Fading Wiretap Channels Research Articles

Performance Analysis of Short Packet Communications With Multiple Eavesdroppers

This paper studies the performance of short packet communications in the presence of multiple eavesdroppers. We start our investigation by examining the fading wiretap channel, where the communication is overheard by multiple non-colluding single antenna eavesdroppers. A closed-form expression for the average secrecy throughput is derived, when the transmitter has a single antenna. The Monte-Carlo simulations show a close match of the analytical expression with the numerical results. Moreover, the optimal blocklength value that maximizes the secrecy throughput is determined, when the communication is observed by single and multiple eavesdroppers. We then extend our analysis for the case of a multiple-antenna transmitter and consider artificial noise (AN) to confuse the eavesdroppers. A closed-form expression for the average secrecy throughput is obtained for the scenario of a two-antenna transmitter and two eavesdroppers with a single antenna. The results demonstrate the validity of the approximation when compared with Monte-Carlo simulations. The results further reveal that an increased number of antennas at the transmitter is associated with higher average secrecy throughput and applying AN helps to eliminate the harm of the eavesdroppers.

Analysis of side information impact on the physical layer security performances in wireless wiretap channel

AbstractInformation‐theoretic analysis of the communication systems performances is of practical and theoretical importance. In this article, we study side information impact on physical layer security in a Rayleigh fading wiretap channel by deriving closed‐form expressions for the average secrecy capacity (ASC), secrecy outage probability (SOP), secrecy coverage region (SCR), and specifically, the asymptotic behavior of SOP. The results, while including previous works as special cases, show that side information has positive effects over ASC and SOP, and also, it increases the SCR, as expected intuitively. Numerical evaluations have been done to support the claims.

Secrecy Performance of Eigendecomposition-Based FTN Signaling and NOFDM in Quasi-Static Fading Channels

In this paper, we investigate the information-theoretic secrecy performance of recent precoded faster-than-Nyquist signaling (FTN) with the aid of optimal power allocation in eigenspace. More specifically, the secrecy rate and secrecy outage probability of a fading wiretap channel, which was derived for classical Nyquist-based orthogonal signaling transmission, is extended to those of our eigendecompsition-based FTN (E-FTN) signaling for a quasi-static frequency-flat Rayleigh fading channel. Our performance results demonstrate that the proposed E-FTN signaling scheme exhibits improvements in secrecy rate and secrecy outage probability over conventional Nyquist-based and FTN signaling transmission, assuming employment of a root-raised cosine filter. We also show that the same benefits as those of single-carrier E-FTN signaling are attainable by its non-orthogonal multicarrier counterpart, where subcarrier spacing is set lower than that of orthogonal frequency-division multiplexing.

Transmission rate conditions for distributed filtering in sensor networks against eavesdropper

This paper studies the distributed secure estimation problem of sensor networks (SNs) in the presence of eavesdroppers. In an SN, sensors communicate with each other through digital communication channels, and the eavesdropper overhears the messages transmitted by the sensors over fading wiretap channels. The increasing transmission rate plays a positive role in the detectability of the network while playing a negative role in the secrecy. Two types of SNs under two cooperative filtering algorithms are considered. For networks with collectively observable nodes and the Kalman filtering algorithm, by studying the topological entropy of sensing measurements, a sufficient condition of distributed detectability and secrecy, under which there exists a code–decode strategy such that the sensors’ estimation errors are bounded while the eavesdropper’s error grows unbounded, is given. For collectively observable SNs under the consensus Kalman filtering algorithm, by studying the topological entropy of the sensors’ covariance matrices, a necessary condition of distributed detectability and secrecy is provided. A simulation example is given to illustrate the results.

Well-Rounded Lattices: Towards Optimal Coset Codes for Gaussian and Fading Wiretap Channels

The design of lattice coset codes for wiretap channels is considered. Bounds on the eavesdropper's correct decoding probability and information leakage are first revisited. From these bounds, it is explicit that both the information leakage and error probability are controlled by the average flatness factor of the eavesdropper's lattice, which we further interpret geometrically. It is concluded that the minimization of the (average) flatness factor of the eavesdropper's lattice leads to the study of well-rounded lattices, which are shown to be among the optimal in order to achieve these minima. Constructions of some well-rounded lattices are also provided.

