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On Deep Holes of Projective Reed-Solomon Codes over Finite Fields with Even Characteristic
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作者 XU Xiaofan 《Wuhan University Journal of Natural Sciences》 CAS CSCD 2023年第1期15-19,共5页
Projective Reed-Solomon code is an important class of maximal distance separable codes in reliable communication and deep holes play important roles in its decoding.In this paper,we obtain two classes of deep holes of... Projective Reed-Solomon code is an important class of maximal distance separable codes in reliable communication and deep holes play important roles in its decoding.In this paper,we obtain two classes of deep holes of projective Reed-Solomon codes over finite fields with even characteristic.That is,let F_(q) be finite field with even characteristic,k∈{2,q-2},and let u(x)be the Lagrange interpolation polynomial of the first q components of the received vector u∈F_(q)+1 q Suppose that the(q+1)-th component of u is 0,and u(x)=λx^(k)+f_(≤k-2)(x),λx^(q-2)+f_(≤k-2)(x),where λ∈F^(*)_(q) and f_(≤k-2)(x)is a polynomial over F_(q) with degree no more than k-2.Then the received vector u is a deep hole of projective Reed-Solomon codes PRS(F_(q),k).In fact,our result partially solved an open problem on deep holes of projective Reed-Solomon codes proposed by Wan in 2020. 展开更多
关键词 finite field even characteristic projective reed-solomon code deep hole
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FAST ALGORITHM FOR REED-SOLOMON CODE AND THE HARDWARE IMPLEMENTATION
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作者 张毓忠 滕建辅 周长华 《Transactions of Tianjin University》 EI CAS 1995年第1期83+80-83,共5页
This paper described a signal processor for the Reed-Solomon (R-S) code using micro-programming. For the purpose of fast encoding and decoding,a formula for detecting two errors is derived, and the Qian search method... This paper described a signal processor for the Reed-Solomon (R-S) code using micro-programming. For the purpose of fast encoding and decoding,a formula for detecting two errors is derived, and the Qian search method for the decoding process is improved. The number of searches is significantly reduced from 256 to 4. At the same time, the circuit is simplified and the speed is increased. For the convenience of programming, a micro-programming compiling package is developed. The package can be used for programming of different formats of R-S code signal processors of DAB, MD and DCC. The software and the hardware can be used for error correcting, error detecting and error compensation of different formats of R-S code. 展开更多
关键词 R-S code ENCODING DECODING Qian search
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On Reed-Solomon Codes 被引量:3
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作者 Qunying LIAO 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2011年第1期89-98,共10页
The complexity of decoding the standard Reed-Solomon code is a well-known open problem in coding theory.The main problem is to compute the error distance of a received word.Using the Weil bound for character sum estim... The complexity of decoding the standard Reed-Solomon code is a well-known open problem in coding theory.The main problem is to compute the error distance of a received word.Using the Weil bound for character sum estimate,Li and Wan showed that the error distance can be determined when the degree of the received word as a polynomial is small.In the first part,the result of Li and Wan is improved.On the other hand,one of the important parameters of an error-correcting code is the dimension.In most cases,one can only get bounds for the dimension.In the second part,a formula for the dimension of the generalized trace Reed-Solomon codes in some cases is obtained. 展开更多
关键词 reed-solomon code Weil bound Error distance Rational function Trace reed-solomon code Trace map
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On error distance of Reed-Solomon codes 被引量:9
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作者 LI YuJuan WAN DaQing 《Science China Mathematics》 SCIE 2008年第11期1982-1988,共7页
The complexity of decoding the standard Reed-Solomon code is a well known open prob-lem in coding theory. The main problem is to compute the error distance of a received word. Using the Weil bound for character sum es... The complexity of decoding the standard Reed-Solomon code is a well known open prob-lem in coding theory. The main problem is to compute the error distance of a received word. Using the Weil bound for character sum estimate, we show that the error distance can be determined precisely when the degree of the received word is small. As an application of our method, we give a significant improvement of the recent bound of Cheng-Murray on non-existence of deep holes (words with maximal error distance). 展开更多
