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Keywords = additive white gaussian noise (AWGN)

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21 pages, 4928 KB  
Article
Deep Learning-Based Classification of Plunging Breaker Conditions Using Simulation Radar HRRP Sea-Surface Scattering Data
by Imran Ullah, Chunlei Dong, Xiao Meng, Yue Liu, Muneeb Ullah, Mehwish Khalid Butt, Muhammad Iqbal and Lixin Guo
Remote Sens. 2026, 18(18), 3102; https://doi.org/10.3390/rs18183102 - 10 Sep 2026
Abstract
Electromagnetic scattering from plunging breaking waves generates strong sea-surface radar returns that degrade radar-based maritime surveillance and target detection performance. This study develops a deep learning framework for automatic classification of simulated plunging-breaker scattering conditions using high-range-resolution profile (HRRP) data. The electromagnetic scattering [...] Read more.
Electromagnetic scattering from plunging breaking waves generates strong sea-surface radar returns that degrade radar-based maritime surveillance and target detection performance. This study develops a deep learning framework for automatic classification of simulated plunging-breaker scattering conditions using high-range-resolution profile (HRRP) data. The electromagnetic scattering data are generated using a physics-based Capillary Wave Modification Facet Scattering Model (CWMFSM) combined with ray-tracing techniques. Eight simulated plunging-breaker scattering conditions are constructed by combining two wind speeds, 7 m/s and 10 m/s, with four temporal conditions, Δt1, Δt10, Δt14, and Δt16. A total of 8000 HRRP samples are generated, with 100 normalized range-cell features extracted from each sample. Two deep learning classifiers, an artificial neural network (ANN) and a one-dimensional residual convolutional neural network (1D ResNet CNN), are comparatively evaluated. The ANN achieves an overall classification accuracy of 96%, compared with 91% for the 1D ResNet CNN under the simulated dataset and adopted model configurations. Robustness analysis under controlled additive white Gaussian noise (AWGN) conditions further shows that classification performance decreases as the signal-to-noise ratio is reduced, while noise-augmented training improves the robustness of both classifiers. Overall, the results demonstrate the feasibility of HRRP-based deep learning for distinguishing simulated plunging-breaker scattering conditions from sea-surface radar returns, providing a basis for further investigation of sea-clutter characterization and maritime radar applications. Full article
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24 pages, 514 KB  
Article
Task-Oriented Semantic Feature Transmission for Robust EEG Motor Imagery Decoding Under Additive White Gaussian Noise
by Hossein Ahmadi and Luca Mesin
Sensors 2026, 26(18), 5728; https://doi.org/10.3390/s26185728 - 9 Sep 2026
Viewed by 77
Abstract
Remote electroencephalography (EEG) systems require compact representations that remain useful when communication noise corrupts the transmitted message. We evaluated whether task-oriented residual refinement of filter bank common spatial pattern (FBCSP) features compressed by principal component analysis (PCA) improves four-class motor imagery (MI) decoding [...] Read more.
