基于GF(q)上纠错码的生成矩阵的验证方案

基于GF（q）上纠错码的生成矩阵提出了一身份验证方案，证明了在随机预言模型中给出的协议是一零知识交互证明，并显示出通过参数的适当选取，此方案是安全的。     

CMMB标准中LDPC码编码方法研究

对移动多媒体广播（CMMB）标准中的低密度奇偶校验（LDPC）码的校验矩阵结构进行了分析,针对其结构确立了一种可行的编码方法,即基于R.M.Neal的理论采用LU分解法。总结并验证了三种实用的三角矩阵（LU算法）,经过比较,在提出的算法中选择一个最优的方案进行编码。仿真结果表明,所选方法能够正确编码,且具有先进性,对于具体硬件实现有很好的实用价值。同时所列的三种LU算法,对于其他满足条件的矩阵也是通用的。     

基于WSNM-RPCA的图像降噪算法

通常情况下,鲁棒主成分分析（RPCA）在数据矩阵的正部分条目被任意损坏,或是缺少部分条目的情况下,依然可以恢复数据矩阵的主成分,但RPCA中采用核范数最小化（NNM）,往往会过度缩小秩分量,限制了分离的质量,因此使用加权Schatten-p范数的最小化（WSNM）来代替核范数的最小化,以取得更好的低秩逼近效果。灰度图像和彩色图像均可以用低秩矩阵去近似,因此可以用基于WSNM的RPCA模型来对含有随机噪声的图像进行恢复。经实验验证,与基于核范数的RPCA相比,基于WSNM的RPCA模型可以更有效地提高降噪的效果。     

多进制LDPC译码算法的研究

多进制LDPC码是将二进制LDPC码推广到有限域GF（q）,其校验矩阵的元素不再是（0,1）,而是集合（0,1,…,q-1）,译码仍然采用高效的基于置信度传播的迭代译码算法。这里主要推导了多进制译码算法的迭代公式,分析证明了基于快速傅里叶变换（FFT）理论的改进算法,最后通过仿真手段验证和分析了基于FFT的多进制译码算法的优越性能。     

矩阵求逆的FPGA实现

矩阵求逆广泛应用于数字通信领域,利用现场可编程门阵列（FPGA）实现能充分发挥硬件的速度优势,实现高速通信。目前,已有文献对上下三角矩阵求逆的硬件算法进行阐述,而对任意满秩矩阵求逆的硬件算法尚未深入的研究。提出了基于下上三角矩阵分解（LU分解）对任意满秩矩阵求逆的理论算法及超高速集成电路硬件描述语言（VHDL）硬件描述,并分别用软件仿真和硬件仿真进行验证。通过对比,硬件设计仿真的结果与预期结果吻合。     

基于多尺度低秩模型的心脏磁共振成像方法研究

本文提出一种基于多尺度低秩模型（MSL,Multi-Scale Low rank）的磁共振成像方法,该方法将矩阵分解成多尺度的块低秩矩阵之和,并将多尺度块低秩矩阵之和的最小化作为约束条件用于磁共振成像.两种不同的心脏磁共振数据用于验证本文所提出算法重构磁共振成像的精度.实验结果表明,相比于k-t SLR（k-t Sparsity Low Rank）和L+S（Low Rank plus Sparse）方法,所提出的MSL方法具有更好的重建效果,获得更高的重构信差比（signal to error ratio）,并具有更好地结构相似性,但需要更长的重构时间.     

关于秩距离BCH码的校验矩阵及其秩距离

本文基于秩距离码提出了秩距离BCH码,给出了其校验矩阵的形式,并讨论了所给秩距离BCH码为最大秩距离HCH码时,码的生成多项式的根应满足的条件。     

GF(p)上方程组的求解及矩阵的求逆

讨论了GF(p)上线性方程组的求解,给出了简化形式下GF(p)上线性方程组的通解形式,并给出了GF(p)上某些常见满秩矩阵的逆的具体表达式。     

弹载导引头雷达ΣΔ-STAP低秩矩阵恢复检测方法

当弹载导引头雷达检测运动目标时,由于海杂波谱严重扩展,和差波束空时自适应处理（ΣΔ-STAP）方法抑制海杂波能力非常有限,提出了一种基于低秩矩阵恢复的弹载导引头雷达ΣΔ-STAP方法。该方法基于低秩矩阵恢复理论建立弹载导引头雷达ΣΔ-STAP信号模型,首先采用ΣΔ-STAP方法预处理海杂波;然后利用鲁棒主成份分析（RPCA）技术从距离多普勒数据矩阵中分离出含有目标成分的稀疏矩阵;最后从距离多普勒谱图中有效地检测出运动目标。仿真实验验证了该方法在低信噪比情况下的有效性和鲁棒性。      

