Quantum error-correction codes are immeasurable resources for quantum computing and quantum communication.However,the existing decoders are generally incapable of checking node duplication of belief propagation(BP)on ...Quantum error-correction codes are immeasurable resources for quantum computing and quantum communication.However,the existing decoders are generally incapable of checking node duplication of belief propagation(BP)on quantum low-density parity check(QLDPC)codes.Based on the probability theory in the machine learning,mathematical statistics and topological structure,a GF(4)(the Galois field is abbreviated as GF)augmented model BP decoder with Tanner graph is designed.The problem of repeated check nodes can be solved by this decoder.In simulation,when the random perturbation strength p=0.0115-0.0116 and number of attempts N=60-70,the highest decoding efficiency of the augmented model BP decoder is obtained,and the low-loss frame error rate(FER)decreases to 7.1975×10^(-5).Hence,we design a novel augmented model decoder to compare the relationship between GF(2)and GF(4)for quantum code[[450,200]]on the depolarization channel.It can be verified that the proposed decoder provides the widely application range,and the decoding performance is better in QLDPC codes.展开更多
In this paper, we have proved that the lower bound of the number of real multiplications for computing a length 2(t) real GFT(a,b) (a = +/-1/2, b = 0 or b = +/-1/2, a = 0) is 2(t+1) - 2t - 2 and that for computing a l...In this paper, we have proved that the lower bound of the number of real multiplications for computing a length 2(t) real GFT(a,b) (a = +/-1/2, b = 0 or b = +/-1/2, a = 0) is 2(t+1) - 2t - 2 and that for computing a length 2t real GFT(a,b)(a = +/-1/2, b = +/-1/2) is 2(t+1) - 2. Practical algorithms which meet the lower bounds of multiplications are given.展开更多
图信号处理(Graph signal processing,GSP)是由谱图理论发展起来的新研究领域。图傅里叶变换(Graph Fourier transformation,GFT)是图信号关于图拉普拉斯矩阵特征函数的展开,也是GSP的基础。对路图的GFT进行分析,发现GFT得到的特征值谱...图信号处理(Graph signal processing,GSP)是由谱图理论发展起来的新研究领域。图傅里叶变换(Graph Fourier transformation,GFT)是图信号关于图拉普拉斯矩阵特征函数的展开,也是GSP的基础。对路图的GFT进行分析,发现GFT得到的特征值谱与经典的傅里叶变换(Fourier transformation,FT)频谱有一一对应关系,同时,特征值谱的幅值与特征矢量也有对应关系。将GFT引入滚动轴承故障诊断,提出基于GFT特征提取和K-均值聚类的滚动轴承故障诊断方法。该方法先用GFT将滚动轴承的路图信号变换到特征值谱域;再计算特征值谱的统计量作为故障特征;最后运用K-均值聚类分类器识别滚动轴承的故障类型。对实际轴承振动信号的分析结果表明,基于GFT和K-均值聚类的故障诊断方法能准确有效地识别滚动轴承故障。展开更多
首先论述新型图信号处理(Graph Signal Processing,GSP)技术的基本概念和相关研究进展,其中包括图拓扑结构、图傅里叶变换、滤波及图学习。鉴于语音信号是一种非平稳和非线性的信号,为此,文中研究基于GSP技术的语音信号的图映射理论,即...首先论述新型图信号处理(Graph Signal Processing,GSP)技术的基本概念和相关研究进展,其中包括图拓扑结构、图傅里叶变换、滤波及图学习。鉴于语音信号是一种非平稳和非线性的信号,为此,文中研究基于GSP技术的语音信号的图映射理论,即将时域语音信号映射为图域的语音图信号,通过设计语音图信号的图拓扑结构和图邻接矩阵来研究语音图信号的内在潜藏关系,进而设计优于经典DSP的语音图信号消噪算法和系统。在此研究基础上,进一步讨论相关实际应用问题,例如麦克风阵列环境下如何通过GSP技术处理麦克风阵列声源(说话人)的定位及追踪问题。期望基于GSP技术语音图信号处理理论,为语音识别、合成、编码、增强等各个领域的图信号处理奠定理论基础。展开更多
基金the National Natural Science Foundation of China(Grant Nos.11975132 and 61772295)the Natural Science Foundation of Shandong Province,China(Grant No.ZR2019YQ01)the Higher Education Science and Technology Program of Shandong Province,China(Grant No.J18KZ012).
文摘Quantum error-correction codes are immeasurable resources for quantum computing and quantum communication.However,the existing decoders are generally incapable of checking node duplication of belief propagation(BP)on quantum low-density parity check(QLDPC)codes.Based on the probability theory in the machine learning,mathematical statistics and topological structure,a GF(4)(the Galois field is abbreviated as GF)augmented model BP decoder with Tanner graph is designed.The problem of repeated check nodes can be solved by this decoder.In simulation,when the random perturbation strength p=0.0115-0.0116 and number of attempts N=60-70,the highest decoding efficiency of the augmented model BP decoder is obtained,and the low-loss frame error rate(FER)decreases to 7.1975×10^(-5).Hence,we design a novel augmented model decoder to compare the relationship between GF(2)and GF(4)for quantum code[[450,200]]on the depolarization channel.It can be verified that the proposed decoder provides the widely application range,and the decoding performance is better in QLDPC codes.
文摘In this paper, we have proved that the lower bound of the number of real multiplications for computing a length 2(t) real GFT(a,b) (a = +/-1/2, b = 0 or b = +/-1/2, a = 0) is 2(t+1) - 2t - 2 and that for computing a length 2t real GFT(a,b)(a = +/-1/2, b = +/-1/2) is 2(t+1) - 2. Practical algorithms which meet the lower bounds of multiplications are given.
文摘首先论述新型图信号处理(Graph Signal Processing,GSP)技术的基本概念和相关研究进展,其中包括图拓扑结构、图傅里叶变换、滤波及图学习。鉴于语音信号是一种非平稳和非线性的信号,为此,文中研究基于GSP技术的语音信号的图映射理论,即将时域语音信号映射为图域的语音图信号,通过设计语音图信号的图拓扑结构和图邻接矩阵来研究语音图信号的内在潜藏关系,进而设计优于经典DSP的语音图信号消噪算法和系统。在此研究基础上,进一步讨论相关实际应用问题,例如麦克风阵列环境下如何通过GSP技术处理麦克风阵列声源(说话人)的定位及追踪问题。期望基于GSP技术语音图信号处理理论,为语音识别、合成、编码、增强等各个领域的图信号处理奠定理论基础。
