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Recent advances in deep learning have led to a paradigm shift in reversible steganography. A fundamental pillar of reversible steganography is predictive modelling which can be realised via deep neural networks. However, non-trivial errors exist in inferences about some out-of-distribution and noisy data. In view of this issue, we propose to consider uncertainty in predictive models based upon a theoretical framework of Bayesian deep learning. Bayesian neural networks can be regarded as self-aware machinery; that is, a machine that knows its own limitations. To quantify uncertainty, we approximate the posterior predictive distribution through Monte Carlo sampling with stochastic forward passes. We further show that predictive uncertainty can be disentangled into aleatoric and epistemic uncertainties and these quantities can be learnt in an unsupervised manner. Experimental results demonstrate an improvement delivered by Bayesian uncertainty analysis upon steganographic capacity-distortion performance.

The solution of time fractional partial differential equations in general exhibit a weak singularity near the initial time. In this article we propose a method for solving time fractional diffusion equation with nonlocal diffusion term. The proposed method comprises L1 scheme on graded mesh, finite element method and Newton's method. We discuss the well-posedness of the weak formulation at discrete level and derive \emph{a priori} error estimates for fully-discrete formulation in $L^2(\Omega)$ and $H^1(\Omega)$ norms. Finally, some numerical experiments are conducted to validate the theoretical findings.

This paper proposes a novel broadband transmission technology, termed delay alignment modulation (DAM), which enables the low-complexity equalization-free single-carrier communication, yet without suffering from inter-symbol interference (ISI). The key idea of DAM is to deliberately introduce appropriate delays for information-bearing symbols at the transmitter side, so that after propagating over the time-dispersive channel, all multi-path signal components will arrive at the receiver simultaneously and constructively. We first show that by applying DAM for the basic multiple-input single-output (MISO) communication system, an ISI-free additive white Gaussian noise (AWGN) system can be obtained with the simple zero-forcing (ZF) beamforming. Furthermore, the more general DAM scheme is studied with the ISI-maximal-ratio transmission (MRT) and the ISI-minimum mean-square error (MMSE) beamforming. Simulation results are provided to show that when the channel is sparse and/or the antenna dimension is large, DAM not only resolves the notorious practical issues suffered by orthogonal frequency-division multiplexing (OFDM) such as high peak-to-average-power ratio (PAPR), severe out-of-band (OOB) emission, and vulnerability to carrier frequency offset (CFO), with low complexity, but also achieves higher spectral efficiency due to the saving of guard interval overhead.

Non-orthogonal multiple access (NOMA) is considered a key technology for improving the spectral efficiency of fifth-generation (5G) and beyond 5G cellular networks. NOMA is beneficial when the channel vectors of the users are in the same direction, which is not always possible in conventional wireless systems. With the help of a reconfigurable intelligent surface (RIS), the base station can control the directions of the channel vectors of the users. Thus, by combining both technologies, the RIS-assisted NOMA systems are expected to achieve greater improvements in the network throughput. However, ideal phase control at the RIS is unrealizable in practice because of the imperfections in the channel estimations and the hardware limitations. This imperfection in phase control can have a significant impact on the system performance. Motivated by this, in this paper, we consider an RIS-assisted uplink NOMA system in the presence of imperfect phase compensation. We formulate the criterion for pairing the users that achieves minimum required data rates. We propose adaptive user pairing algorithms that maximize spectral or energy efficiency. We then derive various bounds on power allocation factors for the paired users. Through extensive simulation results, we show that the proposed algorithms significantly outperform the state-of-the-art algorithms in terms of spectral and energy efficiency.

In this paper, a cyclic-prefixed single-carrier (CPSC) transmission scheme with phase shift keying (PSK) signaling is presented for broadband wireless communications systems empowered by a reconfigurable intelligent surface (RIS). In the proposed CPSC-RIS, the RIS is configured according to the transmitted PSK symbols such that different cyclically delayed versions of the incident signal are created by the RIS to achieve cyclic delay diversity. A practical and efficient channel estimator is developed for CPSC-RIS and the mean square error of the channel estimation is expressed in closed-form. We analyze the bit error rate (BER) performance of CPSC-RIS over frequency-selective Nakagami-$m$ fading channels. An upper bound on the BER is derived by assuming the maximum-likelihood detection. Furthermore, by resorting to the concept of index modulation (IM), we propose an extension of CPSC-RIS, termed CPSC-RIS-IM, which enhances the spectral efficiency. In addition to conventional constellation information of PSK symbols, CPSC-RIS-IM uses the full permutations of cyclic delays caused by the RIS to carry information. A sub-optimal receiver is designed for CPSC-RIS-IM to aim at low computational complexity. Our simulation results in terms of BER corroborate the performance analysis and the superiority of CPSC-RIS(-IM) over the conventional CPSC without an RIS and orthogonal frequency division multiplexing with an RIS.

