Time and power allocation for the Gaussian wiretap channel with feedback of secret keys

This paper solves the time and power allocation problem for the simplest feedback scheme for the Gaussian wiretap channel, which is based on the transmission of random secret keys to be used in a one time pad manner. Specifically, the optimal transmission powers at Alice and Bob, as well as the time sharing factor between the feedback and feedforward channels, are given by the solution of a non-convex optimization problem, which is found by means of the golden section algorithm and the sequential solution of several convex optimization problems. Additionally, an specific and highly efficient procedure for the solution of the inner convex optimization problems is provided, which avoids the need for general purpose optimization packages. Finally, several simulation results illustrate the potential secrecy gains achievable with a feedback scheme as simple as the one considered in this paper

The Secrecy Capacity of The Gaussian Wiretap Channel with Rate-Limited Help

The Gaussian wiretap channel with rate-limited help, available at the legitimate receiver (Rx) or/and transmitter (Tx), is studied under various channel configurations (degraded, reversely degraded and non-degraded). In the case of Rx help and all channel configurations, the rate-limited help results in a secrecy capacity boost equal to the help rate irrespective of whether the help is secure or not, so that the secrecy of help does not provide any capacity increase. The secrecy capacity is positive for the reversely-degraded channel (where the no-help secrecy capacity is zero) and no wiretap coding is needed to achieve it. More noise at the legitimate receiver can sometimes result in higher secrecy capacity. The secrecy capacity with Rx help is not increased even if the helper is aware of the message being transmitted. The same secrecy capacity boost also holds if non-secure help is available to the transmitter (encoder), in addition to or instead of the same Rx help, so that, in the case of the joint Tx/Rx help, one help link can be omitted without affecting the capacity. If Rx/Tx help links are independent of each other, then the boost in the secrecy capacity is the sum of help rates and no link can be omitted without a loss in the capacity. Non-singular correlation of the receiver and eavesdropper noises does not affect the secrecy capacity and non-causal help does not bring in any capacity increase over the causal one.Comment: An extended version of the paper presented at the IEEE International Symposium on Information Theory, Helsinki, Finland, June 26 - July 1, 2022; submitted to IEEE Trans. Info. Theor

Joint Power Control in Wiretap Interference Channels

Interference in wireless networks degrades the signal quality at the terminals. However, it can potentially enhance the secrecy rate. This paper investigates the secrecy rate in a two-user interference network where one of the users, namely user 1, requires to establish a confidential connection. User 1 wants to prevent an unintended user of the network to decode its transmission. User 1 has to transmit such that its secrecy rate is maximized while the quality of service at the destination of the other user, user 2, is satisfied, and both user's power limits are taken into account. We consider two scenarios: 1) user 2 changes its power in favor of user 1, an altruistic scenario, 2) user 2 is selfish and only aims to maintain the minimum quality of service at its destination, an egoistic scenario. It is shown that there is a threshold for user 2's transmission power that only below or above which, depending on the channel qualities, user 1 can achieve a positive secrecy rate. Closed-form solutions are obtained in order to perform joint optimal power control. Further, a new metric called secrecy energy efficiency is introduced. We show that in general, the secrecy energy efficiency of user 1 in an interference channel scenario is higher than that of an interference-free channel

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

Priority-Aware Secure Precoding Based on Multi-Objective Symbol Error Ratio Optimization

The secrecy capacity based on the assumption of having continuous distributions for the input signals constitutes one of the fundamental metrics for the existing physical layer security (PHYS) solutions. However, the input signals of real-world communication systems obey discrete distributions. Furthermore, apart from the capacity, another ultimate performance metric of a communication system is its symbol error ratio (SER). In this paper, we pursue a radically new approach to PHYS by considering rigorous direct SER optimization exploiting the discrete nature of practical modulated signals. Specifically, we propose a secure precoding technique based on a multi-objective SER criterion, which aims for minimizing the confidential messages’ SER at their legitimate user, while maximizing the SER of the confidential messages leaked to the illegitimate user. The key to this challenging multi-objective optimization problem is to introduce a priority factor that controls the priority of directly minimizing the SER of the legitimate user against directly maximizing the SER of the leaked confidential messages. Furthermore, we define a new metric termed as the security-level, which is related to the conditional symbol error probability of the confidential messages leaked to the illegitimate user. Additionally, we also introduce the secure discrete-input continuous-output memoryless channel (DCMC) capacity referred to as secure-DCMC-capacity, which serves as a classical security metric of the confidential messages, given a specific discrete modulation scheme. The impacts of both the channel’s Rician factor and the correlation factor of antennas on the security-level and the secure-DCMC-capacity are investigated. Our simulation results demonstrate that the proposed priority-aware secure precoding based on the direct SER metric is capable of securing transmissions, even in the challenging scenario, where the eavesdropper has three receive antennas, while the legitimate user only has a single one

Distributed secrecy for information theoretic sensor network models

This dissertation presents a novel problem inspired by the characteristics of sensor networks. The basic setup through-out the dissertation is that a set of sensor nodes encipher their data without collaboration and without any prior shared secret materials. The challenge is dealt by an eavesdropper who intercepts a subset of the enciphered data and wishes to gain knowledge of the uncoded data. This problem is challenging and novel given that the eavesdropper is assumed to know everything, including secret cryptographic keys used by both the encoders and decoders. We study the above problem using information theoretic models as a necessary first step towards an understanding of the characteristics of this system problem. This dissertation contains four parts. The first part deals with noiseless channels, and the goal is for sensor nodes to both source code and encipher their data. We derive inner and outer regions of the capacity region (i.e the set of all source coding and equivocation rates) for this problem under general distortion constraints. The main conclusion in this part is that unconditional secrecy is unachievable unless the distortion is maximal, rendering the data useless. In the second part we thus provide a practical coding scheme based on distributed source coding using syndromes (DISCUS) that provides secrecy beyond the equivocation measure, i.e. secrecy on each symbol in the message. The third part deals with discrete memoryless channels, and the goal is for sensor nodes to both channel code and encipher their data. We derive inner and outer regions to the secrecy capacity region, i.e. the set of all channel coding rates that achieve (weak) unconditional secrecy. The main conclusion in this part is that interference allows (weak) unconditional secrecy to be achieved in contrast with the first part of this dissertation. The fourth part deals with wireless channels with fading and additive Gaussian noise. We derive a general outer region and an inner region based on an equal SNR assumption, and show that the two are partially tight when the maximum available user powers are admissible