Remote electroencephalography (EEG) systems require compact representations that remain useful when communication noise corrupts the transmitted message. We evaluated whether task-oriented residual refinement of filter bank common spatial pattern (FBCSP) features compressed by principal component analysis (PCA) improves four-class motor imagery (MI) decoding without increasing the transmitted dimension. The BNCI2014-001 dataset was assessed in nine subjects using bidirectional subject-specific cross-session evaluation. All methods transmitted K{16,32,64} power-normalized real values through additive white Gaussian noise (AWGN) at seven signal-to-noise ratios (SNRs) and a noise-free reference. Balanced accuracy was averaged over 20 paired noise realizations per noisy condition, and paired subject-level differences were evaluated with exact joint sign-flip max-|t| inference. At K=32, the proposed method achieved 41.10%, 49.46%, and 56.15% balanced accuracy at 10, 5, and 0 dB, compared with 38.63%, 46.28%, and 53.26% for conventional FBCSP–PCA transmission. Ten of the 24 semantic-versus-conventional comparisons were significant after family-wise max-|t| correction, including all nine comparisons at 10, 5, and 0 dB. Receiver-only controls closely reproduced conventional performance at all three message dimensions, whereas alternative loss weights, uniform-SNR training and selection, and removal of the 0 dB/noise-free reference-condition guard retained positive low-SNR gains. Overall, baseline-preserving task-oriented refinement improved MI decision robustness under severe AWGN without increasing the number of transmitted values. Full article
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12 pages, 1088 KB  
Communication
Approximate SER Analysis of LoRa Communication with Timing and Frequency Offset
by Haozhe Zhang, Ruixiang Qi, Wenqing Zhao, Chen Dai, Guangzu Liu, Linlin Sun and Jun Zou
Electronics 2026, 15(16), 3671; https://doi.org/10.3390/electronics15163671 - 17 Aug 2026
Viewed by 237
Abstract
In high-mobility LoRa communications, carrier frequency offset (CFO) stemming from low-cost crystal oscillators causes signal energy to disperse across frequency bins. To quantify the impact of CFO and sampling time offset (STO) induced by sampling rate conversion on the symbol error rate (SER), [...] Read more.
In high-mobility LoRa communications, carrier frequency offset (CFO) stemming from low-cost crystal oscillators causes signal energy to disperse across frequency bins. To quantify the impact of CFO and sampling time offset (STO) induced by sampling rate conversion on the symbol error rate (SER), this paper derives approximate SER bounds under Additive White Gaussian Noise (AWGN) channels. Simulations verify these bounds, revealing that low spreading factors (SFs) combined with high STO and CFO induce significant energy leakage and performance degradation. Furthermore, Low Rate Optimization (LRO) is employed to enhance signal robustness. The proposed SER bounds are shown to hold for LRO-enhanced systems, with simulations confirming that LRO effectively improves overall performance. Full article
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23 pages, 3067 KB  
Article
Task-Oriented Deep Joint Source-Channel Coding with Semantic-Aware Adaptive Quantization for Autonomous Driving
by Xin Wang, Haiqiang Chen, Youming Sun, Xiangcheng Li and Min Xie
Sensors 2026, 26(16), 5035; https://doi.org/10.3390/s26165035 - 8 Aug 2026
Viewed by 302
Abstract
In autonomous driving and intelligent transportation, vehicles need to share visual perception information to extend sensing range, but conventional separate source-channel coding can suffer from the cliff effect under harsh vehicular channels, causing downstream perception failures. This paper proposes an end-to-end semantic communication [...] Read more.
In autonomous driving and intelligent transportation, vehicles need to share visual perception information to extend sensing range, but conventional separate source-channel coding can suffer from the cliff effect under harsh vehicular channels, causing downstream perception failures. This paper proposes an end-to-end semantic communication system for autonomous-driving semantic segmentation. The system adopts SegFormer-B2 as the semantic encoder, performs feature modulation conditioned on the signal-to-noise ratio SNR, applies semantic-aware adaptive bit-width quantization based on Gumbel-Softmax, and uses a task-oriented decoder to directly produce segmentation maps. Experiments on Cityscapes evaluate the system under additive white Gaussian noise (AWGN) and per-channel independent block Rayleigh fading channels, with comparisons against a JPEG-based separate baseline and fixed-bit-width variants. Under AWGN, the proposed system maintains a mean intersection over union above 0.70 at SNR=6dB, while the conventional baseline fails at SNR=0dB with an mIoU of 0.02, indicating improved robustness against the cliff effect. The results also show a non-monotonic relationship between quantization precision and segmentation performance: fixed 4-bit quantization can outperform fixed 6-bit quantization because finer quantization is more sensitive to channel noise. Under Rayleigh fading, adaptive quantization may suffer from semantic-channel mismatch, providing useful observations for future channel-aware semantic resource allocation. Full article
(This article belongs to the Section Intelligent Sensors)
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20 pages, 1536 KB  
Article
A Multiplier-Free Dual-Hadamard Architecture for Peak-to-Average Power Ratio Reduction in OFDM Systems
by Mengwan Jiang, Yusheng Mei, Minchen Shi and Dejin Kong
Electronics 2026, 15(14), 3099; https://doi.org/10.3390/electronics15143099 - 14 Jul 2026
Viewed by 308
Abstract
Orthogonal frequency division multiplexing (OFDM) is widely used in broadband wireless communication systems because of its high spectral efficiency, flexible subcarrier allocation, and robustness against frequency-selective fading. However, the high peak-to-average power ratio (PAPR) of OFDM signals reduces the power efficiency of high-power [...] Read more.