Secure Degrees of Freedom of MIMO Two-Way Wiretap Channel With no CSI Anywhere

This article considers a two-way multiple-input multiple-output (MIMO) Rayleigh block fading wiretap channel with two full-duplex nodes (Alice and Bob) exchanging messages simultaneously and wiretapped by a $ {N}_{ {e}}$ -antennas eavesdropper (Eve). The channel state remains unchanged over a coherence interval T and is unknown to all terminals, including Alice, Bob, and Eve, at the beginning of the coherence interval. We first show the expression of the optimal signal waveform for Alice and Bob, which maximizes the sum secrecy rate, should be the products of independent random diagonal matrices and isotropically distributed unitary matrices. Then, conditioned on large T and small $ {N}_{ {e}}$ , the upper-bound for the secure degree of freedom (s.d.o.f.) of the two-way wiretap channel is derived, and a constant-norm-signaling (CNS) scheme is presented to achieve this theoretical bound. Finally, we formulate an optimization problem of the s.d.o.f. achieved by the CNS scheme for general cases with arbitrary T and $ {N}_{ {e}}$ , and solve this problem by exploring the monotonicity of the achievable s.d.o.f.. Our result shows that the optimal s.d.o.f. can be independent of coherence time T and becomes the product of the numbers of legitimate nodes’s transmitter antennas (NLNTA) for large $ {N}_{ {e}}$ and small NLNTA.

Copula-Based Analysis of Physical Layer Security Performances Over Correlated Rayleigh Fading Channels

This paper studies performance analysis of physical layer security in a Rayleigh fading wiretap channel, where, the main (transmitter-to-legitimate receiver) and eavesdropper (transmitter-to-eavesdropper) channel coefficients are correlated. By exploiting the novel approach called Copula theory, we derive closed-form expressions for average secrecy capacity (ASC), secrecy outage probability (SOP), and secrecy coverage region (SCR). Moreover, to more evaluate the impact of channel correlation, the asymptotic behavior of SOP in high signal-to-noise ratio (SNR) regime and other scenarios is studied, and finally, the analytical results are illustrated numerically under the positive dependence, independence, and negative dependence structures. Based on the insights from this analysis, we found that the effect of correlated fading on the performance of physical layer security can be helpful or harmful in different scenarios, depending on the structure of dependency between the main and eavesdropper channels.

Secrecy Performance of an Artificial Noise Assisted Transmission Scheme With Active Eavesdropper

In this letter, the performance of an artificial noise assisted ON-OFF scheme for a Rayleigh fading wiretap channel under active attack is analyzed. The closed-form expressions for various performance metrics such as generalized secrecy outage probability (GSOP) and average fractional equivocation (AFE) has been obtained. The developed results take account of the degree of self-interference cancellation at the eavesdropper, which results due to its full-duplex operation. The derived results help to explore the role of artificial noise transmission and fading on the secrecy performance of the system under active attack. The work explores the trade-off between transmission probability and GSOP with the help of artificial noise transmission. The derived results also characterizes the performance of the artificial noise assisted scheme when the eavesdropper is passive.

Physical layer security over fading wiretap channels through classic coded transmissions with finite block length and discrete modulation

The chance to use existing coded transmission schemes for achieving some security at the physical layer besides reliability is of interest for many applications. In this paper, we assess the levels of physical layer security achievable by classic coding schemes over fading wiretap channels, taking into account the effects of finite block lengths and discrete modulations. In order to take these practical constraints into account, some previous works use the error rates experienced by legitimate receivers and eavesdroppers as reliability and security metrics, respectively. However, having a high error rate at the eavesdropper is a necessary but not a sufficient condition for security, thus we resort to more robust information theoretic security metrics for such a purpose. By focusing on mutual information security, we estimate the average number of attempts required by an attacker to recover the whole message in practical conditions and under outage constraints. Based on this metric, higher layer cryptographic protocols can be designed to achieve robust security built upon the physical layer. We obtain lower bounds on the wiretapper equivocation about the secret message, subject to some outage probability, and assess their tightness. We provide some examples considering classic coding and modulation techniques like extended Bose–Chaudhuri–Hocquenghem codes and convolutional codes with binary signaling.

