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Winograd for NTT: A Case Study on Higher-Radix and Low-Latency Implementation of NTT for Post Quantum Cryptography on FPGA

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS 2024年第12期71卷 6396-6409页

作者： Mandal, Suraj Roy, Debapriya Basu Indian Inst Technol Kanpur Dept Comp Sci & Engn Kanpur 208016 India

Number Theoretic Transform (NTT) plays an important role in efficiently implementing lattice-based cryptographic algorithms like CRYSTALS-Kyber, Dilithium, and FALCON. Existing implementations of NTT for these algorithms are mostly based on radix-2 or radix-4 realization of Cooley-Tukey and Gentleman-Sande architectures. In this work, we explore an alternative method of performing NTT known as Winograd's NTT that requires fewer number of modular multipliers than the conventional Coole-Tukey/Gentleman-Sande for higher radix NTT. We have proposed three different low-latency implementations of Winograd's NTT, applicable to CRYSTALS-Dilithium, FALCON, and CRYSTALS-Kyber, respectively. Our first implementation of Winograd NTT focuses on radix- 16 NTT multiplication unit for polynomials of length 256 and can be directly used for CRYSTALS-Dilithium. The NTT of CRYSTALS-Dilithium is also benefited from our proposed K-RED modular multiplication. Our radix-16-based Winograd outperforms existing Cooley-Tukey/Gentleman-Sande based NTT multipliers of CRYSTALS-Dilithium. Our second implementation of NTT is based on radix- 8 Winograd structure with a novel modular multiplication method that targets polynomials of length 512 and can be directly applied for FALCON. For CRYSTALS-Kyber, we have designed a radix-16 Winograd Butterfly Unit (BFU) that can be configured as two parallel radix-8 Winograd BFUs during mixed-radix computation. To the best of our knowledge, this is the first work that applied the Winograd technique for NTT multiplication for post-quantum secure lattice-based cryptographic algorithms.

关键词： Polynomials Logic gates signal processing algorithms Pulse width modulation Low latency communication Memory management Adders Pipelines Homomorphic encryption Field programmable gate arrays Number theoretic transformation (NTT) CRYSTALS-Dilithium FALCON CRYSTALS-Kyber Winograd

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Coordinate Descent Detection algorithms Using Adaptive Moment Estimation for MDL-Impaired Mode Division Multiplexing Systems

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IEEE ACCESS 2024年 12卷 170027-170040页

作者： Mi, Shuchao Zhang, Jianyong Yan, Baorui Shen, Yifan Wang, Muguang Fan, Guofang Zhang, Peiying Beijing Jiaotong Univ Key Lab All Opt Network & Adv Telecommun EMC Beijing 100044 Peoples R China Beijing Jiaotong Univ Inst Lightwave Technol Beijing 100044 Peoples R China China Univ Petr East China Qingdao Inst Software Coll Comp Sci & Technol Qingdao 266580 Peoples R China

The performance of mode division multiplexing (MDM) systems is limited by mode-dependent loss (MDL), which seriously deteriorates the unitarity of the transmission matrix, making the traditional detection algorithms ineffective. In order to mitigate the effect of MDL in MDM transmission and improve the efficiency of digital signal processing at the receiver, a novel coordinate descent (CD)-based box-constrained detection algorithm using adaptive moment estimate (CDbox-Adam) is proposed. In the process of each coordinate update for the CDbox detection algorithm, the adaptive moment estimation (Adam) method adaptively updates the step size for different parameters from the first moment estimate and the second moment estimate of the gradients. To simplify the process of each coordinate updating of the CDbox-Adam algorithm, the CDbox-Adamax detection algorithm is also proposed. The CDbox-Adamax detection algorithm generalizes the 2-norm update rule of weights to the infinite norm. At the same time, an early stop criterion is proposed to efficiently avoid unnecessary iterations. Simulation results show that the early stop criterion reduces the number of iterations of the proposed detection algorithms. For a 12-mode MDM system impaired by MDL, the average number of iterations of the proposed detection algorithms is less than the CDbox detection algorithm. Thus, the proposed detection algorithms present lower computational complexity than the CDbox detection algorithm. Furthermore, compared with the conventional minimum mean square error (MMSE) detection algorithm, the proposed detection algorithms, CDbox-Adam and CDbox-Adamax, gain signal to noise ratio (SNR) improvement of 2.3 dB and 1.6 dB at BER = 10(-5) when MDL = 5 dB with QPSK and 16QAM, respectively. In the presence of MDL = 5 dB and 10 dB, when compared with the proposed detection algorithms with perfect CSI, the proposed detection algorithms with LS channel estimation requires 5.1 dB and 2.5 dB more of SNR to get