关键词 reed-solomon code error distance deep hole character sum 30P12 32C12
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On deep holes of standard Reed-Solomon codes 被引量:10
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作者 WU RongJun HONG ShaoFang 《Science China Mathematics》 SCIE 2012年第12期2447-2455,共9页
Determining deep holes is an important open problem in decoding Reed-Solomon codes. It is well known that the received word is trivially a deep hole if the degree of its Lagrange interpolation polynomial equals the di... Determining deep holes is an important open problem in decoding Reed-Solomon codes. It is well known that the received word is trivially a deep hole if the degree of its Lagrange interpolation polynomial equals the dimension of the Reed-Solomon code. For the standard Reed-Solomon codes [p-1, k]p with p a prime, Cheng and Murray conjectured in 2007 that there is no other deep holes except the trivial ones. In this paper, we show that this conjecture is not true. In fact, we find a new class of deep holes for standard Reed-Solomon codes [q-1, k]q with q a power of the prime p. Let q≥4 and 2≤k≤q-2. We show that the received word u is a deep hole if its Lagrange interpolation polynomial is the sum of monomial of degree q-2 and a polynomial of degree at most k-1. So there are at least 2(q-1)qk deep holes if k q-3. 展开更多
关键词 deep hole reed-solomon code cyclic code BCH code DFT IDFT
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A Low Power Error Detection in the Syndrome Calculator Block for Reed-Solomon Codes: RS(204,188) 被引量:1
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作者 Richard Huynh 葛宁 杨华中 《Tsinghua Science and Technology》 SCIE EI CAS 2009年第4期474-477,共4页
Reed-Solomon (RS) codes have been widely adopted in many modern communication systems. This paper describes a new method for error detection in the syndrome calculator block of RS decoders. The main feature of this ... Reed-Solomon (RS) codes have been widely adopted in many modern communication systems. This paper describes a new method for error detection in the syndrome calculator block of RS decoders. The main feature of this method is to prove that it is possible to compute only a few syndrome coeffi- cients -- less than half-- to detect whether the codeword is correct. The theoretical estimate of the prob- ability that the new algorithm failed is shown to depend on the number of syndrome coefficients computed. The algorithm is tested using the RS(204,188) code with the first four coefficients. With a bit error rate of 1 ~ 104, this method reduces the power consumption by 6% compared to the basic RS(204,188) decoder. The error detection algorithm for the syndrome calculator block does not require modification of the basic hardware implementation of the syndrome coefficients computation. The algorithm significantly reduces the computation complexity of the syndrome calculator block, thus lowering the power needed. 展开更多
关键词 reed-solomon codes syndrome calculator block error detection bit error rate
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New concatenated soft decoding of Reed-Solomon codes with lower complexities
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作者 BIAN Yin-bing,FENG Guang-zeng School of Telecommunication and Information Engineering,Nanjing University of Posts and Telecommunications,Nanjing 210003,China 《The Journal of China Universities of Posts and Telecommunications》 EI CSCD 2009年第3期4-7,23,共5页
To improve error-correcting performance, an iterative concatenated soft decoding algorithm for Reed-Solomon (RS) codes is presented in this article. This algorithm brings both complexity as well as advantages in per... To improve error-correcting performance, an iterative concatenated soft decoding algorithm for Reed-Solomon (RS) codes is presented in this article. This algorithm brings both complexity as well as advantages in performance over presently popular sot~ decoding algorithms. The proposed algorithm consists of two powerful soft decoding techniques, adaptive belief propagation (ABP) and box and match algorithm (BMA), which are serially concatenated by the accumulated log-likelihood ratio (ALLR). Simulation results show that, compared with ABP and ABP-BMA algorithms, the proposed algorithm can bring more decoding gains and a better tradeoff between the decoding performance and complexity. 展开更多
