This paper investigates nonlinear vector quantization strategies for efficient gradient compression in deep neural network training, based on Helmert-domain decorrelation combined with A-law and μ -law companding. By pairing gradient coefficients and applying the pairwise Helmert transform prior to semilogarithmic companding, the proposed method reduces precision requirements while preserving convergence stability. An adaptive switching mechanism selects between low-bit and high-bit quantization regions based on local gradient statistics, without additional hyperparameter tuning. We evaluate the approach on a multi-layer perceptron (MLP) for tabular prediction and a convolutional neural network (CNN) on CIFAR-10. Both companding schemes closely track the full-precision (FP32) loss and accuracy trajectories, while achieving substantial communication reduction and low gradient root mean square error (RMSE). Additional comparisons against quantized stochastic gradient descent (QSGD), Top-k sparsification, error-feedback sign SGD (EFSignSGD), and PowerSGD show that the proposed Helmert-based companding framework offers a favorable trade-off between accuracy and compression, particularly in bandwidth-constrained distributed training. These results indicate that proposed Helmert-based companding in the decorrelated gradient domain provides an effective and scalable alternative to conventional gradient compression techniques. In particular, it achieves stable convergence at moderate compression ratios, while maintaining lower gradient distortion and reduced communication cost, making it especially suitable for bandwidth-constrained distributed and federated training environments.

A novel quasi–Newton optimization method based on a low–order rational Padé approximation, for estimating curvature information along the descent direction, has been proposed. The method constructs a Padé [2/2] model of the objective function restricted to a one dimensional search line and extracts a scalar curvature surrogate that replaces the Hessian in a directional sense. This leads to an adaptive curvature scaled gradient update that requires neither Hessian evaluations nor matrix updates. It is shown that the proposed Padé based curvature estimate is a consistent approximation of the directional Rayleigh quotient of the Hessian. Global convergence to stationary points is established under standard smoothness assumptions when the method is combined with Armijo backtracking, and linear convergence is obtained under strong convexity. A detailed truncation/round-off analysis reveals that the Padé curvature estimate satisfies: γ_k = λ _k + 𝒪(h^2) + 𝒪( u/h^p) , which explains the numerical instability observed for excessively small finite difference steps. Extensive numerical experiments on a broad set of benchmark problems demonstrate that the Padé [2/2] method achieves competitive or superior performance compared to classical quasi–Newton and curvature scaled gradient methods in terms of iteration count, function evaluations, and CPU time. In addition, the results indicate that the simpler Padé [1/1] approximation already provides a meaningful curvature estimate, while the [2/2] model offers improved robustness and accuracy without sacrificing computational efficiency.

This paper introduces an adaptive A-semilogarithmic gradient quantization framework aimed at reducing memory overhead and computational complexity during the training of deep neural networks. The approach employs a semilogarithmic companding function parameterized by a dynamically adjusted scaling factor A, which evolves in response to the statistical properties of gradients throughout the training process. Two distinct quantization strategies are proposed and evaluated: The switching piecewise A-quantizer, which adaptively toggles between low-bit uniform and high-bit semilogarithmic quantization according to an exponentially weighted moving-average (EMA) estimate of gradient variance; and the hybrid A-quantizer, which statically partitions the gradient domain, applying uniform quantization in low-magnitude regions and semilogarithmic companding in high-magnitude regions. The proposed methods are empirically evaluated on both multilayer perceptron (MLP) and convolutional neural network (CNN) architectures using tabular and image-classification benchmarks, including DCCC, CIFAR-10, CIFAR-100, and ImageNet. Quantitative results demonstrate that both models achieve comparable classification accuracy to full-precision (FP32) baselines while significantly reducing gradient reconstruction error. Notably, the hybrid A-quantizer consistently yields better validation accuracy, reduced RMSE, and improved convergence behavior relative to its switching counterpart. These findings underscore the effectiveness of hybrid semilogarithmic quantization as a robust and efficient solution for training deep models in resource-constrained or bandwidth-limited environments, with strong potential for scalable deployment across diverse hardware platforms.

