Mutual information neural estimation (MINE) and related variational estimators are increasingly used as empirical eavesdropper-leakage indicators in wireless physical-layer security (PLS) systems that lack a closed-form secrecy rate. We ask whether, given a matched estimation target, such estimators recover the true eavesdropper mutual information (MI). Across three wiretap systems of increasing complexity—a Gaussian wiretap, an orthogonal frequency-division multiple access (OFDMA) Rayleigh-fading wiretap, and a discrete-codebook sparse code multiple access (SCMA) wiretap test bed—we compare each held-out estimate against its own numerically computed reference, spanning four lower-bound estimators (DV/MINE, NWJ, SMILE, InfoNCE) and one upper-bound estimator (CLUB). Three findings emerge. i) A three-tier reliability hierarchy (estimator-vs-reference slopes $0.98 / 0.76 / 0.05$ ): the estimate tracks the truth for the Gaussian wiretap, underestimates it for the discrete codebook, and collapses for the OFDMA fading channel. ii) The fading collapse persists even with the matched target $(Y_{E},H_{E})$ —recovering only 5–17% of the true conditional MI despite larger budgets and longer training, consistent with a function-class/finite-sample limitation under the tested protocols rather than a simple training-length failure. All four lower-bound estimators collapse; CLUB is not a reliable substitute—it overestimates the truth on the calibrated systems yet itself falls below the true MI under fading—so neither bound direction gives a reliable absolute leakage value. iii) Paired-design rankings are preserved only for single-parameter, large-separation comparisons; under multiple coupled variables ranking falls to chance on the hardest high-leakage pairs and is at best weakly rank-correlated overall (Kendall $\tau = 0.27$ ). We conclude that a near-zero neural MI estimate can coincide with substantial true leakage, so—for the tested estimators, critic families, sample budgets, and channel models—these estimators are unsafe as absolute eavesdropper-leakage indicators in the tested fading-mixture regime and should be used for comparative ranking only under matched, single-parameter, clearly separated designs, not for coupled multi-variable selection.
Mutual information neural estimation (MINE) and related variational estimators are increasingly used as empirical eavesdropper-leakage indicators in wireless physical-layer security (PLS) systems that lack a closed-form secrecy rate. We ask whether, given a matched estimation target, such estimators recover the true eavesdropper mutual information (MI). Across three wiretap systems of increasing complexity—a Gaussian wiretap, an orthogonal frequency-division multiple access (OFDMA) Rayleigh-fading wiretap, and a discrete-codebook sparse code multiple access (SCMA) wiretap test bed—we compare each held-out estimate against its own numerically computed reference, spanning four lower-bound estimators (DV/MINE, NWJ, SMILE, InfoNCE) and one upper-bound estimator (CLUB). Three findings emerge. i) A three-tier reliability hierarchy (estimator-vs-reference slopes 0.98/0.76/0.05 ): the estimate tracks the truth for the Gaussian wiretap, underestimates it for the discrete codebook, and collapses for the OFDMA fading channel. ii) The fading collapse persists even with the matched target (YE,HE) —recovering only 5–17% of the true conditional MI despite larger budgets and longer training, consistent with a function-class/finite-sample limitation under the tested protocols rather than a simple training-length failure. All four lower-bound estimators collapse; CLUB is not a reliable substitute—it overestimates the truth on the calibrated systems yet itself falls below the true MI under fading—so neither bound direction gives a reliable absolute leakage value. iii) Paired-design rankings are preserved only for single-parameter, large-separation comparisons; under multiple coupled variables ranking falls to chance on the hardest high-leakage pairs and is at best weakly rank-correlated overall (Kendall τ=0.27 ). We conclude that a near-zero neural MI estimate can coincide with substantial true leakage, so—for the tested estimators, critic families, sample budgets, and channel models—these estimators are unsafe as absolute eavesdropper-leakage indicators in the tested fading-mixture regime and should be used for comparative ranking only under matched, single-parameter, clearly separated designs, not for coupled multi-variable selection.
Recently, some researches are devoted to the topic of end-to-end learning a physical layer secure communication system based on autoencoder under Gaussian wiretap channel. However, in those works, the reliability and security of the encoder model were learned through necessary decoding outputs of not only legitimate receiver but also the eavesdropper. In fact, the assumption of known eavesdropper's decoder or its output is not practical. To address this issue, in this paper we propose a dual mutual information neural estimation (MINE) based neural secure communications model. The security constraints of this method is constructed only with the input and output signal samples of the legal and eavesdropper channels and benefit that training the encoder is completely independent of the decoder. Moreover, since the design of secure coding does not rely on the eavesdropper's decoding results, the security performance would not be affected by the eavesdropper's decoding means. Numerical results show that the performance of our model is guaranteed whether the eavesdropper learns the decoder himself or uses the legal decoder.
