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

Low complexity precoding for MIMOME wiretap channels based on cut-off rate

We propose a low complexity transmit signal design scheme for achieving information-theoretic secrecy over a MIMO wiretap channel driven by finite-alphabet inputs. We assume that the transmitter has perfect channel state information (CSI) of the main channel and also knows the statistics of the eavesdropper's channel. The proposed transmission scheme relies on jointly optimizing the precoder matrix and the artificial noise so as to maximize the achievable secrecy rates. In order to lower the computational complexity associated with the transmit signal design, we employ a design metric using the cut-off rate instead of the mutual information. We formulate a gradient-descent based optimization algorithm and demonstrate via extensive numerical examples that the proposed signal design scheme can yield an enhanced secrecy performance compared with the existing solutions in spite of its relatively lower computational complexity. The impacts of the modulation order as well as the number of antennas at the transmitter and receiver ends on the achievable secrecy rates are also investigated. © 2016 IEEE

Power allocation and signal labelling on physical layer security

PhD ThesisSecure communications between legitimate users have received considerable attention recently. Transmission cryptography, which introduces secrecy on the network layer, is heavily relied on conventionally to secure communications. However, it is theoretically possible to break the encryption if unlimited computational resource is provided. As a result, physical layer security becomes a hot topic as it provides perfect secrecy from an information theory perspective. The study of physical layer security on real communication system model is challenging and important, as the previous researches are mainly focusing on the Gaussian input model which is not practically implementable. In this thesis, the physical layer security of wireless networks employing finite-alphabet input schemes are studied. In particular, firstly, the secrecy capacity of the single-input single-output (SISO) wiretap channel model with coded modulation (CM) and bit-interleaved coded modulation (BICM) is derived in closed-form, while a fast, sub-optimal power control policy (PCP) is presented to maximize the secrecy capacity performance. Since finite-alphabet input schemes achieve maximum secrecy capacity at medium SNR range, the maximum amount of energy that the destination can harvest from the transmission while satisfying the secrecy rate constraint is computed. Secondly, the effects of mapping techniques on secrecy capacity of BICM scheme are investigated, the secrecy capacity performances of various known mappings are compared on 8PSK, 16QAM and (1,5,10) constellations, showing that Gray mapping obtains lowest secrecy capacity value at high SNRs. We propose a new mapping algorithm, called maximum error event (MEE), to optimize the secrecy capacity over a wide range of SNRs. At low SNR, MEE mapping achieves a lower secrecy rate than other well-known mappings, but at medium-to-high SNRs MEE mapping achieves a significantly higher secrecy rate over a wide range of SNRs. Finally, the secrecy capacity and power allocation algorithm (PA) of finite-alphabet input wiretap channels with decode-and-forward (DF) relays are proposed, the simulation results are compared with the equal power allocation algorithm

Physical-Layer Security in Wireless Communication Systems

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 $2$, 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 $3$ , 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 $4$, we consider a $K$-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 $\frac{K-1}{K}$ 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