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decoding error probability of random parity-check matrix ensemble over the erasure channel

DESIGNS CODES AND CRYPTOGRAPHY 2025年第1期93卷 51-77页

作者： Chan, Chin Hei Fu, Fang-Wei Xiong, Maosheng Hong Kong Univ Sci & Technol Math Dept Clear Water Bay Hong Kong Peoples R China Nankai Univ Chern Inst Math Tianjin 300071 Peoples R China Nankai Univ LPMC Tianjin 300071 Peoples R China

In this paper we carry out an in-depth study on the average decoding error probability of the random parity-check matrix ensemble over the erasure channel under three decoding principles, namely unambiguous decoding, maximum likelihood decoding and list decoding. We obtain explicit formulas for the average decoding error probabilities of the random parity-check matrix ensemble under these three decoding principles and compute the error exponents. Moreover, for unambiguous decoding, we compute the variance of the decoding error probability of the random parity-check matrix ensemble and the error exponent of the variance, which implies a strong concentration result, that is, roughly speaking, the ratio of the decoding error probability of a random linear code in the ensemble and the average decoding error probability of the ensemble converges to 1 with high probability when the code length goes to infinity.

关键词： Random parity-check matrix ensemble Parity-check codes Erasure channel decoding error probability error exponent List decoding Maximum likelihood decoding Unambiguous decoding

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Finite Blocklength decoding error probability Oriented Resource Allocation for Uplink URLLC Systems

Finite Blocklength Decoding Error Probability Oriented Resou...

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IEEE Conference on Global Communications (IEEE GLOBECOM) - Intelligent Communications for Shared Prosperity

作者： Li, Zhicheng Shen, Hong Xu, Wei Zhu, Pengcheng Zhao, Chunming Southeast Univ Natl Mobile Commun Res Lab Nanjing 210096 Peoples R China Purple Mt Labs Nanjing 211111 Peoples R China

ISBN: (纸本)9798350310900

We study the resource allocation for an uplink ultra reliable and low-latency communication (URLLC) system. The receive beamformer at the base station (BS) and the transmit power of users are jointly optimized to minimize the finite block-length (FBL) decoding error probability. To solve the difficult nonconvex problem, we first acquire a tractable reformulation by approximating the Gaussian Q-function. Although the resultant problem is still nonconvex, we propose an efficient algorithm where the optimal receive beamformer is obtained in closed form and the transmit powers of users are optimized by employing the majorization-minimization (MM) technique. Simulation results and complexity analysis verify the superiority of the proposed algorithm over existing benchmark schemes.

关键词： Ultra reliable and low-latency communication (URLLC) resource allocation decoding error probability majorization-minimization (MM) technique

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Tight Upper Bounds on the BLER of Spinal Codes Over the AWGN Channel

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IEEE TRANSACTIONS ON COMMUNICATIONS 2025年第1期73卷 332-347页

作者： Li, Aimin Wu, Shaohua Chen, Xiaomeng Sun, Sumei Harbin Inst Technol Shenzhen Guangdong Prov Key Lab Aerosp Commun & Networking Shenzhen 518055 Peoples R China Agcy Sci Technol & Res Inst Infocomm Res Singapore 138632 Singapore Peng Cheng Lab Shenzhen 518055 Peoples R China Harbin Inst Technol Shenzhen Dept Elect Engn Shenzhen 518055 Peoples R China Inst Infocomm Res Agcy Sci Technol & Res ASTAR Fusionopolis Singapore 138632 Singapore

This paper establishes an upper bound on the block error rate (BLER) of Spinal codes, the first rateless codes proven to achieve Shannon capacity in additive white Gaussian noise (AWGN) and binary symmetric channels (BSC). Unlike the conventional reliance on the 1965 Gallager random coding bound for deriving upper bounds, as illustrated in 2016 by Yu et al., this study deviates by noting that Gallager's bound may not adequately represent the distinct properties of specific random codes like Spinal codes and may result in loose bounding performance. We thus introduce novel techniques to refine existing results and enhance the bounding tightness. Our main results are two explicit upper bounds on the BLER of Spinal codes over the AWGN channel, accompanied by theoretical proofs that validate their tightness. Potential applications of the bounds and insights for the coding design are explored in this work.

