Low-Density Parity-Check Codes: Research Status and Development Direction

In this paper, we conclude five kinds of methods for construction of the regular low-density parity matrix H and three kinds of methods for the construction of irregular low-density parity-check matrix H. Through the analysis of the code rate and parameters of these eight kinds of structures, we find that the construction of low-density parity-check matrix tends to be more flexible and the parameter variability is enhanced. We propose that the current development cost should be lower with the progress of electronic technology and we need research on more practical Low-Density Parity-Check Codes (LDPC). Combined with the application of the quantum distribution key, we urgently need to explore the research direction of relevant theories and technologies of LDPC codes in other fields of quantum information in the future.

A NOVEL CONSTRUCTION OF QUANTUM LDPC CODES BASED ON CYCLIC CLASSES OF LINES IN EUCLIDEAN GEOMETRIES

The dual-containing (or self-orthogonal) formalism of Calderbank-Shor-Steane (CSS) codes provides a universal connection between a classical linear code and a Quantum Error-Correcting Code (QECC). We propose a novel class of quantum Low Density Parity Check (LDPC) codes constructed from cyclic classes of lines in Euclidean Geometry (EG). The corresponding constructed parity check matrix has quasi-cyclic structure that can be encoded flexibility, and satisfies the requirement of dual-containing quantum code. Taking the advantage of quasi-cyclic structure, we use a structured approach to construct Generalized Parity Check Matrix (GPCM). This new class of quantum codes has higher code rate, more sparse check matrix, and exactly one four-cycle in each pair of two rows. Ex-perimental results show that the proposed quantum codes, such as EG(2,q)II-QECC, EG(3,q)II-QECC, have better performance than that of other methods based on EG, over the depolarizing channel and decoded with iterative decoding based on the sum-product decoding algorithm.

基于奇偶校验极化码的量子密钥纠错方法

为了提升量子密钥分发(QKD)中密钥纠错的性能,提出了一种基于奇偶校验极化码的量子密钥纠错方法。该方法在密钥纠错过程中引入了奇偶校验极化码,并优化了奇偶校验编码策略,利用密钥极化编码后生成的奇偶校验信息完成密钥纠错。仿真结果表明:与现有的基于极化码的密钥纠错方法相比,该方法可以在相同的量子比特误码率下获得更高的纠错效率;当实际QKD实验中的量子比特误码率为0.01048时,其纠错效率达到1.34,安全成码率可达1319 b/s。

基于LDPC码的分布式信源编码的研究

传统的分布式信源编码在城域量子通信中有高误码率和低压缩率的缺点,因此提出一种改进的分布式信源编码算法,在信源译码器的设计中,冗余技术用于纠错检错,基于边信息的和冗余相结合的低密度奇偶校验码设计分布式信源编码。实验表明:这种改进的分布式信源编码算法可以保持高压缩率,并在城域量子通信中系统的内部相关性强时更易于实现。

基于边信息和LDPC的分布式信源编码

传统的分布式信源编码在城域量子通信中有高误码率和低压缩率的缺点,提出了一种改进的分布式信源编码算法,在信源译码器的设计中冗余技术用于纠错检错,基于边信息的和冗余相结合的低密度奇偶校验码设计分布式信源编码.实验表明提出的算法可以保持高压缩率,并在城域量子通信中系统的内部相关性强时更易于实现.

Design of Irregular QC-LDPC Code Based Multi-Level Coded Modulation Scheme for High Speed Optical Communication Systems

In this paper, we focus on the design of irregular QC-LDPC code based multi-level coded modulation(MLCM) scheme by jointly optimizing the component code rate and the degree distribution of the irregular QC-LDPC component code. Firstly, the sub-channel capacities of MLCM systems is analyzed and discussed, based on which the optimal component code rate can be obtained. Secondly, an extrinsic information transfer chart based two-stage searching algorithm is proposed to find the good irregular QC-LDPC code ensembles with optimal component code rates for their corresponding sub-channels. Finally, by constructing the irregular QC-LDPC component codes from the designed ensembles with the aim of possibly enlarging the girth and reducing the number of the shortest cycles, the designed irregular QC-LDPC code based 16QAM and 64QAM MLCM systems can achieve 0.4 dB and 1.2 dB net coding gain, respectively, compared with the recently proposed regular QC-LDPC code based 16QAM and 64QAM MLCM systems.

JOINT SOURCE-CHANNEL DECODING OF HUFFMAN CODES WITH LDPC CODES

In this paper, we present a Joint Source-Channel Decoding algorithm (JSCD) for Low-Density Parity Check (LDPC) codes by modifying the Sum-Product Algorithm (SPA) to account for the source redun-dancy, which results from the neighbouring Huffman coded bits. Simulations demonstrate that in the presence of source redundancy, the proposed algorithm gives better performance than the Separate Source and Channel Decoding algorithm (SSCD).