Orthogonal frequency division multiplexing (OFDM) is widely used in broadband wireless communication systems because of its high spectral efficiency, flexible subcarrier allocation, and robustness against frequency-selective fading. However, the high peak-to-average power ratio (PAPR) of OFDM signals reduces the power efficiency of high-power amplifiers and may introduce nonlinear distortion. To address this problem, this paper proposes a multiplier-free Dual-Hadamard PAPR-reduction architecture. The term multiplier-free refers to the additional precoding and phase-weighting operations introduced by the proposed PAPR reduction module, excluding the common OFDM FFT/IFFT operations. Specifically, the proposed architecture combines fast Walsh–Hadamard transform (FWHT) precoding, interleaved partitioning (ILP), and Hadamard-based partial transmit sequence (H-PTS) weighting. Since the FWHT matrix and the H-PTS phase codebook contain only binary signs, the main additional operations are implemented by additions, subtractions, and sign inversions. Simulation results demonstrate that the proposed method reduces the PAPR relative to conventional OFDM without degrading the system’s bit error rate (BER) performance in an additive white Gaussian noise (AWGN) channel when the side information is recovered correctly. Full article
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15 pages, 1023 KB  
Article
A Quality-Driven Adaptive Coding and Modulation Framework for Enhanced Digital Video Broadcasting over Satellite Networks
by Ubong Ukommi, Mfonobong Uko, Sunday Ekpo and Ikpaya Ikpaya
Technologies 2026, 14(7), 417; https://doi.org/10.3390/technologies14070417 - 8 Jul 2026
Viewed by 395
Abstract
The exponential growth of digital video traffic over satellite networks demands innovative approaches to optimize spectral efficiency while ensuring high quality of experience (QoE). Conventional Adaptive Coding and Modulation (ACM) schemes respond solely to Channel State Information (CSI), neglecting the perceptual importance of [...] Read more.
The exponential growth of digital video traffic over satellite networks demands innovative approaches to optimize spectral efficiency while ensuring high quality of experience (QoE). Conventional Adaptive Coding and Modulation (ACM) schemes respond solely to Channel State Information (CSI), neglecting the perceptual importance of video content. This paper proposes a comprehensive Quality-Driven Adaptive Coding and Modulation (QACM) framework that dynamically allocates physical-layer resources based on joint channel conditions and content-aware quality metrics. The framework introduces a Quality Significance Factor (QSF) that quantifies video complexity and priority, enabling intelligent trade-offs between spectral efficiency and quality robustness. We implement a complete simulation testbed incorporating DVB-S2X-compliant ModCods with multiple code rates (1/2, 3/4, and 5/6) and higher-order constellations (up to 64QAM) over Additive White Gaussian Noise (AWGN) channels. Extensive experimental results using H.264/AVC sequences demonstrate that, while standard ACM achieves 30.14 dB PSNR for high-motion football sequences at 16 dB SNR with 64QAM-1/2, QACM improves this to 41.40 dB by switching to QPSK-1/2, representing an 11.26 dB gain. We provide comprehensive BER analyses across the 0–20 dB SNR range, statistical significance validation (p < 0.01 for quality improvements), computational complexity analysis showing 15.2% overhead, and detailed comparisons with prior arts. The framework demonstrates scalability to higher-order modulations while maintaining 23% weighted QoE improvement over conventional ACM. This work provides a validated, implementable cross-layer solution for next-generation satellite broadcasting systems. Full article
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21 pages, 503 KB  
Article
Hierarchical Modulation Classification with Channel-Type-Guided Blind Preprocessing for High-Order QAM in Multipath Fading Channels
by Sungsoo Park and Gyuyeol Kong
Appl. Sci. 2026, 16(13), 6568; https://doi.org/10.3390/app16136568 - 1 Jul 2026
Viewed by 317
Abstract
Automatic modulation classification (AMC) becomes challenging in multipath fading channels, particularly for high-order quadrature amplitude modulation (QAM) signals whose constellation points are strongly distorted by inter-symbol interference, phase rotation, and fading. This paper presents a channel-type-guided hierarchical AMC framework that combines blind preprocessing [...] Read more.