The impacts of channel estimation errors, inter-cell interference, phase adjustment cost, and computation cost on an intelligent reflecting surface (IRS)-assisted system are severe in practice but have been ignored for simplicity in most existing works. In this paper, we investigate a multi-antenna base station (BS) serving a single-antenna user with the help of a multi-element IRS in the presence of channel estimation errors and inter-cell interference. We consider imperfect channel state information (CSI) at the BS, i.e., imperfect CSIT, and focus on the robust optimization of the BS's instantaneous CSI-adaptive beamforming and the IRS's quasi-static phase shifts. First, we formulate the robust optimization of the BS's instantaneous channel state information (CSI)-adaptive beamforming and IRS's quasi-static phase shifts for the ergodic rate maximization as a very challenging two-timescale stochastic non-convex problem. Then, we obtain a closed-form beamformer for any given phase shifts and a more tractable single-timescale stochastic non-convex problem only for phase shifts. Next, we propose a low-complexity stochastic algorithm to obtain quasi-static phase shifts which correspond to a KKT point of the single-timescale stochastic problem. It is worth noting that the proposed method offers a closed-form robust instantaneous CSI-adaptive beamforming design that can promptly adapt to rapid CSI changes over slots and a robust quasi-static phase shift design of low computation and phase adjustment costs in the presence of channel estimation errors and inter-cell interference. Finally, numerical results demonstrate the notable gains of the proposed robust joint design over existing ones and reveal the practical values of the proposed solutions.

In this paper, we consider downlink low Earth orbit (LEO) satellite communication systems where multiple LEO satellites are uniformly distributed over a sphere at a certain altitude according to a homogeneous binomial point process (BPP). Based on the characteristics of the BPP, we analyze the distance distributions and the distribution cases for the serving satellite. We analytically derive the exact outage probability, and the approximated expression is obtained using the Poisson limit theorem. With these derived expressions, the system throughput maximization problem is formulated under the satellite-visibility and outage constraints. To solve this problem, we reformulate it with bounded feasible sets and propose an iterative algorithm to obtain near-optimal solutions. Simulation results perfectly match the derived exact expressions for the outage probability and system throughput. The analytical results of the approximated expressions are fairly close to those of the exact ones. It is also shown that the proposed algorithm for the throughput maximization is very close to the optimal performance obtained by a two-dimensional exhaustive search.

This letter analyzes the performance of uplink integrated sensing and communications (ISAC) systems where communication users (CUs) and radar targets (RTs) share the same frequency band. Novel expressions are derived to characterize the outage probability, ergodic communication rate, and sensing rate. Besides, the diversity order and high signal-to-noise ratio (SNR) slope are unveiled to gain more insights. It is found that when achieving the same communication rate, the ISAC system enjoys a higher sensing rate than the conventional frequency-division sensing and communications (FDSAC) system where CUs and RTs share isolated bands. All the results are validated by numerical simulations and are in excellent agreement.

We study the class of first-order locally-balanced Metropolis--Hastings algorithms introduced in Livingstone & Zanella (2021). To choose a specific algorithm within the class the user must select a balancing function $g:\mathbb{R} \to \mathbb{R}$ satisfying $g(t) = tg(1/t)$, and a noise distribution for the proposal increment. Popular choices within the class are the Metropolis-adjusted Langevin algorithm and the recently introduced Barker proposal. We first establish a universal limiting optimal acceptance rate of 57% and scaling of $n^{-1/3}$ as the dimension $n$ tends to infinity among all members of the class under mild smoothness assumptions on $g$ and when the target distribution for the algorithm is of the product form. In particular we obtain an explicit expression for the asymptotic efficiency of an arbitrary algorithm in the class, as measured by expected squared jumping distance. We then consider how to optimise this expression under various constraints. We derive an optimal choice of noise distribution for the Barker proposal, optimal choice of balancing function under a Gaussian noise distribution, and optimal choice of first-order locally-balanced algorithm among the entire class, which turns out to depend on the specific target distribution. Numerical simulations confirm our theoretical findings and in particular show that a bi-modal choice of noise distribution in the Barker proposal gives rise to a practical algorithm that is consistently more efficient than the original Gaussian version.

This work proposes a novel model and numerical formulation for lubricated contact problems describing the mutual interaction between two deformable 3D solid bodies and an interposed fluid film. The solid bodies are consistently described based on nonlinear continuum mechanics allowing for finite deformations and arbitrary constitutive laws. The fluid film is modelled as a quasi-2D flow problem on the interface between the solids governed by the averaged Reynolds equation. The averaged Reynolds equation accounts for surface roughness utilizing spatially homogenized, effective fluid parameters and for cavitation through a positivity constraint imposed on the pressure field. In contrast to existing approaches, the proposed model accounts for the co-existence of frictional contact tractions and hydrodynamic fluid tractions at every local point on the contact surface of the interacting bodies and covers the entire range from boundary lubrication to mixed, elastohydrodynamic, and eventually to full film hydrodynamic lubrication in one unified modelling framework with smooth transition between these different regimes. Critically, the model relies on a recently proposed regularization scheme for the mechanical contact constraint combining the advantages of classical penalty and Lagrange multiplier approaches by expressing the mechanical contact pressure as a function of the effective gap between the solid bodies while at the same time limiting the minimal gap value occurring at the (theoretical) limit of infinitely high contact pressures. From a physical point of view, this approach can be considered as a model for the elastic deformation of surface asperities, with a bounded magnitude depending on the interacting solids' surface roughness. A consistent and accurate model behavior is demonstrated and validated by employing several challenging and practically relevant benchmark test cases.