关键词 reed-solomon codes soft decoding adaptive belief propagation box and match decoding algorithm LLR accumulation
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High Speed Versatile Reed-Solomon Decoder for Correcting Errors and Erasures
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作者 王华 范光荣 +1 位作者 王平勤 匡镜明 《Journal of Beijing Institute of Technology》 EI CAS 2008年第1期81-86,共6页
A new Chien search method for shortened Reed-Solomon (RS) code is proposed, based on this, a versatile RS decoder for correcting both errors and erasures is designed. Compared with the traditional RS decoder, the we... A new Chien search method for shortened Reed-Solomon (RS) code is proposed, based on this, a versatile RS decoder for correcting both errors and erasures is designed. Compared with the traditional RS decoder, the weighted coefficient of the Chien search method is calculated sequentially through the three pipelined stages of the decoder. And therefore, the computation of the errata locator polynomial and errata evaluator polynomial needs to be modified. The versatile RS decoder with minimum distance 21 has been synthesized in the Xilinx Virtex-Ⅱ series field programmable gate array (FPGA) xe2v1000-5 and is used by coneatenated coding system for satellite communication. Results show that the maximum data processing rate can be up to 1.3 Gbit/s. 展开更多
关键词 reed-solomon code Berlekamp-Massey algorithm error correction codes versatile reed-solomon decoder
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On Ordinary Words of Standard Reed-Solomon Codes over Finite Fields
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作者 Xiaofan Xu Shaofang Hong 《Algebra Colloquium》 SCIE CSCD 2021年第4期569-580,共12页
Reed-Solomon codes are widely used to establish a reliable channel to transmit information in digital communication which has a strong error correction capability and a variety of efficient decoding algorithm.Usually ... Reed-Solomon codes are widely used to establish a reliable channel to transmit information in digital communication which has a strong error correction capability and a variety of efficient decoding algorithm.Usually we use the maximum likelihood decoding(MLD)algorithm in the decoding process of Reed-Solomon codes.MLD algorithm relies on determining the error distance of received word.Dür,Guruswami,Wan,Li,Hong,Wu,Yue and Zhu et al.got some results on the error distance.For the Reed-Solomon code C,the received word u is called an ordinary word of C if the error distance d(u,C)=n-deg u(x)with u(x)being the Lagrange interpolation polynomial of u.We introduce a new method of studying the ordinary words.In fact,we make use of the result obtained by Y.C.Xu and S.F.Hong on the decomposition of certain polynomials over the finite field to determine all the ordinary words of the standard Reed-Solomon codes over the finite field of q elements.This completely answers an open problem raised by Li and Wan in[On the subset sum problem over finite fields,Finite Fields Appl.14(2008)911-929]. 展开更多
关键词 reed-solomon code ordinary word Lagrange interpolation polynomial finite field
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Finite Geometry and Deep Holes of Reed-Solomon Codes over Finite Local Rings
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作者 Jun Zhang Haiyan Zhou 《Communications in Mathematical Research》 CSCD 2022年第2期206-222,共17页
In this paper, we first propose the maximum arc problem, normal rational curve conjecture, and extensions of normal rational curves over finite local rings, analogously to the finite geometry over finite fields. We th... In this paper, we first propose the maximum arc problem, normal rational curve conjecture, and extensions of normal rational curves over finite local rings, analogously to the finite geometry over finite fields. We then study the deep hole problem of generalized Reed-Solomon (RS) codes over finite local rings. Several different classes of deep holes are constructed. The relationship between finite geometry and deep holes of RS codes over finite local rings are also studied. 展开更多
关键词 Finite geometry finite local ring reed-solomon code covering radius deep hole
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SUBSPACE SUBCODES OF GENERALIZED REED-SOLOMON CODES 被引量:1
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作者 崔杰 裴君莹 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2001年第4期503-508,共6页
In this paper, the subspace subcodes of generalized Reed-Solomn codes are codes are introduced and the fomulas to compute the dimensions of these codes are given.