Automatic modulation classification (AMC) becomes challenging in multipath fading channels, particularly for high-order quadrature amplitude modulation (QAM) signals whose constellation points are strongly distorted by inter-symbol interference, phase rotation, and fading. This paper presents a channel-type-guided hierarchical AMC framework that combines blind preprocessing with deep learning. In the first stage, the received in-phase and quadrature (IQ) signal is downsampled and preprocessed using blind signal processing techniques. Blind source separation (BSS) is used for additive white Gaussian noise (AWGN) and flat fading channels, whereas the constant modulus algorithm (CMA) followed by BSS is used for multipath fading channels. A convolutional neural network (CNN) then performs first-stage modulation classification and generates a QAM-family flag. If the first-stage output corresponds to a QAM-family signal, a second-stage refinement path is activated. In this path, a convolutional denoising autoencoder (CDAE) is applied to the original received signal to mitigate multipath-induced distortion, followed by BSS preprocessing and a dedicated CNN classifier for 16-QAM, 64-QAM, and 256-QAM. Simulation results over AWGN, flat fading, and multipath Rician fading channels show that the proposed hierarchy improves high-order QAM classification in the considered settings, especially for 64-QAM and 256-QAM under multipath fading with stronger time variation. Multi-frame Softmax averaging further improves decision stability. The results support the use of classical blind preprocessing and selective CDAE-based refinement as a practical, complementary front end for AMC in controlled multipath simulation scenarios, while real over-the-air validation and automatic channel-category detection remain future work. Full article
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35 pages, 1355 KB  
Article
Robustness of Large Vision Language Model Features Under Wireless Channel Degradation for Medical Visual Question Answering
by Merve Güllü and Necaattin Barışçı
Appl. Sci. 2026, 16(13), 6425; https://doi.org/10.3390/app16136425 - 27 Jun 2026
Viewed by 327
Abstract
Deploying medical visual question answering (VQA) systems over wireless networks introduces a fundamental challenge: channel-induced image degradation may corrupt the visual representations extracted by large vision-language models (VLMs), leading to unreliable diagnostic decisions. We investigate the robustness of frozen LLaVA-1.6, BLIP-2, and BioViL-T [...] Read more.
