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Monte Carlo Integration Using Elliptic Curves

Chinese Annals of Mathematics,Series B 2025年第2期46卷 241-260页

作者： Chung Pang MOK Huimin ZHENG Shanghai Institute for Mathematics and Interdisciplinary Sciences Department of Mathematics Nanjing University Jiangsu National Center for Applied Mathematics College of Information and Network Engineering Anhui Science and Technology University

The authors carry out numerical experiments with regard to the Monte Carlo integration method, using as input the pseudorandom vectors that are generated by the algorithm proposed in [Mok, C. P., Pseudorandom Vector Generation Using Elliptic Curves and Applications to Wiener Processes, Finite Fields and Their Applications, 85, 2023,102129], which is based on the arithmetic theory of elliptic curves over finite fields. They consider integration in the following two cases: The case of Lebesgue measure on the unit hypercube [0, 1]d, and as well as the case of Wiener measure. In the case of Wiener measure, the construction gives discrete time simulation of an independent sequence of standard Wiener processes, which is then used for the numerical evaluation of FeynmanKac formulas.

关键词： 11K45 65C05 65C10 65M75 Elliptic curves Feynman-Kac formulas Finite fields Monte Carlo integration Pseudorandom vectors

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Edge-Subset Lattice and Its Application to Linear network Error Correction coding

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IEEE Transactions on information Theory 2025年

作者： Guang, Xuan Cui, Ruopu Yeung, Raymond W. Tianjin300071 China The Chinese University of Hong Kong Institute of Network Coding Department of Information Engineering SAR Hong Kong

In this paper, we first explore the underlying mathematical structure of edge subsets on a finite directed acyclic graph in using a lattice-theoretic approach. We prove that a collection of edge subsets, depending on different conditions it satisfies, together with the corresponding "cut-separating" partial order, can form a meet-semilattice, a join-semilattice or a lattice. The bottom and top thus derived generalize the concept of the primary minimum cut introduced by Guang and Yeung (2018) and hence we provide a new way from the lattice-theoretic point of view to understand the primary minimum cut and its existence and uniqueness. The introduced concepts and obtained results regarded as a bridge connect graph theory and lattice theory, which appear to be of fundamental interest in graph theory, lattice theory, and even beyond. In addition, we consider linear network error correction (LNEC) coding when errors may occur on edges of a communication network of which the topology is known. In LNEC coding, the minimum required field size for the existence of LNEC codes, in particular LNEC maximum distance separable (MDS) codes which are regarded as a most important type of optimal codes, is an open problem not only of theoretical interest but also of practical importance. By applying the approach of the above edge-subset (semi-)lattice, we obtain an improved upper bound on the minimum required field size for the existence of LNEC (MDS) codes. We quantify the improvement over the existing results by both theoretical analysis and numerical simulations and thus show that the improvement is in general significant. The improved upper bound, which is graph-theoretic, depends only on the network topology and requirement of the error correction capability but not on a specific code construction. We also develop an efficient algorithm that can compute the bound in a linear time of the number of edges. © 1963-2012 IEEE.

关键词： Lattice theory

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Proving information Inequalities by Gaussian Elimination

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IEEE Transactions on information Theory 2025年第4期71卷 2315-2328页

作者： Guo, Laigang Yeung, Raymond W. Gao, Xiao-Shan Beijing Normal University Laboratory of Mathematics and Complex Systems Ministry of Education School of Mathematical Sciences Beijing China The Chinese University of Hong Kong N.T. Institute of Network Coding the Department of Information Engineering Hong Kong Chinese Academy of Sciences University of Chinese Academy of Sciences Key Laboratory of Mathematics Mechanization Institute of Systems Science AMSS Beijing China

The proof of information inequalities and identities under linear constraints on the information measures is an important problem in information theory. For this purpose, ITIP and other variant algorithms have been developed and implemented, which are all based on solving a linear program (LP). Building on our recent work [23], we developed in this paper an enhanced approach for solving this problem. © 1963-2012 IEEE.