关键词： Multiplexing Simulation Channel estimation Estimation signal processing algorithms Receivers Propagation losses Detection algorithms Computational complexity signal to noise ratio Mode division multiplexing MDL detection algorithm channel estimation BER

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Time-Frequency-Space EEG Decoding Model Based on Dense Graph Convolutional Network for Stroke

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IEEE JOURNAL OF BIOMEDICAL AND HEALTH INFORMATICS 2024年第9期28卷 5214-5226页

作者： Leng, Jiancai Li, Han Shi, Weiyou Gao, Licai Lv, Chengyan Wang, Chen Xu, Fangzhou Zhang, Yang Jung, Tzyy-Ping Qilu Univ Technol Shandong Acad Sci Int Sch Optoelect Engn Jinan 250353 Shandong Peoples R China Shandong Univ Tradit Chinese Med Affiliated Hosp Rehabil & Phys Therapy Dept Jinan 250011 Shandong Peoples R China Univ Calif San Diego Inst Neural Computat Inst Engn Med La Jolla CA 92093 USA Univ Calif San Diego Dept Bioengn La Jolla CA 92093 USA

Stroke, a sudden cerebrovascular ailment resulting from brain tissue damage, has prompted the use of motor imagery (MI)-based Brain-Computer Interface (BCI) systems in stroke rehabilitation. However, analyzing EEG signals from stroke patients is challenging because of their low signal-to-noise ratio and high variability. Therefore, we propose a novel approach that combines the modified S-transform (MST) and a dense graph convolutional network (DenseGCN) algorithm to enhance the MI-BCI performance across time, frequency, and space domains. MST is a time-frequency analysis method that efficiently concentrates energy in EEG signals, while DenseGCN is a deep learning model that uses EEG feature maps from each layer as inputs for subsequent layers, facilitating feature reuse and hyper-parameters optimization. Our approach outperforms conventional networks, achieving a peak classification accuracy of 90.22% and an average information transfer rate (ITR) of 68.52 bits per minute. Moreover, we conduct an in-depth analysis of the event-related desynchronization/event-related synchronization (ERD/ERS) phenomenon in the deep-level EEG features of stroke patients. Our experimental results confirm the feasibility and efficacy of the proposed approach for MI-BCI rehabilitation systems.

关键词： Electroencephalography Stroke (medical condition) Motors signal processing algorithms Electrodes Task analysis Brain modeling Electroencephalogram motor imagery brain-computer interface dense graph convolutional network stroke

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Improved Alias-and-Separate Speech Coding Framework With Minimal Algorithmic Delay

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IEEE JOURNAL OF SELECTED TOPICS IN signal processing 2024年第8期18卷 1414-1426页

作者： Lee, Eunkyun Beack, Seungkwon Shin, Jong Won Gwangju Inst Sci & Technol Sch Elect Engn & Comp Sci Gwangju 61005 South Korea Elect & Telecommun Res Inst Daejeon 34129 South Korea