Deploying medical visual question answering (VQA) systems over wireless networks introduces a fundamental challenge: channel-induced image degradation may corrupt the visual representations extracted by large vision-language models (VLMs), leading to unreliable diagnostic decisions. We investigate the robustness of frozen LLaVA-1.6, BLIP-2, and BioViL-T hidden-state features under additive white Gaussian noise (AWGN), Rayleigh fading, and six combined JPEG-compression-plus-channel conditions (quality factors q{20,50,70}) across signal-to-noise ratios (SNRs) from 5 to +20 dB. A lightweight MLP classifier is trained exclusively on clean features and evaluated on channel-degraded features, enabling controlled analysis of representation robustness without retraining. We introduce the Feature Robustness Score (FRS), defined as the difference between cosine similarity and normalized L2 drift of clean versus degraded features, together with a validation-set FRS threshold analysis as a label-free retraining criterion. A wavelet sub-band energy analysis further characterizes the spectral distribution of channel-induced feature drift. Experiments on PathVQA and VQA-RAD reveal four key findings: (1) LLaVA-1.6 features maintain cosine similarity above 0.98 across all eight channel conditions and all SNR levels, with statistically significant MLP gains at every tested point (p<0.05, McNemar’s test); (2) BLIP-2 and BioViL-T features are less stable but still support consistent MLP improvements, with BioViL-T performing competitively on VQA-RAD, suggesting domain alignment matters; (3) JPEG compression quality (q=20,50,70) has negligible impact on feature drift, establishing VLM features as JPEG quality-invariant; and (4) wavelet analysis confirms that channel noise primarily affects high-frequency detail bands while preserving low-frequency semantic content. Full article
(This article belongs to the Special Issue Deep Learning and Its Applications in Natural Language Processing)
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13 pages, 1874 KB  
Article
Comparative Evaluation of MLP, 1D-CNN and LSTM for Waveform Classification in Additive White Gaussian Noise
by Beza Negash Getu and Nuhamin Kifle Semu
Algorithms 2026, 19(7), 505; https://doi.org/10.3390/a19070505 - 24 Jun 2026
Viewed by 383
Abstract
Accurate waveform classification in noisy environments is an important task in modern communications, radar signal analysis, biomedical signal interpretation, industrial monitoring and other signal processing systems. This paper investigates the performance of three neural network architectures: Multilayer Perceptron (MLP), one-dimensional Convolutional Neural Network [...] Read more.
Accurate waveform classification in noisy environments is an important task in modern communications, radar signal analysis, biomedical signal interpretation, industrial monitoring and other signal processing systems. This paper investigates the performance of three neural network architectures: Multilayer Perceptron (MLP), one-dimensional Convolutional Neural Network (1D-CNN), and Long Short-Term Memory (LSTM) for multiclass waveform classification in the presence of Additive White Gaussian Noise (AWGN). A time series dataset consisting of multiple waveform classes is generated and corrupted with AWGN across a wide range of signal-to-noise ratio (SNR) levels to simulate noisy signal distortion conditions. The three models are trained and evaluated under identical conditions to ensure a fair comparison. Their classification performance is evaluated in terms of accuracy, Confusion Matrix (CM), Receiver Operating Characteristic (ROC) curve and the Area Under the ROC curve (AUC) across varying SNR values. Simulation results demonstrate that the 1D-CNN effectively captures local temporal patterns and achieves superior robustness in classification at moderate and high SNR levels. The LSTM model demonstrates the ability to capture temporal dependencies in sequential waveform data but exhibits sensitivity to waveform variations due to amplitude, phase and frequency changes and noise at lower SNR values. The MLP, although computationally simpler, shows comparatively limited performance in low-SNR conditions due to its lack of temporal feature extraction capability. For the case of multiclass deterministic waveforms, the accuracy of classification for the 1D-CNN and LSTM is nearly 100% at SNR = 5 dB showing their robustness in classification, whereas the accuracy of MLP is approximately 70% that shows poor classification in noisy conditions. When there is random amplitude, frequency and phase variations in the waveforms, the accuracy of the 1D-CNN and MLP increases with SNR, and 1D-CNN superior to MLP. However, the LSTM accuracy fails to improve with SNR, resulting in poor classification performance in such a scenario. The results provide an insight into the suitability of different neural architectures for waveform classification tasks in noisy communication or other time series applications and highlight the advantages of convolutional feature extraction for robust signal recognition. Full article
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15 pages, 1304 KB  
Article
Polar-SLM-CPM: A Joint Algorithm for High-Efficiency PAPR Suppression in Satellite COFDM Systems
by Jinsong Xu, Manrong Wang, Xiaoxuan Zhu and Yan Zhu
Information 2026, 17(6), 571; https://doi.org/10.3390/info17060571 - 9 Jun 2026
Viewed by 243
Abstract
The high peak-to-average power ratio (PAPR) of orthogonal frequency division multiplexing (OFDM) signals poses a significant challenge for power-limited satellite transponders, leading to power amplifier nonlinearity and reduced system efficiency. This paper proposes a novel joint algorithm named Polar-SLM-CPM for efficient PAPR suppression [...] Read more.