关键词： information theory

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Inequalities Revisited

arXiv

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arXiv 2025年

作者： Yeung, Raymond W. Institute of Network Coding Department of Information Engineering The Chinese University of Hong Kong N.T. Hong Kong

In the past over two decades, very fruitful results have been obtained in information theory in the study of the Shannon entropy. This study has led to the discovery of a new class of constraints on the Shannon entropy called non-Shannon-type inequalities. Intimate connections between the Shannon entropy and different branches of mathematics including group theory, combinatorics, Kolmogorov complexity, probability, matrix theory, etc, have been established. All these discoveries were based on a formality introduced for constraints on the Shannon entropy, which suggested the possible existence of constraints that were not previously known. We assert that the same formality can be applied to inequalities beyond information theory. To illustrate the ideas, we revisit through the lens of this formality three fundamental inequalities in mathematics: the AM-GM inequality in algebra, Markov’s inequality in probability theory, and the Cauchy-Scharwz inequality for inner product spaces. Applications of this formality have the potential of leading to the discovery of new inequalities and constraints in different branches of mathematics. © 2025, CC BY-NC-ND.

关键词： Group theory

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An overview on IRS-enabled sensing and communications for 6G: architectures, fundamental limits, and joint beamforming designs

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Science China(information Sciences) 2025年第5期68卷 170-193页

作者： Xianxin SONG Yuan FANG Feng WANG Zixiang REN Xianghao YU Ye ZHANG Fan LIU Jie XU Derrick Wing Kwan NG Rui ZHANG Shuguang CUI School of Science and Engineering (SSE) Shenzhen Future Network of Intelligence Institute (FNii-Shenzhen)and Guangdong Provincial Key Laboratory of Future Networks of Intelligence The Chinese University of Hong Kong Department of Electrical Engineering City University of Hong Kong School of Information Engineering Guangdong University of Technology Key Laboratory of Wireless-Optical Communications Chinese Academy of Sciences School of Information Science and Technology University of Science and Technology of China Computer School Beijing Information Science and Technology University National Mobile Communications Research Laboratory School of Information Science and Engineering Southeast University School of Electrical Engineering and Telecommunications University of New South Wales School of Science and Engineering Shenzhen Research Institute of Big Data The Chinese University of Hong Kong Department of Electrical and Computer Engineering National University of Singapore

This study presents an overview on intelligent reflecting surface(IRS)-enabled sensing and communication for the forthcoming sixth-generation(6G) wireless networks, in which IRSs are strategically deployed to proactively reconfigure wireless environments to improve both sensing and communication(S&C) performance. First, we exploit a single IRS to enable wireless sensing in the base station's(BS's) non-line-of-sight(NLoS) area. In particular, we present three IRS-enabled NLoS target sensing architectures with fully-passive, semi-passive, and active IRSs, respectively. We compare their pros and cons by analyzing the fundamental sensing performance limits for target detection and parameter estimation. Next, we consider a single IRS to facilitate integrated sensing and communication(ISAC), in which the transmit signals at the BS are used for achieving both S&C functionalities, aided by the IRS through reflective beamforming. We present joint transmit signal and receiver processing designs for realizing efficient ISAC, and jointly optimize the transmit beamforming at the BS and reflective beamforming at the IRS to balance the fundamental performance tradeoff between S&C. Furthermore, we discuss multi-IRS networked ISAC, by particularly focusing on multi-IRS-enabled multi-link ISAC, multi-region ISAC, and ISAC signal routing, respectively. Finally, we highlight various promising research topics in this area to motivate future work.