The rate at which the envelope of a fading signal exhibits local extrema describes its short-term oscillatory behavior and is directly linked to Doppler spread and time-selective channel dynamics. In this letter, we derive a closed-form approximation for the normalized level extremum rate (LER) in Nakagami-m fading channels by modeling the second-order envelope derivative conditioned on the instantaneous envelope level. The resulting expression is compact, depends explicitly on the fading parameter m, the envelope level, and the maximum Doppler frequency fD, and does not require explicit evaluation of trivariate joint densities or complex derivative-based integrals. Monte-Carlo simulations based on time-domain extrema detection confirm the consistency of the analytical model with simulation results across a broad range of fading conditions. The result provides an efficient analytical tool for characterizing envelope dynamics in mobility affected wireless channels.

paper presents an adaptive & micro;quasilogarithmic gradient quantization framework aimed at reducing memory and computational demands during deep neural network training. The approach employs a companding function with a dynamically adjusted & micro; parameter that adapts to the statistical properties of gradients. Two quantization strategies are developed: a switching & micro;-quantizer that toggles between low-bit uniform and high-bit quasilogarithmic modes based on gradient variance, and a hybrid & micro;-quantizer that statically applies uniform quantization to small gradients and quasilogarithmic to larger ones. Experiments on multiple-layer perceptron (MLP) and convolution neural network (CNN) models trained on CIFAR-10 show that both quantizers retain classification accuracy close to full-precision (FP32) baselines while significantly reducing gradient reconstruction error (RMSE). The hybrid variant consistently achieves better validation accuracy, lower RMSE, and faster convergence than the switching scheme. These results highlight the potential of hybrid quasilogarithmic quantization as an efficient and scalable solution for training deep models in memory or bandwidth constrained environments.

This work investigates the effectiveness of block transform coding (BTC) as a lightweight, training-free quantization strategy for compressing the weights of pretrained deep neural networks. The proposed method applies a rule-based block transform with variance and root mean square error (RMSE)-driven stopping criteria, enabling substantial reductions in bit precision while preserving the statistical structure of convolutional and fully connected layer weights. Unlike uniform 8-bit quantization, BTC dynamically adjusts bit usage across layers and achieves significantly lower distortion for the same compression budget. We evaluate BTC across many pretrained architectures and tabular benchmarks. Experimental results show that BTC consistently reduces storage to 4–7.7 bits per weight while maintaining accuracy within 2–3% of the 32-bit floating point (FP32) baseline. To further assess scalability and baseline strength, BTC is additionally evaluated on large-scale ImageNet models and compared against a calibrated percentile-based uniform post-training quantization method. The results show that BTC achieves a substantially lower effective bit-width while incurring only a modest accuracy reduction relative to calibration-aware 8-bit quantization, highlighting a favorable compression–accuracy trade-off. BTC also exhibits stable behavior across successive post-training quantization (PTQ) configurations, low quantization noise, and smooth RMSE trends, outperforming naïve uniform quantization under aggressive compression. These findings confirm that BTC provides a scalable, architecture-agnostic, and training-free quantization mechanism suitable for deployment in memory- and computing-constrained environments.

Optimizing energy consumption is critical for extending network lifetime and ensuring re-liable data collection in UAV-assisted wireless sensor networks (WSNs). In the proposed work, an enhanced MAC protocol is developed, i.e., Duty-Cycle-Aware Bit-Mapped (DCABM). The proposed method estimates the active nodes per communication cycle based on their duty cycles and assigns transmission slots using a bit-mapping approach. The protocol is evaluated using the IEEE 802.15.4 standard with CC2420 radio parameters, considering varying network sizes, event occurrence prob-abilities, and packet sizes. The comparative analysis of the proposed method is compared with con-ventional UAV _EBMA and UAV _ETDMA methods. The results demonstrate that DCABM sig-nificantly reduces energy consumption. Specifically, DCABM achieves up to 42% energy savings compared to UAV _ETDMA and approximately 31% reduction compared to UAV _EBMA un-der high event occurrence conditions. Additionally, across increasing node densities and packet sizes, DCABM consistently maintains superior energy efficiency, making it suitable for scalable and event-driven WSN applications with UAV support.