On Physical Layer Security Over Fox's $H$-Function Wiretap Fading Channels

Most of the well-known fading distributions, if not all of them, could be encompassed by the Fox's H-function fading. Consequently, we investigate the physical layer security over Fox's H-function fading wiretap channels, in the presence of non-colluding and colluding eavesdroppers. In particular, for the non-colluding scenario, closed-form expressions are derived for the secrecy outage probability (SOP), the probability of non-zero secrecy capacity, and the average secrecy capacity. These expressions are given in terms of either univariate or bivariate Fox's H-function. In order to show the effectiveness of our derivations, three metrics are respectively listed over the following frequently used fading channels, including Rayleigh, Weibull, Nakagami-m, α - μ, Fisher-Snedecor (F-S) F, and extended generalized-K. Our tractable results are not only straightforward and general, but also feasible and applicable, especially the SOP, which is usually limited to the lower bound in the literature due to the difficulty of deriving closed-from analytical expressions. For the colluding scenario, a super eavesdropper equipped with maximal ratio combining (MRC) or selection-combining (SC) schemes is characterized. The lower bound of SOP and exact PNZ are thereafter derived with closed-form expressions in terms of the multivariate Fox's H-function. In order to validate the accuracy of our analytical results, Monte Carlo simulations are subsequently conducted for the aforementioned fading channels. One can observe that for the former non-colluding scenario, we have perfect agreement between the exact analytical and simulation results, and highly accurate approximations between the exact and asymptotic analytical results. On the contrary, the SOP and PNZ of colluding eavesdropper is greatly degraded with the increase of the number of eavesdroppers. Also, the so-called super eavesdropper with MRC is much powerful to wiretap the main channel than the one with SC.

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 toward a practical implementation of physical layer security. With this motivation, this paper 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.

Fountain-Coding-Based Secure Communications Exploiting Outage Prediction and Limited Feedback

This paper develops a fountain-coding-based scheme to secure communications over fading wiretap channels, in which the transmission between the legitimate nodes is overheard by a malicious eavesdropper. The transmitter first splits its message into K source packets and generates a potentially infinite number of fountain-coded packets, each of which is the XOR of distinct source packets chosen according to the channel feedback. Based on the characteristics of fountain-coded transmissions, a sufficient number of independent coded packets have to be successfully received to recover the original source message. Therefore, secrecy is guaranteed if the legitimate receiver can accumulate the required number of coded packets before the eavesdropper does. To realize this, we propose to exploit outage prediction and channel feedback to optimize the fountain encoding procedure. To be more specific, upon the reception of any packet, the receiver predicts the conditional outage probability of the next slot's transmission based on the current channel state and notifies the transmitter to adjust the structure of the fountain code accordingly. In this manner, the encoder design matches well with the time-varying channel conditions of the legitimate link such that the receiver can achieve a high accumulation rate for the fountain packets. Meanwhile, because of the mismatch between the fountain encoder and the eavesdropper's channel, it is extremely difficult for the eavesdropper to collect enough independent fountain-coded packets, and transmission secrecy is thus guaranteed. Simulation results demonstrate that the proposed scheme outperforms the existing candidate solutions in terms of the intercept probability, the decoding delay at the legitimate receiver, and the achievable throughput, as well as the quality-of-service violating probability.