Toward Efficient Quantum Key Distribution Reconciliation

In this paper, we propose how to construct a reconciliation method for the BB84 Quantum Key Distribution (QKD) protocol. Theoretically, it is unconditionally secure because it is based on the quantum laws of physics, rather than the assumed computational complexity of mathematical problems. BB84 protocol performances can be reduced by various errors and information leakages such as limited intrinsic efficiency of the protocol, imperfect devices and eavesdropping. The proposed reconciliation method allowed to weed out these errors by using Turbo codes. Since their high error correction capability implies getting low errors, this method has high performance especially when compared to the last method presented in the literature based on Low-Density Parity Check codes (LDPC). In particular, we demonstrate that our method leads to a significant improvement of the protocol security and of the Bit Error Rate (BER) even with great eavesdropping capability.

Study on the Optimized Demodulation and Decoding of the BICM-ID system coded with LDPC

The demodulation and decoding solution commonly used in the bit interleaving code modulation and the LDPC coded demodulation and decoding system of the iterative decoding （BICM-ID） is to report the soft information output from the decoder of the receiver to the demodulator as priori information for completing the decoding. However, this will give rise to the reduction of the minimum Euclidean distances between codes, so that the performances of the system decline under non-fading Gaussian channel. According to this problem, an optimized iterative demodulation decoding solution is proposed and also is analyzed using simulation. The result shows that this solution can improve the demodulation and decoding performances of LDPC coded modulation and demodulation system.

量子密钥分发误码协调算法分析

误码消除是量子密钥分发过程的关键技术之一。分析了奇偶-汉明单向函数纠错算法的原理,给出了对原始量子密钥进行误码协调的步骤及表达式,对这种算法的纠错能力进行了理论和实验分析。结果显示,当原始密钥误码率为11%时,利用该纠错技术能够完全消除误码,且最终密钥生成效率与密钥的原始误码率直接相关。

一种基于量子纠错编码的量子密钥分配协议

量子加密从物理机制上保证了密钥分配的绝对安全,然而由于量子密钥分配过程中量子信道存在噪声,使得传输效率不高的量子密钥分配效率进一步降低。量子低密度奇偶校验(量子LDPC)码由于在码长和码率的选择方面具有巨大的灵活性,且信赖于稀疏图,已成为目前量子纠错编码的研究热点。该文借鉴经典纠错编码能够提高传输可靠性的特性,针对BB84协议,设计一种基于量子LDPC码的BB84协议。通过数值仿真,分析量子LDPC码对BB84协议的密钥传输效率的影响。结果表明基于量子纠错码的BB84协议的密钥传输效率得到提高,验证了在含噪量子信道中基于量子LDPC码的量子密钥分配协议的有效性。

一种基于BIBD的量子LDPC码构造新方法

利用均衡不完全区组设计(Balance Imcomplete Block Designs,BIBD)的半结构化低密度奇偶校验(LowDensity Parity Check,LDPC)码设计方法,该文提出了一种获得自对偶CSS(Calderbank-Shor-Steane)式的量子LDPC码的校验矩阵的新构造方法。由于构造出的量子码校验矩阵稀疏,有且仅有一个4环(girth 4),在置信传播迭代译码算法下可获得良好的性能。数值计算结果表明,对于该构造方法得到的GF(6t+1)和GF(12t+1)量子LDPC码,比基于BIBD的其他构造方法所得到的量子码的码长更长、量子校验矩阵更加稀疏、性能也更加优越。

高效容错可逆的汉明码编码和检测电路

为了检验传输过程中数据的可靠性，设计了容错可逆的汉明码电路。提出了一种新型的可逆逻辑门（FVG），并且完成了FVG门等价的量子实现。利用FVG门和现有的容错可逆门，实现了汉明码编码电路和检测电路。以（7，4）汉明码设计为实例，根据量子代价和延迟对其进行性能评估，结果证明该电路比现有电路的性能提高10％-20％，仿真实验结果显示，电路逻辑结构正确，性能可靠。

量子LDPC码在BB84协议中的应用研究

针对BB84量子密钥分配协议中量子信道存在噪声,设计一种带有量子纠错码的改进的BB84协议模型,在模型中用量子低密度奇偶校验码(量子LDPC)作为纠错码对发送量子态进行编码。通过数值仿真,从密钥传输效率的角度分析量子纠错编码对BB84协议的影响。结果表明量子LDPC码能克服噪声,提高了密钥传输效率,验证了在含噪量子信道中改进的BB84协议模型的有效性。