关键词： Codes Upper bound AWGN channels error probability Maximum likelihood decoding Spine Hash functions Spinal codes decoding error probability ML decoding upper bounds rateless codes

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Age-of-Information-Oriented Security Transmission Scheme for UAV-Aided IoT Networks

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IEEE INTERNET OF THINGS JOURNAL 2025年第8期12卷 9570-9582页

作者： Wang, Jiaxing Guo, Shao Wang, Jingjing Bai, Lin Beihang Univ Sch Cyber Sci & Technol Beijing 100191 Peoples R China Peng Cheng Lab Shenzhen 518000 Peoples R China Beihang Univ Hangzhou Innovat Inst Hangzhou 310051 Peoples R China Zhongguancun Lab Beijing 100191 Peoples R China

Owing to the advantage of flexible deployment of uncrewed aerial vehicles (UAVs), the problem of long-distance transmission of sensor devices in Internet of Things (IoT) networks can be effectively addressed. However, the line-of-sight (LoS) channels of UAVs also make the transmitted data vulnerable to interception by eavesdroppers. In this article, a security transmission scheme is proposed for UAV-aided IoT networks, in which a UAV with variable transmission power is deployed between the sensor device and the monitor. In addition, the concept of Age of Information (AoI) is introduced to measure the freshness of information, while the difference between the AoI of the eavesdropper and the monitor is considered as the metric for the security transmission performance. To enhance system security, we derive a closed-form solution for the AoI difference and propose a UAV deployment algorithm to maximize the gap. The simulation results demonstrate a strong agreement with the theoretical analysis, and the proposed method can significantly improve the security communication performance of the system compared with the traditional method.

关键词： Autonomous aerial vehicles Security Internet of Things Monitoring Relays Temperature sensors Performance evaluation Temperature measurement Simulation Information age Age of Information (AoI) decoding error probability Internet of Things (IoT) security transmission uncrewed aerial vehicle (UAV) communications

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Performance Analysis of Active Reconfigurable Intelligent Surface-Aided URLLC Systems

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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 2024年第11期73卷 17842-17847页

作者： Fang, Manlin Li, Jianqing Liu, Yuanwei Chen, Zhen Zhang, Xiu Yin Huizhou Univ Sch Comp Sci & Engn Huizhou 516006 Peoples R China South China Univ Technol Sch Elect & Informat Engn Guangzhou 516007 Peoples R China Univ Hong Kong Dept Elect & Elect Engn Hong Kong Peoples R China

In this paper, we investigate an active reconfigurable intelligent surfaces (RIS)-aided ultra-reliable low-latency communication (URLLC) system, where the active RIS can amplify the incident signals rather than only reflecting them has done in passive modules. By utilizing the Jensen's inequality and the moment-matching method, two closed-form expressions for the average achievable rate and the average decoding error probability are derived with the optimal shift-phase and the optimal amplification factor. Moreover, the derived expressions are utilized to provide some insights, including the power scaling law, the high signal-to-noise ratio (SNR) slope and the diversity order. Simulation results show that the performance of the small-scale active RIS significantly outperforms the large-scale passive RIS in the URLLC system.

关键词： Ultra reliable low latency communication Signal to noise ratio Rician channels error probability decoding Reliability Vectors Active reconfigurable intelligent surface (RIS) ultra-reliable low-latency communication (URLLC) achievable rate decoding error probability

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User Scheduling Based CLI Mitigation Scheme for NAFD Cell-Free Systems Toward mURLLC

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IEEE COMMUNICATIONS LETTERS 2024年第5期28卷 1211-1215页

作者： Song, Xiangning Sun, Xiaoyu Li, Jiamin Wang, Dongming Zhang, Hongbiao You, Xiaohu South East Univ Natl Mobile Commun Res Lab Nanjing 210096 Peoples R China China Mobile Res Inst Beijing 100053 Peoples R China

In network-assisted full-duplex (NAFD) systems, where uplink (UL) and downlink (DL) communications occur simultaneously, the emergence of massive ultra-reliable low-latency communications (mURLLC) with high density of mobile users brings about severe cross-link interference (CLI) from UL users to DL users. To analyze and mitigate the impact of inter-user CLI, the closed-form expression of decoding error probability is derived and a novel user scheduling based CLI mitigation scheme is designed to jointly maximize the number of served users and system service rate, which determines how many users should be admitted by the network in a timeslot and how the users should be split into groups. To address this optimization problem, we explore an algorithm based on a Deep Q Network (DQN) with low complexity. Numerical results validate the effectiveness of the proposed solution. Moreover, the proposed scheme provides up to 33.9% better rate performance when compared to random user scheduling while guaranteeing the quality of service (QoS) requirements and power constraints.

