基于双边类型低密度奇偶校验码的连续变量量子密钥分发多维数据协调

在连续变量量子密钥分发(CVQKD)多维数据协调过程中,低密度奇偶校验码(LDPC)的纠错性能直接影响协调效率和传输距离。构造了一种双边类型的低密度奇偶校验码(TET-LDPC),引入了类似于重复累积码中的累积结构以提高其纠错性能,在多维数据协调算法中得到了更小的收敛信噪比、更高的协调效率以及更远的传输距离。仿真结果表明:当TET-LDPC的码率为0.5,分组码长为2×10~5时,收敛信噪比降至1.02dB,协调效率达到了98.58%,安全密钥率达到17.61kb/s,CVQKD系统的传输距离提高为44.9km。     

连续变量量子密钥分发多维数据协调算法优化

针对连续变量量子密钥分发(CVQKD)通信距离较短的问题,在多维数据协调方案的基础上,利用连续密度进化和差分进化方法,设计出优质度数分布的低密度奇偶校验(LDPC)码,并提出LDPC码码字重复方法,进一步提高多维数据协调的效率,有效地降低了收敛信噪比,延长了信息传输距离。实验仿真结果表明:在分组码长为106时,收敛信噪比能够降低至-6dB以下,协调效率可达90.27%,提取到的安全密钥量为0.22kb/s,信息传输距离超过80km,该方法可有效延长CVQKD系统的通信距离。     

LDPC码在量子密钥分配多维协商算法中的应用

密钥协商是量子密钥分配(QKD)的重要环节,影响着QKD的密钥率和安全距离.作为一种低信噪比时较为高效的密钥协商方案,多维协商算法被很好地应用在高斯调制连续变量QKD中,延长了通信距离.本文研究了二进制LDPC码在多维协商算法中的应用方案,进而扩展到多进制LDPC码.仿真表明,相比二进制LDPC码,利用多进制LDPC码能够使多维协商性能获得明显增益.     

连续变量量子密钥分发多维数据协调算法

数据协调是量子密钥分发的重要组成部分,特别是连续变量量子密钥分发远程化的关键环节。在Leverrier等关于多维协调安全性证明的基础上,给出了面向多维协调的低密度奇偶校验码(LDPC)错误校正算法,考查了该算法的最小收敛信噪比阈值,并估算出基于这种多维数据协调方案的量子密钥分发的最大密钥传输距离,经过协调效率的计算以及噪声分析估算出最大安全密钥量。算法仿真结果表明:Alice和Bob之间的传输距离与分层错误校正协议(SEC)相比,从30km增加到47km左右,译码速度是SEC的4倍左右,密钥传输速率可以达到8.61kb/s。     

基于PEG算法的连续变量量子密钥分发多维数据协调

针对连续变量量子密钥分发系统数据协调过程中效率偏低而造成的密钥量不易提取的问题,本文引入PEG(Progressive-edge-growth)算法构造合适度分布的LDPC校验矩阵,译码时采用LLR-BP译码算法。仿真结果表明,相同度分布下PEG方法构造出的校验矩阵比传统Mackay方法构造出的校验矩阵在译码时,能够更快达到收敛,并且在码率为0.5,码长为10~5时,PEG协调方案协调效率达到93.4%,提取到的安全密钥量为5.41 kb/s,信息传输距离为44.5 km。     

低密度奇偶校验码在光通信中的性能

低密度奇偶校验码(LDPC)不仅有逼近香农限的良好性能, 而且译码复杂度较低, 结构灵活, 是近年信道编码领域的研究热点, 在光通信系统中有广泛的应用前景。针对非规则Tanner图上构造的低密度奇偶校验长码具有良好的性能, 以及其在光通信系统中的应用, 构造了几种LDPC码, 并采用置信传播(BP)译码, 在加性高期白噪声(AWGN)信道、二相移相键空(BPSK)调制下进行了计算机仿真。根据规则LDPC码和非规则LDPC码的误码率(BER)和FER曲线, 对规则码和非规则LDPC码在编译码方面以及性能方面作了分析和比较, 进而对构造在光通信系统中具有实用价值的LDPC码提出了看法。通过理论分析与仿真结果表明LDPC 码型具有良好的性能, 可以节省硬件开销, 比较适用于光通信系统中, 可作为超强前向纠错码型的候选码。     

基于OpenCL/GPU异构计算的高速数据协调系统设计

针对当前连续变量量子密钥分发时数据协调运算速度低的问题,本文提出一种采用GPU与OpenCL异构计算的多维数据协调方案,并提出了一种静态双向十字链表存储超大规模LDPC码的校验矩阵,以适应OpenCL平台特殊要求。实验仿真结果显示,当码长为2×105时,在保证有效数据协调且相同码率的前提下,GPU平均译码速率可达到CPU的4.2倍,但牺牲了部分精度。     

非二进制低密度奇偶校验码在16QAM光传输系统中的性能

以16-相正交幅度调制(16QAM)为例,分析比较了伽罗华(GF(2 m))域上m=1,2,4时,3种低密度奇偶校验(LDPC)码在16QAM光传输系统中的性能.分析表明,无论在纠错性能还是译码效率方面,4进制LDPC码比16进制LDPC码具有更大优势.为进一步改善高阶调制光传输系统中非二进制低密度奇偶校验(NB-LDPC)码的性能,在16QAM系统下的4进制LDPC码中引入水印位符号.与传统的非二进制LDPC译码方案相比,水印位方案的平均迭代次数显著下降,即引入水印位可以极大地提高NB-LDPC码的译码效率.当误码率BER=10-5时水印位方案可以改善0.1dB的净编码增益.     