The high peak-to-average power ratio (PAPR) of orthogonal frequency division multiplexing (OFDM) signals poses a significant challenge for power-limited satellite transponders, leading to power amplifier nonlinearity and reduced system efficiency. This paper proposes a novel joint algorithm named Polar-SLM-CPM for efficient PAPR suppression in satellite coded OFDM (COFDM) systems. The core of this scheme is a deeply integrated design that synergistically combines polar coding, intelligent selective mapping (SLM), and adaptive continuous phase modulation (CPM). Unlike conventional approaches that treat these components separately, our method leverages the constant-envelope property of CPM for inherent PAPR limitation, employs a gradient-learning-optimized intelligent SLM mechanism for efficient low-PAPR sequence search, and utilizes capacity-approaching polar codes to guarantee transmission reliability. The synergistic operation is mathematically modeled and extensively evaluated via MATLAB simulations. Results demonstrate that the proposed algorithm achieves a substantial PAPR reduction of approximately 4.2 dB at a complementary cumulative distribution function (CCDF) of 103 while maintaining bit error rate (BER) performance comparable to conventional polar-coded OFDM under additive white Gaussian noise (AWGN) channels. Further analyses on synchronization, computational complexity (Big-O), parameter sensitivity, spectral efficiency trade-offs, and robustness in realistic nonlinear/phase-noise channels are provided, confirming the scheme’s practical viability. This work presents a balanced and effective solution for enhancing the power efficiency and signal integrity of next-generation integrated satellite communication and navigation systems employing COFDM-CPM waveforms. Full article
(This article belongs to the Section Information Processes)
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28 pages, 6635 KB  
Article
Advanced Fault Detection of Permanent Magnet Faults in Offshore Wind Turbine Generators Using Finite Element Analysis and Deep Transfer Learning
by Hüseyin Tayyer Canseven, Mustafa Ercire, Merve Cömert, Abdurrahman Ünsal and Nur Sarma
Machines 2026, 14(6), 665; https://doi.org/10.3390/machines14060665 - 8 Jun 2026
Cited by 2 | Viewed by 500
Abstract
As the offshore wind industry scales toward 15 MW capacity, the reliability of Direct-Drive Permanent Magnet Synchronous Generators (DD-PMSGs) becomes critical. However, real-world run-to-failure data for these massive, multi-pole machines is virtually non-existent, creating a barrier for developing effective data-driven diagnostic systems. This [...] Read more.
