An Overview of Physical Layer Security with Finite-Alphabet Signaling

Providing secure communications over the physical layer with the objective of achieving perfect secrecy without requiring a secret key has been receiving growing attention within the past decade. The vast majority of the existing studies in the area of physical layer security focus exclusively on the scenarios where the channel inputs are Gaussian distributed. However, in practice, the signals employed for transmission are drawn from discrete signal constellations such as phase shift keying and quadrature amplitude modulation. Hence, understanding the impact of the finite-alphabet input constraints and designing secure transmission schemes under this assumption is a mandatory step towards a practical implementation of physical layer security. With this motivation, this article reviews recent developments on physical layer security with finite-alphabet inputs. We explore transmit signal design algorithms for single-antenna as well as multi-antenna wiretap channels under different assumptions on the channel state information at the transmitter. Moreover, we present a review of the recent results on secure transmission with discrete signaling for various scenarios including multi-carrier transmission systems, broadcast channels with confidential messages, cognitive multiple access and relay networks. Throughout the article, we stress the important behavioral differences of discrete versus Gaussian inputs in the context of the physical layer security. We also present an overview of practical code construction over Gaussian and fading wiretap channels, and we discuss some open problems and directions for future research.Comment: Submitted to IEEE Communications Surveys & Tutorials (1st Revision

An Overview of Physical Layer Security with Finite Alphabet Signaling

Providing secure communications over the physical layer with the objective of achieving secrecy without requiring a secret key has been receiving growing attention within the past decade. The vast majority of the existing studies in the area of physical layer security focus exclusively on the scenarios where the channel inputs are Gaussian distributed. However, in practice, the signals employed for transmission are drawn from discrete signal constellations such as phase shift keying and quadrature amplitude modulation. Hence, understanding the impact of the finite-alphabet input constraints and designing secure transmission schemes under this assumption is a mandatory step towards a practical implementation of physical layer security. With this motivation, this article reviews recent developments on physical layer security with finite-alphabet inputs. We explore transmit signal design algorithms for single-antenna as well as multi-antenna wiretap channels under different assumptions on the channel state information at the transmitter. Moreover, we present a review of the recent results on secure transmission with discrete signaling for various scenarios including multi-carrier transmission systems, broadcast channels with confidential messages, cognitive multiple access and relay networks. Throughout the article, we stress the important behavioral differences of discrete versus Gaussian inputs in the context of the physical layer security. We also present an overview of practical code construction over Gaussian and fading wiretap channels, and discuss some open problems and directions for future research

Learning End-to-End Codes for the BPSK-constrained Gaussian Wiretap Channel

Finite-length codes are learned for the Gaussian wiretap channel in an end-to-end manner assuming that the communication parties are equipped with deep neural networks (DNNs), and communicate through binary phase-shift keying (BPSK) modulation scheme. The goal is to find codes via DNNs which allow a pair of transmitter and receiver to communicate reliably and securely in the presence of an adversary aiming at decoding the secret messages. Following the information-theoretic secrecy principles, the security is evaluated in terms of mutual information utilizing a deep learning tool called MINE (mutual information neural estimation). System performance is evaluated for different DNN architectures, designed based on the existing secure coding schemes, at the transmitter. Numerical results demonstrate that the legitimate parties can indeed establish a secure transmission in this setting as the learned codes achieve points on almost the boundary of the equivocation region

On the Secrecy Performance of Interference Exploitation with PSK: A non-Gaussian Signaling Analysis

Interference exploitation has recently been shown to provide significant security benefits in multi-user communication systems. In this technique, the known interference is designed to be constructive to the legitimate users and disruptive to the malicious receivers. Accordingly, this paper analyzes the secrecy performance of constructive interference (CI) precoding technique in multi-user multiple-input single-output (MU-MISO) systems with phase-shift-keying (PSK) signals and in the presence of multiple passive eavesdroppers. The secrecy performance of CI technique is comprehensively investigated in terms of symbol error probability (SEP), secrecy sum-rate, and intercept probability (IP). Firstly, new and exact analytical expressions for the average SEP of the legitimate users and the eavesdroppers are derived. In addition, for simplicity and in order to provide more insights, very accurate approximations of the average SEPs are presented in closed-form. Departing from classical Gaussian rate analysis, we employ finite constellation rate expressions to investigate the secrecy sum-rate. In this regard, closed-form analytical expression of the ergodic secrecy sum-rate is obtained. Then, based on the new secrecy sum-rate expression we propose adaptive modulation (AM) scheme with the aim to enhance the secrecy performance. Finally, we present analytical expressions of the IP with fixed and adaptive modulations. The analytical and simulation results demonstrate that, the interference exploitation technique can provide additional up to 17dB gain in the transmit SNR in terms of SEP, and up to 10dB gain in terms of the secrecy sum-rate and the IP, compared to the conventional interference suppression technique. Furthermore, significant performance improvement up to 66% can be achieved with the proposed AM scheme

Algorithms for Globally-Optimal Secure Signaling over Gaussian MIMO Wiretap Channels Under Interference Constraints

Multi-user Gaussian MIMO wiretap channel is considered under interference power constraints (IPC), in addition to the total transmit power constraint (TPC). Algorithms for \textit{global} maximization of its secrecy rate are proposed. Their convergence to the secrecy capacity is rigorously proved and a number of properties are established analytically. Unlike known algorithms, the proposed ones are not limited to the MISO case and are proved to converge to a \textit{global} rather than local optimum in the general MIMO case, even when the channel is not degraded. In practice, the convergence is fast as only a small to moderate number of Newton steps is required to achieve a high precision level. The interplay of TPC and IPC is shown to result in an unusual property when an optimal point of the max-min problem does not provide an optimal transmit covariance matrix in some (singular) cases. To address this issue, an algorithm is developed to compute an optimal transmit covariance matrix in those singular cases. It is shown that this algorithm also solves the dual (nonconvex) problems of \textit{globally} minimizing the total transmit power subject to the secrecy and interference constraints; it provides the minimum transmit power and respective signaling strategy needed to achieve the secrecy capacity, hence allowing power savings.Comment: accepted for publicatio

Subspace Decomposition of Coset Codes

A new method is explored for analyzing the performance of coset codes over the binary erasure wiretap channel (BEWC) by decomposing the code over subspaces of the code space. This technique leads to an improved algorithm for calculating equivocation loss. It also provides a continuous-valued function for equivocation loss, permitting proofs of local optimality for certain finite-blocklength code constructions, including a code formed by excluding from the generator matrix all columns which lie within a particular subspace. Subspace decomposition is also used to explore the properties of an alternative secrecy code metric, the chi squared divergence. The chi squared divergence is shown to be far simpler to calculate than equivocation loss. Additionally, the codes which are shown to be locally optimal in terms of equivocation are also proved to be globally optimal in terms of chi squared divergence.Comment: 36 pages, 2 figures, submitted to Transactions on Information Theor