Intrigued by the rapid growth and expand of wireless devices, data security is increasingly playing a significant role in our daily transactions and interactions with different entities. Possible examples, including e-healthcare information and online shopping, are becoming vulnerable due to the intrinsic nature of wireless transmission medium and the widespread open access of wireless links. Traditionally, the communication security is mainly regarded as the tasks at the upper layers of layered protocol stack, security techniques, including personal access control, password protection, and end-to-end encryption, have been widely studied in the open literature. More recently, plenty of research interests have been drawn to the physical layer forms of secrecy. As a new but appealing paradigm at physical layer, physical layer security is based on two pioneering works: (i) Shannon’s information-theoretic formulation and (ii) Wyner’s wiretap formulation. \n \nOn account of the fundamental of physical layer security and the different nature of various wireless network, this dissertation is supposed to further fill the lacking of the existing research outcomes. To be specific, the contributions of this dissertation can be summarized as three-fold:(i) exploration of secrecy metrics to more general fading channels; (ii) characterization a new fading channel model and its reliability and security analysis in digital communication systems; and (iii) investigation of physical layer security over the random multiple-input multiple-output (MIMO) α −μ fading channels. \n \nTaking into account the classic Alice-Bob-Eve wiretap model, the first contribution can be divided into four aspects: (i) we have investigated the secrecy performance over single-input single-output (SISO) α −μ fading channels. The probability of non-zero (PNZ) secrecy capacity and the lower bound of secrecy outage probability (SOP) are derived for the special case when the main channel and wiretap channel undergo the same non-linearity fading parameter, i.e., α. Later on, for the purpose of filling the gap of lacking closed-form expression of SOP in the open literature and extending the obtained results in chapter 2 to the single-input multiple-output (SIMO) α − μ wiretap fading channels, utilizing the fact that the received signal-tonoise ratios (SNRs) at the legitimate receiver and eavesdropper can be approximated as new α −μ distributed random variables (RVs), the SOP metric is therefore derived, and given in terms of the bivariate Fox’s H-function; (ii) the secrecy performance over the Fisher-Snedecor F wiretap fading channels is initially considered. The SOP, PNZ, and ASC are finalized in terms of Meijer’s G-function; (iii) in order to generalize the obtained results over α −μ and Fisher-Snedecor F wiretap fading channels, a more flexible and general fading channel, i.e., Fox’s H-function fading model, are taken into consideration. Both the exact and asymptotic analysis of SOP, PNZ, and average secrecy capacity (ASC), are developed with closed-form expressions; and (iv) finally, motivated by the fact that the mixture gamma (MG) distribution is an appealing tool, which can be used to model the received instantaneous SNRs over wireless fading channels, the secrecy metrics over wiretap fading channels are derived based on the MG approach. \n \nDue to the limited transmission power and communication range, cooperative relays or multi-hop wireless networks are usually regarded as two promising means to address these concerns. Inspired by the obtained results in Chapters 2 and 3, the second main contribution is to propose a novel but simple fading channel model, namely, the cascaded α −μ. This new distribution is advantageous since it encompasses the existing cascaded Rayleigh, cascaded Nakagami-m, and cascaded Weibull with ease. Based on this, both the reliability and secrecy performance of a digital system over cascaded α −μ fading channels are further evaluated. Closed-form expressions of reliability metrics (including amount of fading (AF), outage probability, average channel capacity, and average symbol error probability (ABEP).) and secrecy metrics (including SOP, PNZ, and ASC) are respectively provided. Besides, their asymptotic behaviors are also performed and compared with the exact results. \n \nConsidering the impacts of users’ densities, spatial distribution, and the path-loss exponent on secrecy issue, the third aspect of this thesis is detailed in Chapter 8 as the secrecy investigation of stochastic MIMO system over α −μ wiretap fading channels. Both the stochastic geometry and conventional space-time transmission (STT) scheme are used in the system configuration. The secrecy issue is mathematically evaluated by three metrics, i.e., connection outage, the probability of non-zero secrecy capacity and the ergodic secrecy capacity. Those three metrics are later on derived regarding two ordering scheme, and further compared with Monte-Carlo simulations.
Physical-layer security uses the noise already present in the channel to keep a message secret without making any assumption about the eavesdropper's computing power. In Wyner's wiretap channel model, coset coding uses randomness to map the message to many codewords and protects against information leakage from an active eavesdropper. The secrecy provided by such codes is measured by their equivocation, which is the eavesdropper's remaining uncertainty about the message after she observes her channel. So computing equivocation is an important aspect of analyzing the wiretap channel model. Many channels of practical interest have no closed-form expression for equivocation, and exact calculation has been limited to a few specific channels. This dissertation studies the equivocation analysis of coset codes along two complementary directions. When a channel offers no closed-form solution, we estimate the information leakage with a neural network called the mutual information neural estimator (MINE). And for a discrete memoryless channel, we derive a general framework for the exact equivocation. The first study builds coset codes from short Reed-Muller codes and tests them over the air in a real indoor environment with software-defined radios. In this study, the secrecy is estimated using MINE, and short coset codes are shown to provide a secrecy advantage. The second study proposes a low-density parity-check (LDPC) code that injects artificial noise by flipping a chosen set of coded bits over a Gaussian wiretap channel. The third study moves from estimation to exact analysis. It examines coset coding over the Ghost Modulation wiretap channel, which is modeled as an asymmetric binary crossover erasure channel (ABCEC). Then it derives exact expressions for both the equivocation and the secrecy capacity. The final study generalizes the exact analysis to any discrete memoryless channel and verifies the framework against well-studied channels. Finally, it applies the developed framework to the asymmetric Z-channel with an efficient formulation that greatly reduces the computational cost.