关键词： Interference decoding Signal to noise ratio Rough surfaces Reliability Quality of service error probability NAFD cell-free systems decoding error probability mURLLC CLI mitigation user scheduling

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Analysis of Rateless Multiple Access Scheme With Maximum Likelihood decoding in an AWGN Channel

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2023年第8期22卷 5240-5252页

作者： Wang, Peng Li, Yonghui Lin, Zihuai Shirvanimoghaddam, Mahyar Park, Ok-Sun Park, Giyoon Vucetic, Branka Univ Sydney Sch Elect & Informat Engn Camperdown NSW 2006 Australia Elect & Telecommun Res Inst Daejeon 34129 South Korea

The rateless multiple access (RMA) scheme is a promising distributed multiple access scheme to achieve simultaneous high reliability, low latency and massive connectivity. In this paper, we investigate the maximum likelihood (ML) decoding performance of the RMA scheme in an Additive white Gaussian noise (AWGN) channel with binary phase-shift keying (BPSK) modulation. For the first time, this paper derives the ensemble weight distribution of the RMA scheme. We derive an upper bound on the decoding error performance of the RMA scheme under ML decoding in an AWGN channel with BPSK modulation. Using the derived bound as the fitness function, we adopt the continuous genetic algorithm to optimize the parameters of the RMA scheme. Simulation results show the tightness of the derived bound and the superiority of the optimized degree distribution over the conventional degree distributions.

关键词： Rateless codes multiple access scheme finite length analysis maximum likelihood (ML) decoding additive white Gaussian noise (AWGN) channels decoding error probability

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probability of error for Optimal Codes in a Reconfigurable Intelligent Surface Aided URLLC System

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IEEE COMMUNICATIONS LETTERS 2023年第8期27卷 2004-2008页

作者： Sui, Likun Lin, Zihuai Univ Sydney Sch Elect & Informat Engn Sydney NSW 2006 Australia

The lower bound on the decoding error probability for the optimal code given a signal-to-noise ratio and a code rate are investigated in this letter for the reconfigurable intelligent surface (RIS) communication system over a Rician fading channel at the short blocklength regime, which is the key characteristic of ultra-reliable low-latency communications (URLLC) to meet the need for strict adherence to quality of service (QoS) requirements. Sphere packing technique is used to derive our main results. The Wald sequential t-test lemma and the Gaussian-Chebyshev quadrature are the main tools to obtain the closed-form expression for the lower bound. Numerical results are provided to validate our results and demonstrate the tightness of our results compared to the Polyanskiy-Poor-Verdu (PPV) bound.

关键词： Index Terms- Reconfigurable intelligent surfaces ultra-reliable and low-latency communications lower bound decoding error probability sphere packing

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Analytical Bounds for the Optimal Code Over the Reconfigurable Intelligent Surface at a Short Blocklength

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IEEE WIRELESS COMMUNICATIONS LETTERS 2023年第9期12卷 1573-1577页

作者： Sui, Likun Lin, Zihuai Univ Sydney Sch Elect & Informat Engn Sydney NSW 2006 Australia

The lower and upper bounds on the decoding error probability for the optimal code given a signal-to-noise ratio and a code rate are investigated in this letter for the reconfigurable intelligent surface (RIS) communication system at the short blocklength regime. The sphere packing technique is used to derive our main results. The Wald sequential ${t}$ -test lemma and the Riemann sum are the main tools to obtain the closed-form expression for both bounds. Numerical results are provided to demonstrate the performances of our derived results.

关键词： Codes Transmitters Wireless communication Upper bound Optimized production technology Receiving antennas Low latency communication Lower bound decoding error probability sphere packing

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Low-density periodical burst correcting codes with decoding probability and detection capability

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JOURNAL OF APPLIED MATHEMATICS AND COMPUTING 2022年第6期68卷 4537-4557页

作者： Das, Pankaj Kumar Haokip, Letminthang Tezpur Univ Dept Math Sci Sonitpur 784028 Assam India

In this paper, we present low-density periodical burst correcting linear codes. Existence of such codes are studied. We also provide decoding error probability of such codes. Weight distribution and Plotkin's type bound for the set of low-density periodical burst errors are also presented. Further, we present weight distribution and Plotkin's type bound for some other periodical bursts which will be detected by such codes.

关键词： Syndrome Low-density periodical burst Weight distribution decoding error probability

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