This paper presents a cryptographic hash function based on the Residue Number System (RNS), designed to enhance security and computational efficiency. The function leverages the parallelism and modular properties of RNS to achieve high-speed processing while maintaining strong diffusion and resistance to various cryptanalytic attacks. Experimental results confirm that the proposed function exhibits a pronounced Avalanche effect, ensuring that minor changes in the input result in significant alterations in the hash output. Additionally, statistical analysis using the ENT test demonstrates a high level of entropy and uniform distribution of hash values, reinforcing the function's unpredictability-an essential characteristic for cryptographic security. The proposed hash function is suitable for applications in digital signatures, data integrity verification, and authentication systems, offering advantages in environments requiring high computational efficiency.

This paper presents a novel approach to analyzing Bluetooth signals using deep learning with neural networks. Due to their complex properties, Bluetooth signals require advanced methods for analysis. Thes neural network model predicts the mean and standard deviation of these signals, utilizing fully connected layers and Tanh and Softmax activation functions. Model performance is evaluated with metrics such as MAE, MSE, RMSE, and R-squared. The research demonstrates that neural networks can accurately extract statistical features from Bluetooth signals, contributing to improvements in wireless communication by optimizing signal analysis and error detection.

In this paper, we are observing a reparable system comprised of several components. The aim is to determine at which repair rate the system achieves the highest availability. To accomplish that, the procedure for the calculation of the repair rate in function of the desired level of availability for the system with a predetermined repair rate threshold is created. The presented approach is based on the exploration of the probability density function (PDF) of a system's repair time by observing the probability that repair rates of its components surpass a determined threshold. The obtained results can be applied in reliability theory, maintenance planning, and many other fields. To prove the application of the developed model, the results are verified by a numerical example for an unmanned vehicle system.

In this study, we present an innovative approach to modelling the propagation channels of land mobile satellite (LMS) systems by employing the η -μ distribution for a comprehensive narrowband channel model, which is crucial for the foundation of wideband models. This model is pivotal for accurately representing the complexities of satellite-to-mobile user channels, especially under non-line-of-sight (NLOS) conditions. By adopting the η -μ distribution, our model transcends the limitations of conventional lognormal-based models by offering a more accessible statistical analysis through expressions for the envelope probability density function (PDF), the cumulative distribution function (CDF), the moment generating function (MGF) and the average channel capacity. The model facilitates easy performance evaluation for various modulation schemes. Numerical results demonstrate its effectiveness in calculating the average bit error rate (ABER) for binary differential phase shift keying (BDPSK), non-coherent binary frequency shifting keying (BFSK), and binary phase shift keying (BPSK) modulation schemes. With computational efficiency and adaptability, this model serves as a valuable tool for practitioners and system designers to analyze and decide on LMS communication systems.

This study introduces a neural network-based approach to estimate the level crossing rate (LCR) and average fade duration (AFD) for wireless fading channels characterized by a κ–μ shadowed model. The feed-forward architecture of the neural network is optimized for modeling the complex dynamics inherent in wireless communications, handling the non-linear relationships and stochastic nature of fading signals effectively. Extensive simulations were conducted using a dataset of one million samples, emphasizing the robustness and predictive accuracy of the model. The network was trained using a binary cross-entropy loss function and the RMSprop optimizer, ensuring efficient learning and generalization capabilities. Results demonstrate the network’s ability to closely approximate the statistical distributions of signal fading, offering valuable insights into the behavior of fading channels, which are critical for optimizing mobile communication systems.