关键词： integrated sensing and communication (ISAC) intelligent reflecting surface (IRS) non-line-of-sight (NLoS) sensing sensing and communication tradeoff

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Enhancing GNSS Signal Authentication through Multi-Antenna Systems

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IEEE Transactions on Wireless Communications 2025年第5期24卷 4361-4376页

作者： Tan, Haijun Xie, Ning Huang, Lei Li, Hongbin Pengcheng National Laboratory of China Control and Network Foundation Laboratory Shenzhen518107 China Shenzhen University State Key Laboratory of Radio Frequency Heterogeneous Integration Guangdong Key Laboratory of Intelligent Information Processing College of Electronics and Information Engineering Shenzhen518060 China Stevens Institute of Technology Department of Electrical and Computer Engineering HobokenNJ07030 United States

The Global Navigation Satellite System (GNSS) receiver has become indispensable in navigation applications due to its affordability and reliable accuracy. Despite its widespread use, GNSS is vulnerable to manipulation by malicious entities within the inherently insecure wireless landscape. This paper proposes innovative GNSS signal authentication strategies that employing multiple antennas to counteract spoofing attacks. Leveraging a multi-antenna framework enhances the distinguishability of spoofing signals over traditional single-antenna configurations. Importantly, the proposed approaches capitalize on spatial characteristics, which are independent of the GNSS signal's intrinsic features, to accurately identify spoofing attacks. Specifically, we propose a Direction-of-Arrival (DOA)-based authentication scheme to address scenarios where authentic signals are blocked during spoofing attacks. Additionally, for situations where both authentic and spoofing signals coexist at the receiver, we propose a Spatial Filter (SF)-based authentication scheme. Through rigorous theoretical analysis and comprehensive simulations, we not only validate the proposed schemes but also demonstrate their robustness and effectiveness in enhancing GNSS signal security. The simulation results, aligning closely with theoretical predictions, underscore the superiority of the proposed schemes in safeguarding against spoofing threats. © 2002-2012 IEEE.

关键词： Satellite antennas

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LASS: A Novel and Economical Data Augmentation Framework Based on Language Models for Debiasing Opinion Summarization 31

LASS: A Novel and Economical Data Augmentation Framework Bas...

引用

31st International Conference on Computational Linguistics, COLING 2025

作者： Zhang, Yanyue Li, Pengfei Lai, Yilong He, Yulan Zhou, Deyu School of Computer Science and Engineering Key Laboratory of Computer Network and Information Integration Ministry of Education Southeast University China Department of Informatics King's College London United Kingdom The Alan Turing Institute United Kingdom

ISBN: (纸本)9798891761964

As more than 70% of reviews in the existing opinion summary data set are positive, current opinion summarization approaches are hesitant to generate negative summaries given the input of negative texts. To address such sentiment bias, a direct approach without the reliance on a specific structure is to generate additional data based on large language models to balance the emotional distribution of the dataset. However, large-scale data augmentation based on large language models faces an apparent disadvantage, the expensive costs. Therefore, in this paper, we propose LASS, a novel data augmentation framework based on both LArge and Small language models for debiaSing opinion summarization. Specifically, a small number of synthesized negative reviews is obtained by rewriting the positive text via a large language model. Then, a disentangle reconstruction model is trained based on the generated data. After training, a large amount of synthetic data can be obtained by decoding the new representation obtained from the combination of different sample representations and filtering based on perplexity degree and sentiment classification. Experiments have proved that LASS can effectively alleviate emotional bias, similar to using only large models, but in a more economical way. © 2025 Association for Computational Linguistics.

关键词： Data assimilation

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Task Offloading in Internet of Vehicles: A DRL-based Approach with Representation Learning for DAG Scheduling

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IEEE Transactions on Mobile Computing 2025年第6期24卷 5045-5060页

作者： Deng, Xiaoheng Yang, Haoyu Zhang, Jingjing Gui, Jinsong Lin, Siyu Wang, Xin Min, Geyong Central South University School of Electronic Information Changsha410075 China Central South University Shenzhen Research Institute China Beijing Jiaotong University School of Electronic and Information Engineering The State Key Laboratory of Rail Traffic Control and Safety Beijing100044 China Key Laboratory of Computing Power Network and Information Security Ministry of Education Shandong Computer Science Center Jinan250014 China University of Exeter Department of Computer Science ExeterEX4 4QF United Kingdom