As the offshore wind industry scales toward 15 MW capacity, the reliability of Direct-Drive Permanent Magnet Synchronous Generators (DD-PMSGs) becomes critical. However, real-world run-to-failure data for these massive, multi-pole machines is virtually non-existent, creating a barrier for developing effective data-driven diagnostic systems. This study proposes a high-fidelity framework for detecting permanent magnet faults in the International Energy Agency (IEA) 15 MW Reference Wind Turbine. Using Finite Element Analysis (FEA), a dataset (magnetic flux and back electromotive-force (EMF)) capturing the electromagnetic signatures of healthy and faulty states of a PMSG under varying severities is generated. To improve the power of computer vision, 1D time-series signals were transformed into 2D images. Specifically, Gramian Angular Fields (GAFs) and Recurrence Plots (RPs) were applied to magnetic flux density signals, while Markov Transition Fields (MTFs) were applied to back-EMF signals. These representations were then fused into multi-channel Red-Green-Blue (RGB) images and processed via a ResNet-18 Deep Transfer Learning model using a strictly non-overlapping, leakage-free dataset partitioning strategy. The proposed framework achieved a classification accuracy of 99.45% on noise-free data. Furthermore, robustness testing under varying levels of Additive White Gaussian Noise (AWGN) (30 dB, 40 dB, and 50 dB Signal-to-Noise Ratio (SNR)) demonstrated sustained high performance, maintaining over 90% accuracy even under severe 30 dB noise conditions. Comparative analysis proved that this multi-channel fusion significantly outperforms single-channel encoding methods, which collapse under heavy noise, validating the scalability of the framework and applicability for next-generation condition monitoring in harsh offshore environments. Full article
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23 pages, 2899 KB  
Article
Joint Optimization of Four-Edge Type LDPC Codes with Symmetric Decoding Structure Based on EXIT Functions
by Ying You, Guodong Su and Weiwei Lin
Symmetry 2026, 18(5), 794; https://doi.org/10.3390/sym18050794 - 6 May 2026
Viewed by 341
Abstract
Four-edge type low-density parity-check (FET-LDPC) codes, as an important subclass of multi-edge type LDPC codes, offer greater design flexibility and performance potential due to their heterogeneous edge type structure. However, their multi-dimensional degree distribution significantly increases the complexity of optimization. This paper proposes [...] Read more.
Four-edge type low-density parity-check (FET-LDPC) codes, as an important subclass of multi-edge type LDPC codes, offer greater design flexibility and performance potential due to their heterogeneous edge type structure. However, their multi-dimensional degree distribution significantly increases the complexity of optimization. This paper proposes a joint optimization framework for FET-LDPC codes leveraging the symmetric decoding structure inherent in their dual-branch architecture. The main contributions are as follows. First, an improved decoding model is established to analyze the mutual information transmission among the four edge types during iterative decoding, where the symmetry between the accumulator (ACC) and single parity-check (SPC) branches facilitates balanced information exchange. Second, a full-dimensional extrinsic information transfer (FEXIT) chart suitable for FET-LDPC codes is constructed, capturing the mutual information flow across branches. Third, a collaborative optimization model is designed by integrating the FEXIT chart with multi-constraint linear programming (LP) to perform asymmetric optimization for different edge types. The simulation results show that the proposed method achieves significant performance improvement over unoptimized codes in additive white Gaussian noise (AWGN) channels, particularly at a bit error rate (BER) of 10−6. Full article
(This article belongs to the Section A: Computer Science)
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17 pages, 337 KB  
Article
Support Size of ε-Capacity-Achieving Inputs for the Amplitude-Constrained AWGN Channel
by Luca Barletta and Alex Dytso
Entropy 2026, 28(5), 500; https://doi.org/10.3390/e28050500 - 28 Apr 2026
Viewed by 564
Abstract
We study the discrete-time amplitude-constrained additive white Gaussian noise (AWGN) channel from the perspective of near-optimal input distributions in the high-SNR, or equivalently large-amplitude, regime. While it is known that the capacity-achieving input is discrete with finitely many mass points, the precise scaling [...] Read more.