This paper presents the design and application of a novel mother wavelet inspired by the Rician probability density function (PDF), tailored for classifying Line-of-Sight (LOS) and Non-Line-of-Sight (NLOS) propagation conditions. The proposed Rician wavelet filter is constructed by deriving the corresponding low-pass and high-pass filter coefficients using shifted and normalized Rician PDF samples, ensuring compliance with wavelet admissibility and orthogonality criteria. Using this wavelet, we perform discrete wavelet transform (DWT) decomposition of measured channel impulse responses. Energy features extracted from the first three DWT scales are used to train standard classifiers, including Multi-Layer Perceptron (MLP), Support Vector Machine (SVM), and Random Forest (RF). Evaluation on a observed dataset demonstrates that the proposed Rician wavelet outperforms traditional wavelet bases in terms of classification accuracy. Experimental results highlight the potential of PDF-driven wavelet design in enhancing the performance of signal classification tasks in wireless channel environments.

This paper introduces a novel statistical model for the performance analysis of hybrid RF/FSO (radio frequency/free-space optics) communication systems. The RF channel is modeled using the Nakagami-m fading distribution, while the FSO channel is characterized by a Chi-square-inverse Gamma distribution to account for atmospheric turbulence and pointing errors. A closed-form expression for the cumulative distribution function (CDF) of a one-hop hybrid RF/FSO system is derived under a selective combining scheme, formulated as a function of the average signal-to-noise ratio (SNR). The resulting CDF is expressed in terms of the extended generalized bivariate Meijer-G function (EGBMGF). Furthermore, new analytical expressions for the average bit error rate (ABER) are obtained for both the hybrid RF/FSO system and its FSO-only counterpart under coherent binary phase-shift keying (CBPSK) modulation. A detailed comparative analysis is performed across varying channel parameters and turbulence conditions. Numerical results, presented graphically, demonstrate the superior robustness of the proposed hybrid scheme under severe turbulence and misalignment effects.

A novel quasi-Newton method is proposed wherein the Hessian approximation is constructed using orthogonal polynomial quadrature, specifically based on Legendre polynomials. In contrast to traditional approaches that rely on second-order Taylor expansions or finite-difference approximations, the method estimates the second directional derivative through an efficient quadrature formula, providing controlled accuracy and enhanced numerical stability. Theoretical properties of the method, including convergence behavior and error bounds, are rigorously analyzed. Extensive numerical experiments on a wide range of benchmark functions are performed, demonstrating that the proposed approach achieves a favorable balance between computational efficiency and solution accuracy when compared to classical quasi-Newton methods employing scalar Hessian approximations. Additionally, the influence of the number of quadrature nodes on convergence speed and accuracy is systematically investigated.

Performance-Based Logistics (PBL) frameworks prioritize system availability by optimizing maintenance strategies, with repair rate estimation playing a critical role in predictive maintenance planning. This study proposes a machine learning-based approach for repair rate prediction, leveraging fully connected neural networks (FCNNs) and Long Short-Term Memory (LSTM) networks trained on repair rate samples generated from a stochastic model. The FCNN estimates maximum repair rates, while the LSTM predicts minimum repair rates, capturing both steady-state and sequential dependencies in repair rate variations. By eliminating the need for complex mathematical formulations, the proposed methodology provides a scalable and computationally efficient alternative to traditional stochastic models. Extensive performance evaluations demonstrate that the neural networks achieve higher accuracy and lower computational costs compared to stochastic approaches, making them well-suited for real-time predictive maintenance applications. This research enhances decision-making in maintenance planning, optimizes resource allocation, and improves overall system reliability within PBL frameworks.

The manuscript introduces a novel turbulence model for free space optics (FSO) communication, constructed through the amalgamation of two distinct statistical models, rooted in the scintillation theory. A closed-form expression for the probability density function (PDF) and cumulative distribution function (CDF) of the turbulence channel, specifically the Chi-square/inverse Gamma distribution, was deduced. Further the influence of zero boresight pointing errors on the performances of FSO transmission over the obtained atmospheric turbulence channel has been considered. To delve into the intricacies of the channel, an examination of the average bit error rate (ABER) was undertaken as an evaluative metric for the transmitted signal’s quality. The ABER analysis was specifically conducted within the framework of IM/DD (intensity modulation and direct detection) and OOK (on-off keying), considering diverse sets of system parameters and across various turbulence scenarios. In the same manner, ABER analysis has been carried out for the subcarrier intensity modulation (SIM) with differential phase-shift keying (DPSK).