The rapid evolution of the Internet-of-Vehicles (IoV) has amplified the need for mobile computing resources, driving the shift toward offloading tasks to edge servers or vehicles with idle resources to optimize computational efficiency. To this end, an approach based on Deep Reinforcement Learning (DRL) is presented in this paper, termed DVTP, which integrates Variational Graph Attention networks (VGAT) and Transformer models to optimize Directed Acyclic Graph (DAG) task scheduling in vehicular networks. DVTP effectively captures both the spatiotemporal information and task dependencies, enabling more accurate and efficient task offloading decisions. Extensive simulation experiments demonstrate that DVTP outperforms traditional methods in reducing task completion times across various multi-vehicle and multi-edge server scenarios, showcasing its potential for real-world IoV applications. © 2025 IEEE.

关键词： Deep reinforcement learning

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Towards High-Performance network coding: FPGA Acceleration With Bounded-value Generators

arXiv

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arXiv 2025年

作者： Qing, Jiaxin Leong, Philip H.W. Lee, Kin-Hong Yeung, Raymond W. The Chinese University of Hong Kong Hong Kong The School of Electrical and Information Engineering The University of Sydney Australia The Department of Computer Science Engineering The Chinese University of Hong Kong Hong Kong The Department of Information Engineering The Chinese University of Hong Kong Hong Kong The Institute of Network Coding The Chinese University of Hong Kong Hong Kong Limited Hong Kong

network coding enhances performance in network communications and distributed storage by increasing throughput and robustness while reducing latency. Batched Sparse (BATS) codes are a class of capacity-achieving network codes, but their practical applications are hindered by their structure, computational intensity, and power demands of finite field operations. Most literature focuses on algorithmic-level techniques to improve coding efficiency. Optimization with an algorithm/hardware co-designing approach has long been neglected. Leveraging the unique structure of BATS codes, we first present CS-BATS, a hardware-friendly variant. Next we propose a simple but effective bounded-value generator, to reduce the size of a finite field multiplier by up to 70%. Finally, we report on a scalable and resource-efficient FPGA-based network coding accelerator that achieves a throughput of 27 Gbps, a speedup of more than 300 over software. © 2025, CC BY-NC-ND.

关键词： Integrated circuit design

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Robust Frequency Offset Estimation for Coherent DSCM Systems Under Severe Bandwidth Limitation

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IEEE Photonics Technology Letters 2025年

作者： Jin, Yongchao Yang, Yanfu Xiang, Qian Gong, Siyu Cheng, Chen Fan, Linsheng Zuo, Tianjian Harbin Institute of Technology Department of Electronic and Information Engineering Shenzhen China Huawei Technology Company Ltd Network Technology Laboratory Shenzhen China

Since digital subcarrier multiplexing (DSCM) signals require frequency offset estimation (FOE) and compensation before demultiplexing, we propose a robust FOE scheme for DSCM systems that estimates the frequency offset (FO) by calculating the magnitude sum of spectral components within a specified range centered at zero frequency. The scheme remains effective even under severe bandwidth limitation conditions. The experimental results show that with FFT sizes of 2048, the maximum FOE errors are 119 MHz, 123 MHz, and 87 MHz for the 4, 6, and 8 subcarrier DSCM signals, respectively. Additionally, the cumulative distribution functions (CDF) of the FOE error less than 50 MHz are 0.79, 0.81, and 0.82, respectively. Furthermore, the proposed scheme demonstrates stable performance across a wide range of FO and received optical power (ROP). Therefore, the proposed scheme can achieve high FOE accuracy in the presence of severe bandwidth limitation for coherent DSCM systems. © 1989-2012 IEEE.

关键词： Distribution functions

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