Covert communication aims to hide the existence of the transmissions to guarantee the security in wireless communications. In this paper, channel uncertainty is exploited to achieve covert communication in relay networks. The transmitter Alice sends messages to the legitimate receiver Bob with the help of a relay, while the warden Willie wants to detect the existence of the transmission. The channel uncertainty introduces confusions to degrade the performance of Willie’s detection. We show that Alice can transmit O(n) bits in n channel uses covertly with the help of relay and channel uncertainty. Numerical results are shown to illustrate the achievability and the performance of the considered scenario.

Nowadays, the Industrial Internet of Things (IIoT) has played an integral role in Industry 4.0 and produced massive amounts of data for industrial intelligence. These data locate on decentralized devices in modern factories. To protect the confidentiality of industrial data, federated learning (FL) was introduced to collaboratively train shared machine learning (ML) models. However, the local data collected by different devices skew in class distribution and degrade industrial FL performance. This challenge has been widely studied at the mobile edge, but they ignored the rapidly changing streaming data and clustering nature of factory devices, and more seriously, they may threaten data security. In this article, we propose FED GS, which is a hierarchical cloud-edge-end FL framework for 5G empowered industries, to improve industrial FL performance on non-independent and identically distributed (non-j) data. Taking advantage of naturally clustered factory devices, FED GS uses a gradient-based binary permutation algorithm (GBP-CS) to select a subset of devices within each factory and build homogeneous super nodes participating in FL training. Then, we propose a compound-step synchronization protocol to coordinate the training process within and among these super nodes, which shows great robustness against data heterogeneity. The proposed methods are time-efficient and can adapt to dynamic environments, without exposing confidential industrial data in risky manipulation. We prove that FED GS has better convergence performance than FedAvg and give a relaxed condition under which FED GS is more communication efficient. The extensive experiments show that FED GS improves accuracy by 3.5% and reduces training rounds by 59% on average, confirming its superior effectiveness and efficiency on non-i.i.d. data.

A generalized Chinese remainder theorem (CRT) for multiple integers from residue sets has been studied recently, where the correspondence between the remainders and the integers in each residue set modulo several moduli is not known. A robust CRT has also been proposed lately to robustly reconstruct a single integer from its erroneous remainders. In this paper, we consider the reconstruction problem of two integers from their residue sets, where the remainders not only are out of order but also may have errors. We prove that two integers can be robustly reconstructed if their remainder errors are less than M/8, where M is the greatest common divisor of all the moduli. We also propose an efficient reconstruction algorithm. Finally, we present some simulations to verify the efficiency of the proposed algorithm. This paper is motivated from and has applications in the determination of multiple frequencies from multiple undersampled waveforms.

The physical layer security problem with a passive eavesdropper is considered in this letter. We propose a method to obtain everlasting secrecy by exploiting inter-symbol interference (ISI) in eavesdropper. In the proposed method, the pulse shaping filter in the transmitter changes with time in the faster-than-Nyquist (FTN) signaling structure. The filter hopping pattern is pre-shared between the transmitter and the legitimate receiver. Knowing the hopping pattern, the legitimate receiver can mitigate the ISI as that in FTN. Otherwise, the eavesdropper will experience severe interference. The results show that even the eavesdropping link is much better than the legitimate link, a positive secrecy rate is also obtained. The secrecy rates for various examples of the proposed method are evaluated and the comparisons with other information-theoretic security schemes are also shown.

We consider a new mathematical model for the COVID-19 disease with Omicron variant mutation. We formulate in details the modeling of the problem with omicron variant in classical differential equations. We use the definition of the Atangana–Baleanu derivative and obtain the extended fractional version of the omicron model. We study mathematical results for the fractional model and show the local asymptotical stability of the model for infection-free case if ${\mathcal{R}}_0<1$. We show the global asymptotically stable of the model for the disease free case when ${\mathcal{R}}_0\le 1$. We show the existence and uniqueness of solution of the fractional model. We further extend the fractional order model into piecewise differential equation system and give a numerical algorithm for their numerical simulation. We consider the real cases of COVID-19 in South Africa of the third wave March 2021–Sep 2021 and estimate the model parameters and get ${\mathcal{R}}_0\approx 1.4004$. The real parameters values are used to show the graphical results for the fractional and piecewise model.