Optimal Target Secrecy Rate and Power Allocation Policy for a SWIPT System Over a Fading Wiretap Channel

The simultaneous wireless information and power transfer (SWIPT) technique is regarded as a promising approach to enhance performance of wireless networks with limited energy supply. However, due to the broadcast nature of wireless radio, the energy receiver may act as a potential eavesdropper to eavesdrop the information sent to the information receiver. To address this issue, in this paper, we propose an optimization framework of the target secrecy rate and the power allocation ratio based on the secrecy outage probability and the effective secrecy throughput in the SWIPT system over fading wiretap channel. Moreover, we derive the closed-form expression of the secrecy outage probability and the effective secrecy throughput for two secrecy transmission modes. Furthermore, we formulate the effective secrecy throughput maximization problem under the reliability constraint in the on–off and adaptive transmission modes and provide the closed-form optimal solutions of the power allocation ratio and the target secrecy rate. Finally, we provide numerical results that give an insight into the effect of various system parameters on the secrecy outage probability and the effective secrecy throughput, such as the target secrecy rate, the power allocation ratio, and average gains of the main channel and the eavesdropper channel.

Almost Universal Codes for MIMO Wiretap Channels

Despite several works on secrecy coding for fading and MIMO wiretap channels from an error probability perspective, the construction of information-theoretically secure codes over such channels remains an open problem. In this paper, we consider a fading wiretap channel model where the transmitter has only partial statistical channel state information. Our channel model includes static channels, i.i.d. block fading channels, and ergodic stationary fading with fast decay of large deviations for the eavesdropper's channel. We extend the flatness factor criterion from the Gaussian wiretap channel to fading and MIMO wiretap channels, and establish a simple design criterion where the normalized product distance / minimum determinant of the lattice and its dual should be maximized simultaneously. Moreover, we propose concrete lattice codes satisfying this design criterion, which are built from algebraic number fields with constant root discriminant in the single-antenna case, and from division algebras centered at such number fields in the multiple-antenna case. The proposed lattice codes achieve strong secrecy and semantic security for all rates $R<C_b-C_e-\kappa$, where $C_b$ and $C_e$ are Bob and Eve's channel capacities respectively, and $\kappa$ is an explicit constant gap. Furthermore, these codes are almost universal in the sense that a fixed code is good for secrecy for a wide range of fading models. Finally, we consider a compound wiretap model with a more restricted uncertainty set, and show that rates $R<\bar{C}_b-\bar{C}_e-\kappa$ are achievable, where $\bar{C}_b$ is a lower bound for Bob's capacity and $\bar{C}_e$ is an upper bound for Eve's capacity for all the channels in the set.

Analysis of short blocklength codes for secrecy

In this paper, we provide secrecy metrics applicable to physical-layer coding techniques with finite blocklengths over Gaussian and fading wiretap channel models and analyze their secrecy performance over several cases of concatenated code designs. Our metrics go beyond some of the known practical secrecy measures, such as bit error rate and security gap, so as to make lower bound probabilistic guarantees on error rates over short blocklengths both preceding and following a secrecy decoder. Our techniques are especially useful in cases where application of traditional information-theoretic security measures is either impractical or simply not yet understood. The metrics can aid both practical system analysis, including cryptanalysis, and practical system design when concatenated codes are used for physical-layer security. Furthermore, these new measures fill a void in the current landscape of practical security measures for physical-layer security coding and may assist in the wide-scale adoption of physical-layer techniques for security in real-world systems. We also show how the new metrics provide techniques for reducing realistic channel models to simpler discrete memoryless wiretap channel equivalents over which existing secrecy code designs may achieve information-theoretic security.

Secrecy Transmission Scheme Based on 2-D Polar Coding Over Block Fading Wiretap Channels

This letter discusses a secrecy transmission scheme based on 2-D polar coding over block fading wiretap channels. Unlike the previous approaches using 1-D polar coding, we propose to encode the secret bits in two dimensions to adapt to variation of the instantaneous secrecy capacity. In the proposed scheme, intra-block coding in one dimension is used to guarantee reliability, and cross-block coding in the other dimension is used to combat eavesdropping. Theoretical analysis demonstrates that our scheme is able to achieve the maximum perfect secrecy rate asymptotically. Simulation results show that the equivocation rate of eavesdropper is close to the secrecy capacity of the system with finite codelength.