关键词 Generalized reed-solomon codes subspacte subcodes of generalized reed-solomon codes
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Homogeneous Interpolation Problem and Key Equation for Decoding Reed-Solomon Codes 被引量:1
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作者 忻鼎稼 《Science China Mathematics》 SCIE 1994年第11期1387-1398,共12页
The concept of homogeneous interpolation problem (HIP) over fields is introduced.It is discovered that solving HIP over finite fields is equivalent to decoding Reed-Solomon (RS) codes.The Welch-Berlekamp algorithm of ... The concept of homogeneous interpolation problem (HIP) over fields is introduced.It is discovered that solving HIP over finite fields is equivalent to decoding Reed-Solomon (RS) codes.The Welch-Berlekamp algorithm of decoding RS codes is derived;besides,by introducing the concept of incomplete locator of error patterns,the algorithm called incomplete iterative decoding is established. 展开更多
关键词 error CORRECTING codeS reed-solomon codeS functional iteration.
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A Theoretical Method for Estimating Performance of Reed-Solomon Codes Concatenated with Orthogonal Space-Time Block Codes 被引量:3
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作者 LUOTao HAOJian-Jun 《The Journal of China Universities of Posts and Telecommunications》 EI CSCD 2002年第1期30-34,共5页
Based on the studies of Reed-Solomon codes and orthogonalspace-time block codes over Rayleigh fading channel, a theoreticalmethod for estimating performance of Reed-Solomon codes concatenatedwith orthogonal space- tim... Based on the studies of Reed-Solomon codes and orthogonalspace-time block codes over Rayleigh fading channel, a theoreticalmethod for estimating performance of Reed-Solomon codes concatenatedwith orthogonal space- time block codes is presented in this paper.And an upper bound of the bit error rate is also obtained. It isshown through computer simulations that the signal-to-noise ratioreduces about 15 dB or more after orthogonal space-time block codesare concatenate with Reed-Solomon(15,6)codes over Rayleigh fadingchannel, when the bit error rate is 10^-4. 展开更多
关键词 channel codes space-time codes concatenated codes diversity technology
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ENUMERATION RESULTS FOR THE CODEWORDS HAVING NO INNER PERIODS IN REED-SOLOMON CODES
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作者 杨义先 《Chinese Science Bulletin》 SCIE EI CAS 1991年第19期1650-1655,共6页
Let x=(x<sub>0</sub>, …, x<sub>n-1</sub>) be a sequence in the finite field GF(q) with length n, S<sup>i</sup>, x is the i-cyclic shift of x,i.e. S<sup>i</sup>x=(x<... Let x=(x<sub>0</sub>, …, x<sub>n-1</sub>) be a sequence in the finite field GF(q) with length n, S<sup>i</sup>, x is the i-cyclic shift of x,i.e. S<sup>i</sup>x=(x<sub>i</sub>, x<sub>i+1</sub>, …, x<sub>i-1</sub>) (where i+1 means (i+1)rood n). If there exists a positive integer 0【r≤n making S<sup>r</sup>x=x+(u, u, …, u) hold for some u∈GF(q), then the r is called one of the generalized periods of this sequence x. The least one r<sub>min</sub> of such periods is called the minimum generalized period of x. In narticular, if r<sub>min</sub>=n (i. e. the 展开更多
关键词 reed-solomon code error-correcting code sequence.
