre fixe de bits la région de capacité du IRC gaussien. À cette fin, nous dérivons une nouvelle limite supérieure de la capacité et deux stratégies de transmission. La limite supérieure est notamment obtenue grâce à une extension non triviale que nous proposons, de la classe de canaux semi-déterministe et injective à l'origine dérivée par Telatar et Tse pour le canal à interférence.Dans la seconde partie, nous étudions le canal avec espion et rétroaction généralisée ou WCGF (Wiretap Channel with Generalized Feedback). Notre objectif est de développer une stratégie de transmission générale qui englobe les résultats existants pour les différents modèles de rétroaction trouvés dans la littérature. À cette fin, nous proposons deux stratégies de transmission différentes sur la capacité du WCGF sans mémoire. Nous dérivons d'abord une stratégie qui est basée sur le codage source-canal conjoint. Nous introduisons ensuite une seconde stratégie où le signal de rétroaction est utilisé pour générer une clé secrète qui permet de chiffrer le message partiellement ou totalement

Key Agreement over Wiretap Models with Non-Causal Side Information

The security of information is an indispensable element of a communication system when transmitted signals are vulnerable to eavesdropping. This issue is a challenging problem in a wireless network as propagated signals can be easily captured by unauthorized receivers, and so achieving a perfectly secure communication is a desire in such a wiretap channel. On the other hand, cryptographic algorithms usually lack to attain this goal due to the following restrictive assumptions made for their design. First, wiretappers basically have limited computational power and time. Second, each authorized party has often access to a reasonably large sequence of uniform random bits concealed from wiretappers. To guarantee the security of information, Information Theory (IT) offers the following two approaches based on physical-layer security. First, IT suggests using wiretap (block) codes to securely and reliably transmit messages over a noisy wiretap channel. No confidential common key is usually required for the wiretap codes. The secrecy problem investigates an optimum wiretap code that achieves the secrecy capacity of a given wiretap channel. Second, IT introduces key agreement (block) codes to exchange keys between legitimate parties over a wiretap model. The agreed keys are to be reliable, secure, and (uniformly) random, at least in an asymptotic sense, such that they can be finally employed in symmetric key cryptography for data transmission. The key agreement problem investigates an optimum key agreement code that obtains the key capacity of a given wiretap model. In this thesis, we study the key agreement problem for two wiretap models: a Discrete Memoryless (DM) model and a Gaussian model. Each model consists of a wiretap channel paralleled with an authenticated public channel. The wiretap channel is from a transmitter, called Alice, to an authorized receiver, called Bob, and to a wiretapper, called Eve. The Probability Transition Function (PTF) of the wiretap channel is controlled by a random sequence of Channel State Information (CSI), which is assumed to be non-causally available at Alice. The capacity of the public channel is C_P₁∈[0,∞) in the forward direction from Alice to Bob and C_P₂∈[0,∞) in the backward direction from Bob to Alice. For each model, the key capacity as a function of the pair (C_P₁, C_P₂) is denoted by C_K(C_P₁, C_P₂). We investigate the forward key capacity of each model, i.e., C_K(C_P₁, 0) in this thesis. We also study the key generation over the Gaussian model when Eve's channel is less noisy than Bob's. In the DM model, the wiretap channel is a Discrete Memoryless State-dependent Wiretap Channel (DM-SWC) in which Bob and Eve each may also have access to a sequence of Side Information (SI) dependent on the CSI. We establish a Lower Bound (LB) and an Upper Bound (UB) on the forward key capacity of the DM model. When the model is less noisy in Bob's favor, another UB on the forward key capacity is derived. The achievable key agreement code is asymptotically optimum as C_P₁→ ∞. For any given DM model, there also exists a finite capacity C⁰_P₁, which is determined by the DM-SWC, such that the forward key capacity is achievable if C_P₁≥ C⁰_P₁. Moreover, the key generation is saturated at capacity C_P₁= C⁰_P₁, and thus increasing the public channel capacity beyond C⁰_P₁ makes no improvement on the forward key capacity of the DM