Enhancing secrecy rates in a wiretap channel

Reliable communication imposes an upper limit on the achievable rate, namely the Shannon capacity. Wyner's wiretap coding ensures a security constraint and reliability, but results in a decrease of achievable rate. To mitigate the loss in secrecy rate, we propose a coding scheme in which we use sufficiently old messages as key and prove that multiple messages are secure with respect to all the information possessed by the eavesdropper. We also show that we can achieve security in the strong sense. Next, we study a fading wiretap channel with full channel state information of the eavesdropper's channel and use our coding/decoding scheme to achieve a secrecy capacity close to the Shannon capacity of the main channel (in the ergodic sense). Finally, we study a case where the transmitter does not have instantaneous information of the channel state of the eavesdropper, but only its distribution.

Secure On–Off Transmission in Slow Fading Wiretap Channel With Imperfect CSI

This paper investigates the slow fading single-antenna wiretap channel with imperfect channel state information (CSI) and studies an on–off transmission scheme with fixed communication rate, secrecy rate, and transmit power for maximizing the secrecy throughput under the constraints of secrecy outage probability (SOP) and reliability outage probability (ROP). We first solve this problem in a special case without ROP constraint for which the optimal secrecy throughput is obtained under SOP constraint. The result for the special case gives us an upper bound for the secrecy throughput with imperfect CSI. With the help of this special case, a general case with ROP constraint is studied. In this case, the problem is transformed into a one-dimensional (1-D) search problem on a finite interval, which can be solved either by the exhaustive 1-D search to obtain the optimal solution or by the golden search method (GSM) to obtain a suboptimal solution. Simulation results are finally presented to validate the theoretical analysis and show that the performance obtained by using the GSM based 1-D search is very close to that of exhaustive 1-D search.

Semantic Security with Practical Transmission Schemes over Fading Wiretap Channels

We propose and assess an on–off protocol for communication over wireless wiretap channels with security at the physical layer. By taking advantage of suitable cryptographic primitives, the protocol we propose allows two legitimate parties to exchange confidential messages with some chosen level of semantic security against passive eavesdroppers, and without needing either pre-shared secret keys or public keys. The proposed method leverages the noisy and fading nature of the channel and exploits coding and all-or-nothing transforms to achieve the desired level of semantic security. We show that the use of fake packets in place of skipped transmissions during low channel quality periods yields significant advantages in terms of time needed to complete transmission of a secret message. Numerical examples are provided considering coding and modulation schemes included in the WiMax standard, thus showing that the proposed approach is feasible even with existing practical devices.

Secrecy-Enhancing Signaling Schemes for Fast-Varying Wiretap Channels With Only CSI at the Transmitter

This paper proposes secrecy-enhancing signaling schemes to exploit the advantages of having only channel state information (CSI) at the transmitter, but no (or limited) CSI at the receiver and the eavesdropper in fast-fading wiretap channels and also in wiretap channels with Gaussian interference. With only CSI at the transmitter, the transmit signaling can be designed to precompensate for the distortion or the interference on the main channel to facilitate decoding at the receiver while leaving the eavesdropper confused by the uncertainties of its own channel. In fading wiretap channels, truncated channel-inversion and phase-compensation schemes are proposed to achieve this task. Here, truncation is used so that transmission occurs only when the main channel is sufficiently reliable. In wiretap channels with Gaussian interference, a truncated interference-nulling scheme is proposed to enable interference precancellation at the transmitter. The proposed signaling schemes exploit the advantages of having only CSI at the transmitter without employing more complex encoding schemes. The achievable secrecy rates are derived using Gaussian input, and approximate expressions are proposed for the optimization of system parameters. The effectiveness of the proposed transmission schemes and the advantages of having only CSI at the transmitter are demonstrated through numerical simulations.