Alias-and-Separate (AaS) speech coding framework has shown the possibility to encode wideband (WB) speech with a narrowband (NB) speech codec and reconstruct it using speech separation. WB speech is first decimated incurring aliasing and then coded, transmitted, and decoded with a NB codec. The decoded signal is then separated into lower band and spectrally-flipped high band using a speech separation module, which are expanded, lowpass/highpass filtered, and added together to reconstruct the WB speech. The original AaS system, however, has algorithmic delay originated from the overlap-add operation for consecutive segments. This algorithmic delay can be reduced by omitting the overlap-add procedure, but the quality of the reconstructed speech is also degraded due to artifacts on the segment boundaries. In this work, we propose an improved AaS framework with minimum algorithmic delay. The decoded signal is first expanded by inserting zeros in-between samples before being processed by source separation module. As the expanded signal can be viewed as a summation of the frequency-shifted versions of the original signal, the decoded-and-expanded signal is then separated into the frequency-shifted signals, which are multiplied by complex exponentials and summed up to reconstruct the original signal. With carefully designed transposed convolution operation in the separation module, the proposed system requires minimal algorithmic delay while preventing discontinuity at the segment boundaries. Additionally, we propose to employ a generative vocoder to further improve the perceived quality and a modified multi-resolution short-time Fourier transform (MR-STFT) loss. Experimental results on the WB speech coding with a NB codec demonstrated that the proposed system outperformed the original AaS system and the existing WB speech codec in the subjective listening test. We have also shown that the proposed method can be applied when the decimation factor is not 2 in the experiment

关键词： Speech coding Delays Source separation signal processing algorithms Vocoders Speech processing Image reconstruction Speech codecs Graph theory Particle separators Alias-and-Separate speech coding speech separation

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Projection-Based Algorithm and Performance Analysis for TDOA Localization in MPR

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IEEE TRANSACTIONS ON signal processing 2024年 72卷 896-911页

作者： Sun, Yimao Ho, K. C. Xing, Tianyi Yang, Yanbing Chen, Liangyin Sichuan Univ Coll Comp Sci Chengdu 610065 Peoples R China Univ Missouri EECS Dept Columbia MO 65211 USA Univ Elect Sci & Technol China Sch Informat & Commun Engn Chengdu 611731 Peoples R China

In addition to unifying the positioning of a source that yields the coordinates if the source is near and the direction of arrival (DOA) if the source is far, the Modified Polar Representation (MPR) of the source position has a distinct advantage for decoupling the estimation of angle and range. This paper explores such characteristics of MPR for source localization and develops two algorithms for separate estimation through the subspace projection techniques. The first algorithm, null-space projection (NSP), estimates the object direction by itself after subspace projection and then uses the estimated direction to obtain the inverse-range. The second algorithm, independent NSP (INSP), determines the object direction and inverse-range independently from each other. While exploiting separated estimation, we show by analysis that NSP is optimum in reaching the Cramer Rao Lower bound (CRLB) performance under Gaussian noise. Indeed, we have proven NSP is equivalent to general trust region subproblem (GTRS) solution of joint estimation in theory, although both come from different approaches and perspectives. INSP has the attractive benefit of independent estimation and is suitable for distributed or parallel processing, albeit its performance is suboptimal. Furthermore, we have evaluated the theoretical estimation bias of NSP that can be subtracted from NSP to yield the NSP bias subtraction (NSPBS) solution, having bias performance better than the Maximum Likelihood Estimator (MLE). Simulation validates the performance and analysis. While NSP is equivalent to GTRS in theory, NSP has a lower complexity and can be a little more resilient to noise in practice.

关键词： Location awareness Maximum likelihood estimation signal processing algorithms Direction-of-arrival estimation Sun Mathematical models Complexity theory Closed-form solution localization modified polar representation projection time difference of arrival (TDOA)

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DPO: Discrete Prompt Optimization for Vision-Language Models

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IEEE signal processing LETTERS 2025年 32卷 671-675页

作者： Liang, Nanhao Liu, Yong Chinese Acad Sci Hefei Inst Phys Sci Hefei 230031 Peoples R China Univ Sci & Technol China Hefei 230026 Peoples R China

In recent years, the emergence of large vision-language models (VLMs) has catalyzed the development of prompt learning, where networks are trained to enhance VLM performance by learning continuous prompts. However, traditional continuous prompt learning often struggles with challenges like overfitting to Base classes and a lack of interpretability due to the nature of prompt parameterization. To overcome these limitations, we introduce Discrete Prompt Optimization (DPO), a method that optimizes text prompts in discrete word-space. During training, scores are assigned to token embeddings, which are then used to select the most effective token sequence for the downstream task. DPO was tested across 11 diverse datasets, consistently outperforming baseline methods like CLIP and CoOp on Novel classes in most cases. This discrete approach not only reduces overfitting but also enhances transparency and model interpretability, enabling the learning of dataset-specific text prompts that are easily understandable.