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Iterative list decoding approach for Reed-Solomon codes
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作者 Zhang Zhijun Niu Kai Dong Chao 《The Journal of China Universities of Posts and Telecommunications》 EI CSCD 2019年第3期8-14,24,共8页
A novel adaptively iterative list decoding(ILD) approach using for Reed-Solomon(RS) codes was investigated. The proposed scheme is exploited to reduce the complexity of RS Chase algorithm(CA) via an iterative decoding... A novel adaptively iterative list decoding(ILD) approach using for Reed-Solomon(RS) codes was investigated. The proposed scheme is exploited to reduce the complexity of RS Chase algorithm(CA) via an iterative decoding attempt mode. In each decoding attempt process, a test pattern is generated by flipping the bits of the least reliable positions(LRPs) within the received hard-decision(HD) vector. The ILD algorithm continues until a test pattern is successfully decoded by the underlying Berlekamp-Massey algorithm(BMA) of RS codes. Flipping within the same bits, the ILD algorithm provides the same test pattern set as the conventional RS CA, thus there is no degradation in error-rate performance. Without decoding all test patterns, the ILD algorithm can simplify the decoding complexity by its early termination. Simulation results show that the average complexity of the ILD algorithm is much lower than that of the conventional RS CA(and is similar to that of BMA decoding) at high signal-to-noise ratio(SNR) region with no less to the RS CA decoding error-rate performance. 展开更多
关键词 ITERATIVE DECODING soft-decision DECODING reed-solomon codeS LOW-COMPLEXITY DECODING
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三阶扭曲广义Reed-Solomon码
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作者 张月 闫铭 +1 位作者 黄俊松 闫统江 《山东大学学报(理学版)》 北大核心 2025年第5期87-92,共6页
构造三阶扭曲广义里德-所罗门(twisted generalized Reed-Solomon,TGRS)码,刻画了这类码是极大距离可分(maximum distance separable,MDS)码的充要条件,给出MDS码的新型构造方法,拓展了一阶和二阶MDS-TGRS码的研究。
关键词 纠错编码 MDS码 扭曲广义reed-solomon 广义reed-solomon reed-solomon
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Figma2Code:面向Figma设计稿的自动代码生成方法 被引量:1
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作者 朱琳 封颖超杰 +8 位作者 朱航 王斯加 朱闽峰 喻晨昊 张钰荟 许达兴 赵德明 冯玉君 陈为 《计算机辅助设计与图形学学报》 北大核心 2025年第2期321-329,共9页
设计类创作工具已被广泛用于提高用户界面的设计效率,然而,根据设计稿开发代码是一件耗时费力的工作.针对现有的设计稿自动转代码的方案面临的代码可用性和复现结果准确性等问题,基于Figma设计工具提出一种自动代码生成方法——Figma2Co... 设计类创作工具已被广泛用于提高用户界面的设计效率,然而,根据设计稿开发代码是一件耗时费力的工作.针对现有的设计稿自动转代码的方案面临的代码可用性和复现结果准确性等问题,基于Figma设计工具提出一种自动代码生成方法——Figma2Code.首先,通过节点和图层优化提高设计稿元数据质量;其次,采用元数据标注信息的语义理解和图像识别技术识别组件;然后构建一套通用型的中间态数据结构,表示优化后的元数据和识别后的组件属性,以支持多种代码语言的生成;最后,基于模板生成可用代码,并通过函数抽取和元素循环输出提高代码可用性.采用生成代码的复现样式准确度量化评估和基于专家经验的代码可用性定性评估,证明了所提方法的有效性. 展开更多
关键词 设计稿转代码 逆向工程 用户界面 深度学习
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利用扭曲的Reed-Solomon码构造两类极大距离可分纠缠辅助量子纠错码
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作者 潘鑫 高健 《电子与信息学报》 北大核心 2025年第10期3804-3813,共10页
随着量子通信和量子计算技术的飞速发展,高效量子纠错编码技术已成为保障量子系统可靠性的核心需求。传统量子纠错码在参数灵活性和最小距离约束方面存在显著局限性,难以适应复杂量子通信场景中的动态需求。该文基于扭曲的Reed-Solomon(... 随着量子通信和量子计算技术的飞速发展,高效量子纠错编码技术已成为保障量子系统可靠性的核心需求。传统量子纠错码在参数灵活性和最小距离约束方面存在显著局限性,难以适应复杂量子通信场景中的动态需求。该文基于扭曲的Reed-Solomon(TGRS)码,根据码长中i的奇偶性的不同具体讨论矩阵G G^(H)的秩,进一步通过分析该矩阵的秩确定厄米特正交包的维数,从而得到两类极大距离可分纠缠辅助量子纠错码(MDS EAQECCs)。研究发现,通过特定的扭曲操作,所构造的两类MDS EAQECCs不仅能够灵活调整码长,还能显著提升最小距离,突破了传统理论界限。此外,该文利用扭曲操作将两类MDS EAQECCs提升为最大纠缠态极大距离可分纠缠辅助量子纠错码(ME-MDS EAQECCs)。该文研究成果不仅为量子纠错码设计提供了更广泛的参数选择,还为动态量子通信场景中的高效纠错提供了理论支撑。 展开更多
关键词 纠缠辅助量子码 扭曲的reed-solomon 厄米特正交包