基于初等变换的量子码构造

为了探讨一般量子稳定子码的简单构造方法,在满足对偶包含条件C⊥C的约束下,提出了从一类量子稳定子码C=[[N,K,D]]q到量子稳定子码C'=[[N-1,K+1,D']]q的基于矩阵初等变换的构造方法.该方法的优点在于码字构造时,量子稳定子码和经典纠错码都是在Fq上进行操作,无须做Fq2到Fq上的映射转换,也无须使用复杂的数学运算,仅使用内积空间和初等矩阵行变换的相关概念即可构造一类码字的衍生码,因此该构造算法可提高时空效率.另外,该方法构造性的证明简单、易懂,且易于计算机及各种硬件系统实现.研究理论结果显示,该方法对一类量子码的构造非常实用.

应对反应攻击的级联中密度准循环奇偶校验码公钥方案

基于中密度准循环奇偶校验(QC-MDPC)码的McEliece公钥密码(PKC)方案具有较小的密钥量,利于存储,是一类在抵抗量子攻击上发展前景良好的公钥密码体制。然而目前存在一种反应攻击对其安全性产生了较大威胁。攻击者选取特殊的错误图样对大量消息进行加密以获得接收者反馈的译码失败情况,然后通过分析译码失败率与私钥结构的关系从而破解出私钥,该攻击被称为密钥恢复攻击。为应对此攻击,提出了一种将QC-MDPC码与喷泉码进行级联的公钥方案。该方案利用喷泉码的“无码率性”生成大量的加密包来取代反馈重发(ARQ)结构,使攻击者无法获取反馈信息。分析结果表明,所提出的方案能有效抗击密钥恢复攻击,同时还能保证在其他攻击下的安全性。

一种基于稀疏序列的量子CSS码的构造

量子CSS码是一种简单、有效的量子码构造方法,已被应用到各类特性的量子码的构造之中。针对低密度奇偶校验码(LDPC)的优异性能,利用稀疏序列构造LDPC码校验矩阵的方法,提出了一种构造量子低密度奇偶校验码校验矩阵构造方法,采用快速编码算法,获得相应的量子码。最后,以(3,8)(16,6)量子码为例给出量子低密度奇偶校验码的构造过程,以及编码实现的线路图。

一种基于稀疏循环序列的量子低密度校验码的构造

量子纠错编码技术是量子通信和量子计算实用化的基础,迄今为止,量子纠错理论日趋完善,许多经典的编码技术在量子领域中都可以找到其对应的编码方法。针对经典纠错码中最好码之一的低密度奇偶校验码(LDPC),文中提出了一种构造量子LDPC的校验矩阵的改进方法,并与M acKay提出的基于稀疏循环序列的B和U构造法进行比较,结果得到改进的构造法不仅改进了B和U构造法的部分不足之处,而且保留了两种构造法的优点,从而可以提高编码和译码的效率。

连续变量量子密钥分发数据协调加速运算的GPU实现

针对当前连续变量量子密钥分发系统数据协调运算速度低等问题,用GPU实现了基于LDPC的SEC协议下数据协调算法的并行化加速运算,提出用静态双向十字链表的方法高效存储大规模稀疏校验矩阵,从而保证在不牺牲协调效率的前提下提高了译码速率。仿真实验结果表明,在信道信噪比为4.9 d B以上、2×105个连续变量序列可靠协调以及协调效率为91.71%的情况下,基于Geforce GT 650 MB的GPU和2.5 GHz、8 GB内存的CPU硬件平台,译码速率可达16.4 kbit/s,相对于仅CPU平台,计算速度提高15倍以上。

空地量子密钥分发网络中数据协调方案

在空地量子密钥分发网络中,空中平台的硬件设备限制使得后处理阶段数据传输速度以及处理能力减弱。针对空中平台的特性,提出了一种适合空地量子密钥分发网络的数据协调方案。首先,采用量子纠错技术减少原始密钥的误码率;其次,设计了一种新方法用来制备低密度奇偶校验(LDPC)译码算法中的随机置换序列;最后,兼顾LDPC译码算法性能和算法硬件实现复杂度,选取了软判决中最小和译码算法。仿真分析表明:量子纠错处理后的原始密钥误码率明显减少,错误率由29.5%减少为4.4%;使用新方法生成随机置换序列,在保证序列随机性的前提下效率提升,生成长度为10000的随机置换序列所用时间约为0.019 s;LDPC译码算法中最小和译码算法性能适中且硬件实现简单。