关键词： Training Optimization Adaptation models Visualization Overfitting Vectors Vocabulary signal processing algorithms Stochastic processes Standards Prompt learning vision-language model

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Optimal Sample Acquisition for Optimally Weighted PCA From Heterogeneous Quality Sources

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IEEE signal processing LETTERS 2025年 32卷 1425-1429页

作者： Hong, David Balzano, Laura Univ Delaware Dept Elect & Comp Engn Newark DE 19716 USA Univ Michigan Dept Elect Engn & Comp Sci Ann Arbor MI 48109 USA

Modern high-dimensional datasets are often formed by acquiring samples from multiple sources having heterogeneous quality, i.e., some sources are noisier than others. Collecting data in this manner raises the following natural question: what is the best way to collect the data (i.e., how many samples should be acquired from each source) given constraints (e.g., on time or energy)? In general, the answer depends on what analysis is to be performed. In this paper, we study the foundational signal processing task of estimating underlying low-dimensional principal components. Since the resulting dataset will be high-dimensional and will have heteroscedastic noise, we focus on the recently proposed optimally weighted PCA, which is designed specifically for this setting. We develop an efficient method for designing sample acquisitions that optimize the asymptotic performance of optimally weighted PCA given resource constraints, and we illustrate the proposed method through various case studies.

关键词： Principal component analysis Noise signal processing algorithms Costs Soft sensors Software algorithms Optimization Data models Training Image sensors Heterogeneous quality large-dimensional data principal component analysis sample acquisition design

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Sub-Nyquist USF Spectral Estimation: K Frequencies With 6K+4 Modulo Samples

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IEEE TRANSACTIONS ON signal processing 2024年 72卷 5065-5076页

作者： Guo, Ruiming Zhu, Yuliang Bhandari, Ayush Imperial Coll London Dept Elect & Elect Engn London SW7 2AZ England

Digital acquisition of high bandwidth signxals is particularly challenging when Nyquist rate sampling is impractical. This has led to extensive research in sub-Nyquist sampling methods, primarily for spectral and sinusoidal frequency estimation. However, these methods struggle with high-dynamic-range (HDR) signals that can saturate analog-to-digital converters (ADCs). Addressing this, we introduce a novel sub-Nyquist spectral estimation method, driven by the Unlimited Sensing Framework (USF), utilizing a multi-channel system. The sub-Nyquist USF method aliases samples in both amplitude and frequency domains, rendering the inverse problem particularly challenging. Towards this goal, our exact recovery theorem establishes that K sinusoids of arbitrary amplitudes and frequencies can be recovered from 6K+4 modulo samples, remarkably, independent of the sampling rate or folding threshold. In the true spirit of sub-Nyquist sampling, via modulo ADC hardware experiments, we demonstrate successful spectrum estimation of HDR signals in the kHz range using Hz range sampling rates (0.078% Nyquist rate). Our experiments also reveal up to a 33-fold improvement in frequency estimation accuracy using one less bit compared to conventional ADCs. These findings open new avenues in spectral estimation applications, e.g., radars, direction-of-arrival (DoA) estimation, and cognitive radio, showcasing the potential of USF.