高斯量子密钥分发数据协调的性能优化

针对高斯量子密钥分发的数据协调问题,对高斯连续变量进行了最优量化,实现了Alice和Bob之间的互信息量最大。在分层错误校正(SEC)协议和多电平编码/多级解码(MLC/MSD)协议的基础上,各级码流采用了低密度奇偶校验码(LDPC)进行错误校正,并推出了一次硬信息级间迭代更新公式参与MSD译码算法。算法实现中使用双向十字链表方式存贮LDPC码的稀疏矩阵H,并用C语言实现整个数据协调过程,极大地降低了空间复杂度,提高了协调速度。实验仿真结果表明该算法可在信道信噪比4.9dB以上实现2×105个连续变量序列的可靠协调,协调效率达91.71%,在2.4GHz CPU,32G内存服务器平台上的协调速度可达7262bit/s。     

量子高斯密钥分发的逆向数据协调

加密系统中Alice端通过光纤传送相干态量子信号给Bob端,得到的一系列相关的高斯连续变量,然后从中提取出二进制密钥,这一过程称作高斯连续变量量子密钥分发.其中的数据协调步骤,即对相关连续变量的错误校正,是本文的研究问题.本文在分层错误校正协议(SEC)和多电平编码/多级解码(MLC/MSD)协议的基础上,用基于LDPC码的Slepian-Wolf编译码器实现协调.根据连续变量的多级Tanner信息传输流图,本文推导了多级迭代的内信息和外信息置信传播(LLR-BP)更新公式,并用实验比较了MSD三种译码模式的收敛性质及性能.仿真结果表明该算法可在信道信噪比2.5 dB以上实现10000个连续变量序列的可靠协调,协调效率可达92.3％.     

Spherical reconciliation for a continuous-variable quantum key distribution

Information reconciliation is a significant step for a continuous-variable quantum key distribution(CV-QKD) system.We propose a reconciliation method that allows two authorized parties to extract a consistent and secure binary key in a CV-QKD protocol,which is based on Gaussian-modulated coherent states and homodyne detection.This method named spherical reconciliation is based on spherical quantization and non-binary low-density parity-check(LDPC) codes.With the suitable signal-to-noise ratio(SNR) and code rate of non-binary LDPC codes,spherical reconciliation algorithm has a high efficiency and can extend the transmission distance of CV-QKD.     

High-efficiency Gaussian key reconciliation in continuous variable quantum key distribution

Efficient reconciliation is a crucial step in continuous variable quantum key distribution. The progressive-edge-growth(PEG) algorithm is an efficient method to construct relatively short block length low-density parity-check(LDPC) codes. The qua-sicyclic construction method can extend short block length codes and further eliminate the shortest cycle. In this paper, by combining the PEG algorithm and quasi-cyclic construction method, we design long block length irregular LDPC codes with high error-correcting capacity. Based on these LDPC codes, we achieve high-efficiency Gaussian key reconciliation with slice recon-ciliation based on multilevel coding/multistage decoding with an efficiency of 93.7%.     

High efficiency continuous-variable quantum key distribution based on QC-LDPC codes

Seeking good error correcting codes to improve the efficiency of continuous-variable quantum key distribution(CVQKD) reconciliation is a concerning issue. Due to the introduction of multidimensional reconciliation, the error correcting techniques in the classical binary-input additive white Gaussian noise channel are applicable to CVQKD. In this Letter, we apply the quasi-cyclic low-density parity-check(QC-LDPC) codes, which are specified in 5 G protocol, to the reconciliation process. Simulation results show that the reconciliation efficiency can reach 92.6% when the code rate is 22/68 and the signal-to-noise ratio is 0.623. Such a new error correcting code points out a new direction for the development of CVQKD.     