We study the discrete-time amplitude-constrained additive white Gaussian noise (AWGN) channel from the perspective of near-optimal input distributions in the high-SNR, or equivalently large-amplitude, regime. While it is known that the capacity-achieving input is discrete with finitely many mass points, the precise scaling of its support size as a function of the amplitude constraint remains an open problem. In this work, we instead consider the minimal support size required to achieve capacity up to an ε-gap. We introduce the quantity Kε(A), defined as the smallest support size among discrete inputs supported on [A,A] that achieves mutual information within ε of capacity. We show that this relaxed formulation is significantly more tractable and admits sharp characterizations in several vanishing-gap regimes. In particular, for polynomially decaying gaps, ε=Aβ with β1, we establish that Kε(A)=Θ(AlogA) as A. For exponentially small gaps, we obtain bounds of order between AlogA and A3/2. Our approach combines approximation-theoretic bounds for Gaussian mixtures with information-theoretic control of entropy via χ2-divergence, together with a wrapping argument that relates the problem to approximating the uniform distribution on a circle. Beyond the technical results, our framework provides a conceptual explanation for the variety of scaling laws observed in prior numerical studies, suggesting that these may correspond to different regimes of ε-optimality rather than intrinsic properties of the exact optimizer. Full article
13 pages, 4462 KB  
Article
A Lightweight 1D-CNN-Transformer for Bearing Fault Diagnosis Under Limited Data and AWGN Interference
by Yifan Guo, Yijie Zhi, Renyi Qi and Ming Cai
Sensors 2026, 26(9), 2574; https://doi.org/10.3390/s26092574 - 22 Apr 2026
Cited by 4 | Viewed by 1180
Abstract
Intelligent bearing fault diagnosis is essential for maintaining the reliability of rotating machinery. However, deploying deep learning models in industrial environments is often constrained by a lack of labeled data, environmental noise, and strict hardware limits. To address these connected challenges, this paper [...] Read more.
Intelligent bearing fault diagnosis is essential for maintaining the reliability of rotating machinery. However, deploying deep learning models in industrial environments is often constrained by a lack of labeled data, environmental noise, and strict hardware limits. To address these connected challenges, this paper proposes 1D-CNN-Trans, a flexible and resource-efficient hybrid framework. Designed for supervised diagnosis with restricted data, the configurable model combines a compact one-dimensional convolutional neural network (1D-CNN) for local feature extraction, a Transformer encoder for capturing long-range temporal dependencies, and an optional squeeze-and-excitation (SE) module for channel recalibration under favorable conditions. The method is evaluated on two standard mechanical benchmarks under limited sample conditions, controlled additive white Gaussian noise (AWGN), and dynamic non-stationary interference. Experimental results indicate that 1D-CNN-Trans shows improved robustness under interference compared to selected baselines, notably improving accuracy against a standard CNN backbone. Furthermore, findings indicate that while the Transformer ensures noise robustness, channel recalibration (via SE) introduces optimization instability under extreme sparsity and noise. Consequently, we reposition the architecture as a configurable framework where recalibration is conditionally activated. Finally, theoretical complexity analysis is provided to validate the model’s low computational burden, indicating its general feasibility for resource-constrained scenarios. Full article
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32 pages, 4697 KB  
Article
Parameter-Coupled Offset Min-Sum Decoding with Edge-Type Differentiation for MET-LDPC Codes
by Ying You, Guodong Su and Weiwei Lin
Mathematics 2026, 14(8), 1352; https://doi.org/10.3390/math14081352 - 17 Apr 2026
Cited by 1 | Viewed by 447
Abstract
To improve the decoding performance of multi-edge type low-density parity-check (MET-LDPC) codes, this paper proposes an edge-type differentiated parameter coupling offset min-sum (EDPC-OMS) decoding algorithm. The contributions are threefold. First, we replace the traditional uniform compensation with edge-type differentiated compensation, resolving the mismatch [...] Read more.
To improve the decoding performance of multi-edge type low-density parity-check (MET-LDPC) codes, this paper proposes an edge-type differentiated parameter coupling offset min-sum (EDPC-OMS) decoding algorithm. The contributions are threefold. First, we replace the traditional uniform compensation with edge-type differentiated compensation, resolving the mismatch between the decoding model and code structure. Second, we introduce a parameter coupling mechanism that enables joint optimization of multiple edge types while maintaining differentiated configurations. Third, a practically feasible design combining precomputation and look-up tables enables dynamic parameter adjustment with moderate additional overhead, achieving a favorable performance–complexity trade-off. Simulation results over additive white Gaussian noise (AWGN) channels and Rayleigh fading channels demonstrate that the proposed algorithm adaptively selects offset factors according to channel conditions and edge types without introducing significant computational complexity, effectively lowering the bit error rate and enhancing decoding capability. Full article
(This article belongs to the Section E: Applied Mathematics)
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