Abstract Physical layer security (PLS) has been proposed to afford an extra layer of security on top of the conventional cryptographic techniques. Unlike the conventional complexity-based cryptographic techniques at the upper layers, physical layer security exploits the characteristics of wireless channels, e.g., fading, noise, interference, etc., to enhance wireless security. It is proved that secure transmission can benefit from fading channels. Accordingly, numerous researchers have explored what fading can offer for physical layer security, especially the investigation of physical layer security over wiretap fading channels. Therefore, this paper aims at reviewing the existing and ongoing research works on this topic. More specifically, we present a classification of research works in terms of the four categories of fading models: (i) small-scale, (ii) large-scale, (iii) composite, and (iv) cascaded. To elaborate these fading models with a generic and flexible tool, three promising candidates, including the mixture gamma (MG), mixture of Gaussian (MoG), and Fox’sH-function distributions, are comprehensively examined and compared. Their advantages and limitations are further demonstrated via security performance metrics, which are designed as vivid indicators to measure how perfect secrecy is ensured. Two clusters of secrecy metrics, namely (i) secrecy outage probability (SOP), and the lower bound of SOP; and (ii) the probability of nonzero secrecy capacity (PNZ), the intercept probability, average secrecy capacity (ASC), and ergodic secrecy capacity, are displayed and, respectively, deployed in passive and active eavesdropping scenarios. Apart from those, revisiting the secrecy enhancement techniques based on Wyner’s wiretap model, the on-off transmission scheme, jamming approach, antenna selection, and security region are discussed.
In this paper, under correlated shadowing channels-a propagation model that accurately reflects real-world wireless environment-we consider a multi-eavesdropper wiretap channel, in which several passive eavesdroppers independently try to intercept the legitimate transmission over the primary communication path from the transmitter (Tx) to the authorized receiver (Rx), constituting a realistic threat model, and analyze the achievable physical layer security (PLS) of wireless system, where, motivated by the proven positive impact of side information (SI) at the Tx on PLS performance, SI is assumed to be available at the Tx. Unlike previous studies that either considered (i) a single eavesdropper under correlated fading channels, with SI present or absent, or (ii) multiple eavesdroppers under independent fading channels, in the absence of SI, this work jointly incorporates SI at the Tx and multiple eavesdroppers under correlated shadowing conditions, yielding a more realistic and effective system model for secure wireless communication. There is no intercorrelation among the eavesdroppers, and the probability of information leakage is zero if none of them can successfully eavesdrop on the transmission. The shadowing experienced over the Tx–authorized Rx channel and the eavesdropper channels (the link between the Tx and each eavesdropper) is modeled using a Log-normal (LN) probability model, which is widely used in communication platforms that rely on wireless transmission to characterize shadowing caused by obstacles and environmental inhomogeneities, based on which we derive fast and accurate approximate closed-form expressions using the Holtzman method (HM) for the average secrecy capacity (ASC), secrecy outage probability (SOP), and the probability of non-zero secrecy capacity (PNSC).The resulting analytical expressions are mathematically tractable, and their validity is confirmed by benchmarking them against Monte Carlo (MC) simulations, and they offer reduced computational complexity and faster execution compared to simulation-based outcomes.
Physical-layer security (PLS) is a promising technique to complement more traditional means of communication security in beyond-5G wireless networks. However, studies of PLS are often based on ideal assumptions such as infinite coding blocklengths or perfect knowledge of the wiretap link’s channel state information (CSI). In this work, we study the performance of finite blocklength (FBL) transmissions using a new secrecy metric — the average information leakage (AIL). We evaluate the exact and approximate AIL with Gaussian signaling and arbitrary fading channels, assuming that the eavesdropper’s instantaneous CSI is unknown. We then conduct case studies that use artificial noise (AN) beamforming to analyze the AIL in both Rayleigh and Rician fading channels. The accuracy of the analytical expressions is verified through extensive simulations, and various insights regarding the impact of key system parameters on the AIL are obtained. Particularly, our results reveal that allowing a small level of AIL can potentially lead to significant reliability enhancements. To improve the system performance, we formulate and solve an average secrecy throughput (AST) optimization problem via both non-adaptive and adaptive design strategies. Our findings highlight the significance of blocklength design and AN power allocation, as well as the impact of their trade-off on the AST.