model. If the CSI is fully known at Bob in addition to Alice, C⁰_P₁=0, and so the public channel has no contribution in key generation when the public channel is in the forward direction. The achievable key agreement code of the DM model exploits both a random generator and the CSI as resources for key generation at Alice. The randomness property of channel states can be employed for key generation, and so the agreed keys depend on the CSI in general. However, a message is independent of the CSI in a secrecy problem. Hence, we justify that the forward key capacity can exceed both the main channel capacity and the secrecy capacity of the DM-SWC. In the Gaussian model, the wiretap channel is a Gaussian State-dependent Wiretap Channel (G-SWC) with Additive White Gaussian Interference (AWGI) having average power Λ. For simplicity, no side information is assumed at Bob and Eve. Bob's channel and Eve's channel suffer from Additive White Gaussian Noise (AWGN), where the correlation coefficient between noise of Bob's channel and that of Eve's channel is given by ϱ. We prove that the forward key capacity of the Gaussian model is independent of ϱ. Moreover, we establish that the forward key capacity is positive unless Eve's channel is less noisy than Bob's. We also prove that the key capacity of the Gaussian model vanishes if the G-SWC is physically degraded in Eve's favor. However, we justify that obtaining a positive key capacity is feasible even if Eve's channel is less noisy than Bob's according to our achieved LB on the key capacity for case (C_P₁, C_P₂)→ (∞, ∞). Hence, the key capacity of the Gaussian model is a function of ϱ. In this thesis, an LB on the forward key capacity of the Gaussian model is achieved. For a fixed Λ, the achievable key agreement code is optimum for any C_P₁∈[0,∞) in both low Signal-to-Interference Ratio (SIR) and high SIR regimes. We show that the forward key capacity is asymptotically independent of C_P₁ and Λ as the SIR goes to infinity, and thus the public channel and the interference have negligible contributions in key generation in the high SIR regime. On the other hand, the forward key capacity is a function of C_P₁ and Λ in the low SIR regime. Contributions of the interference and the public channel in key generation are significant in the low SIR regime that will be illustrated by simulations. The proposed key agreement code asymptotically achieves the forward key capacity of the Gaussian model for any SIR as C_P₁→ ∞. Hence, C_K(∞,0) is calculated, and it is suggested as a UB on C_K(C_P₁,0). Using simulations, we also compute the minimum required C_P₁ for which the forward key capacity is upper bounded within a given tolerance. The achievable key agreement code is designed based on a generalized version of the Dirty Paper Coding (DPC) in which transmitted signals are correlated with the CSI. The correlation coefficient is to be determined by C_P₁. In contrast to the DM model, the LB on the forward key capacity of a Gaussian model is a strictly increasing function of C_P₁ according to our simulations. This fact is an essential difference between this model and the DM model. For C_P₁=0 and a fixed Λ, the forward key capacity of the Gaussian model exceeds the main channel capacity of the G-SWC in the low SIR regime. By simulations, we show that the interference enhances key generation in the low SIR regime. In this regime, we also justify that the positive effect of the interference on the (forward) key capacity is generally more than its positive effect on the secrecy capacity of the G-SWC, while the interference has no influence on the main channel capacity of the G-SWC

Key Agreement with Physical Unclonable Functions and Biometric Identifiers

This thesis addresses security and privacy problems for digital devices and biometrics, where a secret key is generated for authentication, identification, or secure computations. A physical unclonable function (PUF) is a promising solution for local security in digital devices. A low-complexity transform-coding algorithm is developed to make the information-theoretic analysis tractable and motivate a noisy (hidden) PUF source model. The optimal trade-offs between the secret-key, privacy-leakage, and storage rates for multiple measurements of hidden PUFs are characterized. The first optimal and low-complexity code constructions are proposed. Polar codes are designed to achieve the best known rate tuples. The gains from cost-constrained controllable PUF measurements are illustrated to motivate extensions