A Novel Physical Layer Key Generation and Authenticated Encryption Protocol Exploiting Shared Randomness

The use of wireless networks for communication has grown significantly in recent times, and continues to develop further. The broadcast nature of wireless communications makes them susceptible to a wide variety of security attacks. Unlike traditional solutions, which usually handle security at the application layer, the primary concern of this dissertation is to analyse and develop solutions for secure communication using channel coding techniques at the physical-layer. The topic of physical layer authenticated encryption using high rate key generation through shared randomness is investigated in this work. First, a physical layer secret key generation scheme is discussed exploiting channel reciprocity in wireless systems. In order to address the susceptibility of this family of schemes to active attacks, a novel physical layer authentication encryption protocol is presented along with its extension to multi-node networks in the presence of active adversaries. Unlike previous work in the area of generating secret keys through shared randomness, it is demonstrated that the proposed scheme is semantically secure with respect to chosen plaintext and chosen cipher text attacks. Secondly, in order to increase the rate in bits per seconds at which agreed cryptographic keys are been generated, a multi-level quantization algorithm with public feedback is discussed. It is demonstrated that the proposed scheme is superior to direct information distillation approaches and can substantially increase the key generation rates even at low and medium SNRs. Furthermore, the employment of this low-overhead feedback at the information distillation process can largely simplify the information reconciliation process. The proposed secret key generation schemes are tested for randomness such as required for cryptographic keys. The validation test is perfomed with the aid of National Institute of Standards and Technology (NIST) statistical test suite. The P-values obtained in each of the test carried out indicates that the key sequence generated by our algorithm is random

Advances in Resource Allocation Optimization for Multiuser Wireless Systems with Joint Energy and Information Transfer

Ph.DDOCTOR OF PHILOSOPH

Polar codes combined with physical layer security on impulsive noise channels

Ph. D. ThesisThe need for secure communications is becoming more and more impor- tant in modern society as wired and wireless connectivity becomes more ubiquitous. Currently, security is achieved by using well established encryption techniques in the upper layers that rely on computational complexity to ensure security. However, processing power is continu- ally increasing and well-known encryption schemes are more likely to be cracked. An alternative approach to achieving secure communication is to exploit the properties of the communication channel. This is known as physical layer security and is mathematically proven to be secure. Phys- ical layer security is an active research area, with a significant amount of literature covering many different aspects. However, one issue that does not appear to have been investigated in the literature is the effect on physical layer security when the noise in the communication channel is impulsive. Impulsive noise adds large spikes to the transmitted signal for very short durations that can significantly degrade the signal. The main source of impulsive noise in wireless communications is electromag- netic interference generated by machinery. Therefore, this project will investigate the effect of impulsive noise on physical layer security. To ensure a high level of performance, advanced error-correcting codes are needed to correct the multiple errors due to this harsh channel. Turbo and Low-Density Parity-Check (LDPC) codes are capacity-approaching codes commonly used in current wireless communication standards, but their complexity and latency can be quite high and can be a limiting fac- tor when required very high data rates. An alternative error-correcting code is the polar code, which can actually achieve the Shannon capacity on any symmetric binary input discrete memoryless channel (B-DMC). Furthermore, the complexity of polar codes is low and this makes them an attractive error-correcting code for high data rate wireless commu- nications. In this project, polar codes are combined with physical layer security and the performance and security of the system is evaluated on impulsive noise channels for the first time. This project has three contributions: Polar codes designed for impulsive noise channels using density evo- lution are combined with physical layer security on a wire-tap chan- nel experiencing impulsive noise. The secrecy rate of polar codes is maximised. In the decoding of polar codes, the frozen bits play an important part. The posi- tions of the frozen bits has a significant impact on performance and therefore, the selection of optimal frozen bits is presented to opti- mise the performance while maintaining secure communications on impulsive noise wire-tap channels. Optimal puncturing patterns are investigated to obtain polar codes with arbitrary block lengths and can be applied to different modu- lation schemes, such as binary phase shift keying (BPSK) and M- ary Quadrature Amplitude Modulation (QAM), that can be rate compatible with practical communication systems. The punctured polar codes are combined with physical layer security, allowing the construction of a variety of different code rates while maintaining good performance and security on impulsive noise wire-tap chan- nels. The results from this work have demonstrated that polar codes are ro- bust to the effects of impulsive noise channel and can achieve secure communications. The work also addresses the issue of security on im- pulsive noise channels and has provided important insight into scenarios where the main channel between authorised users has varying levels of impulsiveness compared with the eavesdropper's channel. One of the most interesting results from this thesis is the observation that polar codes combined with physical layer security can achieve good perfor- mance and security even when the main channel is more impulsive than the eavesdropper's channel, which was unexpected. Therefore, this thesis concludes that the low-complexity polar codes are an excellent candidate for the error-correcting codes when combined with physical layer security in more harsh impulsive wireless communication channels