低秩循环矩阵的构造方法及其关联的多元LDPC码

在图像处理中,低秩矩阵的冗余信息可用于图像恢复和图像特征提取,而在迭代译码中,校验矩阵的冗余行可以加快译码收敛速度.该文研究一类易于硬件实现的低秩循环矩阵.首先将循环矩阵转换为位置集合,并基于同构理论简化了位置集合的搜索空间,从而基于比特移位方法提出了循环矩阵的构造方法.考虑非零域元素的列赋值与矩阵秩之间的关系,选取Tanner图中没有长度为4的环的循环矩阵,基于非零域元素的列赋值思想提出了不同阶数、不同码率的多元LDPC码构造方法.数值仿真结果表明,与基于PEG算法构造的二元LDPC码比较,所构造的多元LDPC码在BPSK调制方式下在误码字率10-5附近有0.9 dB的增益;在与高阶调制相结合时,有更大的性能提升.此外,所构造的多元LDPC码在迭代5次与50次下的性能几乎一致,这为低时延高可靠通信提供了一种有效的候选编码方案.     

Construction of LDPC codes over GF（q） with modified progressive edge growth

A parity check matrix construction method for constructing a low-density parity-check (LDPC) codes over GF(q) (q>2) based on the modified progressive edge growth (PEG) algorithm is introduced. First, the nonzero locations of the parity check matrix are selected using the PEG algorithm. Then the nonzero elements are defined by avoiding the definition of subcode. A proof is given to show the good minimum distance property of constructed GF(q)-LDPC codes. Simulations are also presented to illustrate the good error performance of the designed codes.     

Low complexity NB-LDPC decoder based on shared comparator architecture for ECN/EVN

Non-binary low density parity check (NB-LDPC) codes are considered as preferred candidate in conditions where short/medium codeword length codes and better performance at low signal to noise ratios (SNR) are required. They have better burst error correcting performance, especially with high order Galois fields (GF). A shared comparator(SCOMP) architecture for elementary of check node (ECN)/elementary of variable node (EVN) to reduce decoder complexity is introduced because high complexity of check node (CN) and variable node (VN) prevent NB-LDPC decoder from widely applications. The decoder over GF(16) is based on the extended min-sum (EMS) algorithm. The decoder matrix is an irregular structure as it can provide better performance than regular ones. In order to provide higher throughput and increase the parallel processing efficiency,the clock which is 8 times of the system frequency is adopted in this paper to drive the CN/VN modules. The decoder complexity can be reduced by 28% from traditional decoder when shared comparator architecture is introduced. The result of synthesis software shows that the throughput can achieve 34 Mbit/s at 10 iterations. The proposed architecture can be conveniently extended to GF such as GF(64) or GF(256). Compared with previous works, the decoder proposed in this paper has better hardware efficiency for practical applications.     

影响多进制LDPC码译码性能因素研究

多进制LDPC码是将二进制LDPC码推广到有限域GF(q),其校验矩阵的元素不再是0和1,而是集合(0,1,2,…,q-1),译码仍然采用高效的基于置信度传播的迭代译码算法。文中主要阐述了准循环多进制LDPC码(QC-LDPC)校验矩阵的构造以及最小和译码算法的原理,然后在高斯白噪声信道(AWGN)中,用Matlab了仿真不同条件下LDPC码的译码性能,比较分析了影响多进制LDPC码译码性能的因素。     

Construction of quasi‐cyclic low‐density parity‐check codes with low encoding complexity

Low encoding complexity is very important for quasi‐cyclic low‐density parity‐check (QC‐LDPC) codes used in wireless communication systems. In this paper, a new scheme is presented to construct QC‐LDPC codes with low encoding complexity. This scheme is called two‐stage particle swarm optimization (TS‐PSO) algorithm, in which both the threshold and girth distribution of QC‐LDPC codes are considered. The proposed scheme is composed of two stages. In the first stage, we construct a binary base matrix of QC‐LDPC code with the best threshold. The matrix is constructed by combining a binary PSO algorithm and the protograph extrinsic information transfer (PEXIT) method. In the second stage, we search an exponent matrix of the QC‐LDPC code with the best girth distribution. This exponent matrix is based on the base matrix obtained in the first stage. Consequently, the parity‐check matrix of the QC‐LDPC code with the best threshold and best girth distribution are constructed. Furthermore, bit error rate performances are compared for the QC‐LDPC codes constructed by proposed scheme, the QC‐LDPC code in 802.16e standard, and the QC‐LDPC code in Tam's study. Simulation results show that the QC‐LDPC codes proposed in this study are superior to both the 802.16e code and the Tam code on the additive white Gaussian noise (AWGN) and Rayleigh channels. Moreover, proposed scheme is easily implemented, and is flexible and effective for constructing QC‐LDPC codes with low encoding complexity. Copyright © 2012 John Wiley & Sons, Ltd.     

