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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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A new upper bound on the ML decoding error probability of linear binary block codes in AWGN interference

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IEEE TRANSACTIONS ON INFORMATION THEORY 2004年第12期50卷 3026-3036页

作者： Yousefi, S Khandani, AK Univ Waterloo Dept Elect & Comp Engn Waterloo ON N2L 3G1 Canada

Performance evaluation of maximum-likelihood (ML) soft-decision-decoded binary block codes is usually carried out using bounding techniques. Many tight upper bounds on the error probability of binary codes are based on the so-called Gallager's first bounding technique (GFBT). The tangential sphere bound (TSB) of Poltyrev which has been believed for many years to offer the tightest bound developed for binary block codes is an example. Within the framework of the TSB and GFBT, we apply a new method referred to as the "added-hyper-plane" (AHP) technique, to the decomposition of the error probability. This results in a bound developed upon the application of two stages of the GFBT with two different Gallager regions culminating in a tightened upper bound beyond the TSB. The proposed bound is simple and only requires the spectrum of the binary code.

关键词： additive white Gaussian noise (AWGN) channel block codes bounds decoding error probability distance spectrum Gallager bounds linear binary block codes maximum-likelihood (ML) decoding probability of error union bound upper bounds

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On improved bounds on the decoding error probability of block codes over interleaved fading channels, with applications to turbo-like codes

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IEEE TRANSACTIONS ON INFORMATION THEORY 2001年第6期47卷 2275-2299页

作者： Sason, I Shamai, S Technion Israel Inst Technol Dept Elect Engn IL-32000 Haifa Israel

We derive here improved upper bounds on the decoding error probability of block codes which are transmitted over fully interleaved Rician fading channels, coherently detected and maximum-likelihood (ML) decoded. We assume that the fading coefficients during each symbol are statistically independent (due to a perfect channel interleaver), and that perfect estimates of these fading coefficients are provided to the receiver. The improved upper bounds on the block and bit error probabilities are derived for fully interleaved fading channels with various orders of space diversity, and are found by generalizing some recently introduced upper bounds for the binary-input additive white Gaussian noise (AWGN) channel. The advantage of these bounds over the ubiquitous union bound is demonstrated for some ensembles of turbo codes and low-density parity-check (LDPC) codes, and it is especially pronounced in a portion of the rate region exceeding the cutoff rate. Our generalization of the Duman and Salehi bound which is based on certain variations of Gallager's bounding technique, is demonstrated to be the tightest reported upper bound. We therefore apply it to calculate numerically upper bounds on the thresholds of some ensembles of turbo-like codes, referring to the optimal NIL decoding. For certain ensembles of uniformly interleaved turbo codes, the upper bounds derived here also indicate good match with computer simulation results of efficient iterative decoding algorithms.

关键词： block codes bounds decoding error probability distance spectrum fading channels input-output weight distribution maximum likelihood (ML) decoding thresholds turbo-like codes

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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 random angle based quantization modulation

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AEU-INTERNATIONAL JOURNAL OF ELECTRONICS AND COMMUNICATIONS 2014年第8期68卷 737-746页

作者： Zhu, Xinshan Gao, Xianwen Ding, Jie Peng, Xujun Dong, Honghui Tianjin Univ Sch Elect Engn & Automat Tianjin 300072 Peoples R China Yangzhou Univ Sch Informat Engn Yangzhou Peoples R China Northeastern Univ Coll Informat Sci & Engn Shenyang 110819 Peoples R China Raytheon BBN Technol Cambridge MA USA Beijing Jiaotong Univ State Key Lab Rail Traff Control & Safety Beijing 100044 Peoples R China

The random angle based quantization modulation (RAQM) is a new watermarking method invariant to valumetric scaling attack. In this paper, the performance of RAQM is theoretically evaluated in two aspects: the embedding distortion and the decoding performance against additive noise attack. The analyses are developed under the assumptions that the host and noise vectors are mutually independent and both of them have independently and identically distributed components. We establish the stochastic models for several concerned signals. Based on them, the expressions of the embedding distortion and the decoding bit-error probability are derived in closed form. We also present the simplified but effective approximations to these analytical results. The analyses allow us to get more insight into the impact of various factors on the performance of RAQM. Numerical simulations confirm the validity of our analyses and exhibit the performance advantage of RAQM over similar modulation techniques. (C) 2014 Elsevier GmbH. All rights reserved.

关键词： Quantization watermarking Spread transform Additive noise Valumetric scaling decoding error probability

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Lattice Network Codes Based on Eisenstein Integers

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IEEE TRANSACTIONS ON COMMUNICATIONS 2013年第7期61卷 2713-2725页

作者： Sun, Qifu Tyler Yuan, Jinhong Huang, Tao Shum, Kenneth W. Chinese Univ Hong Kong Shenzhen Res Inst Inst Network Coding Shenzhen Hong Kong Hong Kong Peoples R China Univ New S Wales Sch Elect Engn & Telecommun Sydney NSW 2052 Australia Chinese Univ Hong Kong Inst Network Coding Hong Kong Hong Kong Peoples R China

In this paper, we investigate lattice network codes (LNCs) constructed from Eisenstein integer based lattices. Quantization and encoding algorithms over Eisenstein integers are first introduced. Then, a union bound estimation (UBE) of the decoding error probability is derived when the shaping region of the LNC is a product of regular hexagons. Next, the Gaussian reduction algorithm is generalized to be applicable to complex lattices over Eisenstein integers such that an optimal coefficient vector can be found in the two-transmitter single-relay system. Based on the UBE, design criteria for optimal LNCs with minimum decoding error probability are formulated and applied to construct both Gaussian integer and Eisenstein integer based good LNCs from rate-1/2 feed-forward convolutional codes by Complex Construction A. The constructed codes provide up to 7.65 dB nominal coding gains over Rayleigh fading channels. Furthermore, we introduce the construction of LNCs from linear codes by Complex Construction B. The nominal coding gains and error performance of the LNCs thus constructed are explicitly analyzed. Examples show that the LNCs constructed by Complex Construction B provide a better tradeoff between code rate and nominal coding gain.

关键词： Compute-and-forward lattice network codes decoding error probability Gaussian reduction for complex lattices complex Construction B

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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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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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