关键词： Hardware Frequency estimation Sensors Estimation Quantization (signal) Noise Vectors Time-domain analysis signal processing algorithms Radar imaging Unlimited sampling sub-Nyquist sampling robust recovery multi-channel architecture spectral estimation

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Ensemble Kalman Filtering Meets Gaussian Process SSM for Non-Mean-Field and Online Inference

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IEEE TRANSACTIONS ON signal processing 2024年 72卷 4286-4301页

作者： Lin, Zhidi Sun, Yiyong Yin, Feng Thiery, Alexandre Hoang Chinese Univ Hong Kong Sch Sci & Engn Future Network Intelligence Inst Shenzhen 518172 Peoples R China Shenzhen Res Inst Big Data Shenzhen 518172 Peoples R China Natl Univ Singapore Dept Stat & Data Sci Singapore 117546 Singapore Chinese Univ Hong Kong Sch Sci & Engn Shenzhen Peoples R China

The Gaussian process state-space models (GPSSMs) represent a versatile class of data-driven nonlinear dynamical system models. However, the presence of numerous latent variables in GPSSM incurs unresolved issues for existing variational inference approaches, particularly under the more realistic non-mean-field (NMF) assumption, including extensive training effort, compromised inference accuracy, and infeasibility for online applications, among others. In this paper, we tackle these challenges by incorporating the ensemble Kalman filter (EnKF), a well-established model-based filtering technique, into the NMF variational inference framework to approximate the posterior distribution of the latent states. This novel marriage between EnKF and GPSSM not only eliminates the need for extensive parameterization in learning variational distributions, but also enables an interpretable, closed-form approximation of the evidence lower bound (ELBO). Moreover, owing to the streamlined parameterization via the EnKF, the new GPSSM model can be easily accommodated in online learning applications. We demonstrate that the resulting EnKF-aided online algorithm embodies a principled objective function by ensuring data-fitting accuracy while incorporating model regularizations to mitigate overfitting. We also provide detailed analysis and fresh insights for the proposed algorithms. Comprehensive evaluation across diverse real and synthetic datasets corroborates the superior learning and inference performance of our EnKF-aided variational inference algorithms compared to existing methods.

关键词： Heuristic algorithms signal processing algorithms Inference algorithms Gaussian processes Computational modeling Kalman filters Approximation algorithms Gaussian process state-space model ensemble Kalman filter online learning variational inference

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Joint Beamforming for RIS-Assisted Integrated Sensing and Communication Systems

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IEEE TRANSACTIONS ON COMMUNICATIONS 2024年第4期72卷 2232-2246页

作者： Xu, Yongqing Li, Yong Zhang, J. Andrew Renzo, Marco Di Quek, Tony Q. S. Beijing Univ Posts & Telecommun Key Lab Universal Wireless Commun Beijing 100876 Peoples R China Univ Technol Sydney UTS Global Big Data Technol Ctr GBDTC Sydney NSW 2007 Australia Univ Technol Sydney UTS Sch Elect & Data Engn Sydney NSW 2007 Australia Univ Paris Saclay CNRS Lab Signaux & Syst Cent Supelec F-91192 Gif Sur Yvette France Singapore Univ Technol & Design Singapore 487372 Singapore Yonsei Univ Yonsei Frontier Lab Seoul 03722 South Korea

Integrated sensing and communications (ISAC) is an emerging technique for the next generation of communication systems. However, due to multiple performance metrics used for communication and sensing, the limited number of degrees-of-freedom (DoF) in optimizing ISAC systems poses a challenge. Reconfigurable intelligent surfaces (RISs) can introduce new DoF for beamforming in ISAC systems, thereby enhancing the performance of communication and sensing simultaneously. In this paper, we propose two optimization techniques for beamforming in RIS-assisted ISAC systems. The first technique is an alternating optimization (AO) algorithm based on the semidefinite relaxation (SDR) method and a one-dimension iterative (ODI) algorithm, which can maximize the radar mutual information (MI) while imposing constraints on the communication rates. The second technique is an AO algorithm based on the Riemannian gradient (RG) method, which can maximize the weighted ISAC performance metrics. Simulation results verify the effectiveness of the proposed schemes. The AO-SDR-ODI method is shown to achieve better communication and sensing performance, than the AO-RG method, at a higher complexity. It is also shown that the mean-squared-error (MSE) of the estimates of the sensing parameters decreases as the radar MI increases.

关键词： Radar Sensors Array signal processing Optimization Measurement Estimation signal processing algorithms Integrated sensing and communication reconfigurable intelligent surface radar mutual information beamforming manifold optimization

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