利用最大偏差比的LDPC码识别算法

随着自适应调制编码技术（简称AMC）的广泛应用,信道编码识别技术已经引起研究人员越来越多的关注。本文提出了一种在AMC技术中基于最大偏差比的LDPC码识别算法。文章首先利用随着自适应调制编码技术（AMC）和低密度奇偶校验码（LDPC）的广泛应用,AMC框架下的LDPC码识别技术已引起研究人员越来越多的关注。已有的识别算法存在识别性能不足的问题,为此,本文提出了一种AMC框架下基于最大偏差比的LDPC码识别算法。文章首先利用软判决接收序列定义了编码校验关系的对数似然比（PLLR）,并对其模值的概率分布函数进行了分析;然后,利用不同校验矩阵下,校验关系对数似然比统计特性的差异,提出了一种可兼顾PLLR均值和方差特征的最大偏差比判决器。仿真结果表明,在AMC框架下,本文识别算法能够有效地完成对LDPC码的识别,且在低信噪比条件下仍能获得较好的识别结果,特别地,针对高码率LDPC码识别问题时,新算法性能优于已有算法。      

基于FPGA的LDPC编码设计

针对低密度奇偶校验码（简称LDPC码）的直接编码运算量较大、复杂度高,根据Richardson和Urbanke（RU）建议的编码方案,介绍一种适于在FPGA上实现,利用有效校验矩阵来降低编码复杂度的LDPC编码方案,给出了编码器设计实现的原理和编码器的结构和基本组成。在QuartusⅡ7．2软件平台上采用基于FPGA的VHDL语言实现了有效的编码过程。结果表明：此方案在保证高效可靠传输的同时降低了实现的复杂度。这种编码方案可灵活应用于不同的校验矩阵日,码长和码率的系统中。     

High-Rate Nonbinary Regular Quasi-Cyclic LDPC Codes for Optical Communications

The parity-check matrix of a nonbinary (NB) low-density parity-check (LDPC) code over Galois field GF(q) is constructed by assigning nonzero elements from GF(q) to the 1s in corresponding binary LDPC code. In this paper, we state and prove a theorem that establishes a necessary and sufficient condition that an NB matrix over GF(q), constructed by assigning nonzero elements from GF(q) to the 1s in the parity-check matrix of a binary quasi-cyclic (QC) LDPC code, must satisfy in order for its null-space to define a nonbinary QC-LDPC (NB-QC-LDPC) code. We also provide a general scheme for constructing NB-QC-LDPC codes along with some other code construction schemes targeting different goals, e.g., a scheme that can be used to construct codes for which the fast-Fourier-transform-based decoding algorithm does not contain any intermediary permutation blocks between bit node processing and check node processing steps. Via Monte Carlo simulations, we demonstrate that NB-QC-LDPC codes can achieve a net effective coding gain of 10.8 dB at an output bit error rate of 10^-12. Due to their structural properties that can be exploited during encoding/decoding and impressive error rate performance, NB-QC-LDPC codes are strong candidates for application in optical communications.     

Design of regular (2,d/sub c/)-LDPC codes over GF(q) using their binary images

In this paper, a method to design regular (2, d_c)- LDPC codes over GF(q) with both good waterfall and error floor properties is presented, based on the algebraic properties of their binary image. First, the algebraic properties of rows of the parity check matrix H associated with a code are characterized and optimized to improve the waterfall. Then the algebraic properties of cycles and stopping sets associated with the underlying Tanner graph are studied and linked to the global binary minimum distance of the code. Finally, simulations are presented to illustrate the excellent performance of the designed codes.     

利用域间映射的多元QC-LDPC码构造

通过定义有限域间的映射关系,提出了一种低复杂度的多元准循环奇偶校验码( QC-LDPC )的构造方法。利用这种方法可将较高阶数有限域的校验矩阵映射到指定的较低有限域上,且能保持原矩阵的结构性与稀疏特性。所构造的多元LDPC码不仅具有较低的译码复杂度且具有准循环特性,在硬件上也易于用移位寄存器实现。在高斯白噪声( AWGN)信道下的仿真结果表明,所构造的多元QC-LDPC码具有良好的编译码性能。当误码率为10-6时,码率为0.765的QC-LDPC码在目标域GF(8)上能获得0.2 dB的性能增益。