连续变量量子密钥分发的数据逆向协调

基于多级编码/多级译码(MLC/MSD)系统实现了连续变量量子密钥分发的逆向数据协调。讨论了高斯连续变量量化过程中使互信息量最大时最佳量化区间的选取,并且通过理论计算给出了信噪比为4dB的情况下各级等价信道的最佳码率。协调方案中选择低密度奇偶校验码(LDPC)作为信道编码,结合边信息译码原理最终通过LDPC迭代译码算法实现了数据的逆向协调。     

基于低密度奇偶校验码的超强前向纠错码设计

光纤中的传输效应(如色散、偏振模色散(PMD)和非线性效应等)会严重影响传输速率和传输距离的进一步提高。因而有必要研究性能更好的新超强前向纠错(Super-FEC) 码型,使其在光通信系统中获得更高的编码增益和更好的纠错性能。简单介绍了低密度奇偶校验(LDPC)码, 然后提出光通信系统中一种基于LDPC码的超强前向纠错(Super-FEC)码型,构造了冗余度为6.68%的新颖LDPC(3969,3720)码, 并给出超强FEC码型的仿真结果。通过与RS(255,239)及BCH(3860,3824)+BCH(2040,1930)进行对比分析, 还分析与探讨了新LDPC码型的编译码电路的设计实现问题。通过理论分析与仿真结果表明这种超强 FEC 码型具有良好的性能, 可以节省硬件开销, 比较适用于光通信系统中, 可作为超强 FEC 码型的候选码。     

Rate compatible reconciliation for continuous-variable quantum key distribution using Raptor-like LDPC codes

In the practical continuous-variable quantum key distribution(CV-QKD) system, the postprocessing process, particularly the error correction part, significantly impacts the system performance. Multi-edge type low-density parity-check(MET-LDPC) codes are suitable for CV-QKD systems because of their Shannon-limit-approaching performance at a low signal-to-noise ratio(SNR).However, the process of designing a low-rate MET-LDPC code with good performance is extremely complicated. Thus, we introduce Raptor-like LDPC(RL-LDPC) codes into the CV-QKD system, exhibiting both the rate compatible property of the Raptor code and capacity-approaching performance of MET-LDPC codes. Moreover, this technique can significantly reduce the cost of constructing a new matrix. We design the RL-LDPC matrix with a code rate of 0.02 and easily and effectively adjust this rate from 0.016 to 0.034. Simulation results show that we can achieve more than 98% reconciliation efficiency in a range of code rate variation using only one RL-LDPC code that can support high-speed decoding with an SNR less than-16.45 d B. This code allows the system to maintain a high key extraction rate under various SNRs, paving the way for practical applications of CV-QKD systems with different transmission distances.     

A novel construction algorithm of the LDPC code for high-speed long-haul optical transmission systems

According to the transmission characteristics of high-speed long-haul optical transmission system, the main construction method of Low-Density Parity-Check (LDPC) code for optical transmission system is presented and a novel construction algorithm of LDPC code is proposed, the theoretical analysis shows that the parity check matrix of the LDPC code constructed by the proposed construction algorithm has no four-girth phenomenon, this is also theoretically proved out. Both the novel LDPC(3969,3720) code with 6.69% redundancy and the novel LDPC(8281,7920) code with 4.56% redundancy for optical transmission systems are constructed by using the presented construction method and proposed construction algorithm. The simulation results show that the net coding gain (NCG) of the two novel LDPC codes at the eighteenth iteration for the BER of 10^?12 are respectively 1.63 dB and 1.49 dB more than that of the RS(255,239) code in ITU-T G.975. Moreover, the decoding of the LDPC code in the hardware can parallel be implemented, so the decoding speed of the two novel LDPC codes are very rapid, the complexities of implementing the two novel LDPC codes, compared with the concatenated codes in ITU-T G.975.1, are relatively lower, furthermore, the hardware overhead and storage space can relatively be saved and the computation complexity can be reduced in implementing the hardware in the future. As a result, the two novel LDPC codes can better be suitable for high-speed long-haul optical transmission systems.     

Construction of Exponent matrix compatible for multiple lifting sizes for 5G New Radio

Rate-compatible non binary LDPC codes are used as coding scheme for data transmission in fifth generation new radio. In this paper, we have presented a method for construction of exponent matrix. We first discuss about the types of the cycles and analyze the cycles that are responsible for the degradation of the error performance of the LDPC codes. At low SNR and higher code rates the occurrence of errors will be high, as the parity bits are less at higher code rates. This becomes a challenge while constructing the exponent matrix. In order to fulfill the challenge, we propose a simple and practical algorithm to construct the exponent matrix. The constructed matrix can be used for various code rates and information lengths. The constructed matrix is based on second lifting size set of 5G standard. Simulation results show that the proposed algorithm is effective and exhibits that the constructed LDPC codes can even perform well at low SNR and at higher code rate.     

Error Estimation at the Information Reconciliation Stage of Quantum Key Distribution

Quantum key distribution (QKD) offers a practical solution for secure communication between two distinct parties via a quantum channel and an authentic public channel. In this work, we consider different approaches to the quantum bit error rate (QBER) estimation at the information reconciliation stage of the post-processing procedure. For reconciliation schemes employing low-density parity-check (LDPC) codes, we develop a novel syndrome-based QBER estimation algorithm. The algorithm suggested is suitable for irregular LDPC codes and takes into account punctured and shortened bits. Testing our approach in a real QKD setup, we show that an approach combining the proposed algorithm with conventional QBER estimation techniques allows one to improve the accuracy of the QBER estimation.