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Correction:Deep Learning-Enhanced Brain Tumor Prediction via Entropy-Coded BPSO in CIELAB Color Space
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作者 Mudassir Khalil Muhammad Imran Sharif +3 位作者 Ahmed Naeem Muhammad Umar Chaudhry Hafiz Tayyab Rauf Adham E.Ragab 《Computers, Materials & Continua》 SCIE EI 2025年第1期1461-1461,共1页
In the article“Deep Learning-Enhanced Brain Tumor Prediction via Entropy-Coded BPSO in CIELAB Color Space”by Mudassir Khalil,Muhammad Imran Sharif,Ahmed Naeem,Muhammad Umar Chaudhry,Hafiz Tayyab Rauf,Adham E.Ragab C... In the article“Deep Learning-Enhanced Brain Tumor Prediction via Entropy-Coded BPSO in CIELAB Color Space”by Mudassir Khalil,Muhammad Imran Sharif,Ahmed Naeem,Muhammad Umar Chaudhry,Hafiz Tayyab Rauf,Adham E.Ragab Computers,Materials&Continua,2023,Vol.77,No.2,pp.2031–2047.DOI:10.32604/cmc.2023.043687,URL:https://www.techscience.com/cmc/v77n2/54831,there was an error regarding the affiliation for the author Hafiz Tayyab Rauf.Instead of“Centre for Smart Systems,AI and Cybersecurity,Staffordshire University,Stoke-on-Trent,ST42DE,UK”,the affiliation should be“Independent Researcher,Bradford,BD80HS,UK”. 展开更多
关键词 Deep code CIELAB
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Detection and Recognition of Spray Code Numbers on Can Surfaces Based on OCR
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作者 Hailong Wang Junchao Shi 《Computers, Materials & Continua》 SCIE EI 2025年第1期1109-1128,共20页
A two-stage algorithm based on deep learning for the detection and recognition of can bottom spray codes and numbers is proposed to address the problems of small character areas and fast production line speeds in can ... A two-stage algorithm based on deep learning for the detection and recognition of can bottom spray codes and numbers is proposed to address the problems of small character areas and fast production line speeds in can bottom spray code number recognition.In the coding number detection stage,Differentiable Binarization Network is used as the backbone network,combined with the Attention and Dilation Convolutions Path Aggregation Network feature fusion structure to enhance the model detection effect.In terms of text recognition,using the Scene Visual Text Recognition coding number recognition network for end-to-end training can alleviate the problem of coding recognition errors caused by image color distortion due to variations in lighting and background noise.In addition,model pruning and quantization are used to reduce the number ofmodel parameters to meet deployment requirements in resource-constrained environments.A comparative experiment was conducted using the dataset of tank bottom spray code numbers collected on-site,and a transfer experiment was conducted using the dataset of packaging box production date.The experimental results show that the algorithm proposed in this study can effectively locate the coding of cans at different positions on the roller conveyor,and can accurately identify the coding numbers at high production line speeds.The Hmean value of the coding number detection is 97.32%,and the accuracy of the coding number recognition is 98.21%.This verifies that the algorithm proposed in this paper has high accuracy in coding number detection and recognition. 展开更多
关键词 Can coding recognition differentiable binarization network scene visual text recognition model pruning and quantification transport model
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