This paper proposes a novel neural network architecture RBF-KAN, integrating the theoretical robustness of Kolmogorov-Arnold Networks (KANs) with the localized features of Radial Basis Function (RBF) networks. To address the low computational efficiency and poor interpretability of original KANs caused by B-spline basis functions, RBF-KAN adopts RBF as the core function for activation parameterization, while retaining KAN’s theoretical guarantees. Experiments on function approximation, basic classification datasets (Moon, Concentric circles, etc.), and the real-world large-scale Adult dataset demonstrate that RBF-KAN achieves competitive accuracy with significantly enhanced efficiency compared to KAN and FourierKAN. Specifically, it reduces parameters by 33%–65% and accelerates inference/training by 65%–99% while maintaining comparable accuracy (e.g., 0.8357 vs. KAN’s 0.8157 on Adult dataset). It exhibits excellent stability and generalization, especially in high-dimensional and large-scale scenarios. This work highlights RBF-KAN’s strengths, limitations, and future directions, underscoring its potential in tackling complex function approximation and classification challenges.

Multichannel interferometry synthetic aperture radar (InSAR) systems enable the reconstruction of terrain height profiles by integrating multiple interferograms obtained from multifrequency or multibaseline configurations. In this paper, we present a robust redundant remainder number system (RRNS) specifically designed for the high-precision determination of terrain height profiles. The proposed method consists of two main steps: First, erroneous remainders are clustered, and the common remainder is estimated optimally. Next, the integral portion is determined using the RRNS. Furthermore, we derive a robust estimation condition that generalizes existing results. To apply the proposed method to real data, we have extended the robust RRNS technique to accommodate practical data conditions. The main improvements are as follows: First, the phase unwrapping model for real numbers is adapted to the integral case by selecting suitable prime numbers. Second, the process of selecting the optimal reconstruction result is enhanced by incorporating redundancy congruence, which involves using two equations for each case. Simulation results demonstrate that the extended method outperforms both the least squares method and the minimum cost flow method.

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.

Multisecret sharing schemes have been widely used in the area of information security, such as cloud storage, group authentication, and secure parallel communications. One of the issues for these schemes is to share and recover multisecret from their shareholders. However, the existing works consider the recovery of multisecret only when the correspondences between the secrets and their shares are definite. In this paper, we propose a multisecret sharing scheme to share and recover two secrets among the participants based on the generalized Chinese Remainder Theorem (GCRT), where the multisecret and their shares are unordered. To overcome the leakage of information, we propose an improved scheme including the improved sharing phase and the recovery phase. The improved scheme has not only a more secure performance but also a lower computation complexity. The conditions for recovery failure and success are also explored.

Random network coding (RNC) is an efficient coding scheme to improve the performance of wireless multicast networks, on the premise that a receiver is able to collect a full set of network-coded packets. However, in resource (time, bandwidth, and so on) constrained communications, a receiver may only receive a partial set of network coded packets, leading to poor system performance. On the other hand, device-to-device (D2D) communications utilize user proximity and spatial diversity to improve the communication efficiency. In this paper, we propose a hybrid multicast and D2D transmission scheme based on adaptive RNC (ARNC) to increase network throughput under packet erasure channels. In the proposed scheme, the packet encoding structure is optimized adaptively according to the network status, such that even if only a partial set of the coded packets are received, the user equipments (UEs) can still decode useful information and regenerate new encoded packet for D2D communications. In particular, the multicast mode and D2D mode are switched dynamically during a scheduling session according to the status of each UE. Under this hybrid mode, we can effectively overcome the effect of erasure channel and improve the overall network throughput. By comparing our scheme with other scheduling methods, we provide simulation results to corroborate the effectiveness of the proposed techniques.

It is known that random network coding (RNC) can be used to improve the performance of wireless multicast networks. However, in the delay sensitive applications, no useful information can be recovered if a user cannot collect a full set of the encoded packets. This becomes more severe for multicast hard deadline constrained prioritized data because of the delivery time limitation and packet interdependency. Meanwhile, the performance of a multicast network is also limited by its bottleneck user(s) due to the heterogeneity of the underlying physical channels. Accordingly, we propose a cross-layer transmission scheme that utilizes beamforming at physical layer and adaptive RNC (ARNC) at network layer to maximize the overall network throughput. Under this joint-design, a smart antennas array that operates the beamforming is used to dynamically allocate the transmitting power among users, and the ARNC is adopted to achieve the network coding gain. In this way, the performance of each user is well balanced and the overall network throughput is increased observably. Furthermore, we propose a sample-based feedback scheme to reduce the system overhead. The analytical and simulation results are shown that the throughput of the network has increased by 30%~40% under our schemes compared with other RNC-based schemes.

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.

In this letter we determine the largest dynamic range within which any two nonnegative integers can be uniquely determined from their residues modulo a set of moduli. We also propose an efficient determination algorithm that extends a recent known result.

Distance estimation using multifrequency phases measurement is a common practice in many areas of engineering. This method brings in the issue of phase ambiguity. Some Chinese remainder theorem (CRT) based phase unwrapping algorithms have been suggested to solve the problem, however, these algorithms either have high complexity or lack precision. In this paper, we propose an efficient algorithm to reconstruct the unknown distance from the contaminated wrapped phases. The proposed method can be separated into two stages. The first stage is to obtain the optimal estimate of the common remainder which is significant to the estimation. In the second stage, the indefinite distance is estimated by using the extended CRT. Simulations test the validity of the proposed algorithm.