不含小环的低密度校验码的代数构造方法

该文提出了一种构造不含小环的规则低密度校验(LDPC)码的代数方法,使用这种方法可以构造出最小环长为8的规则LDPC码．仿真结果显示,在AWGN信道中其性能优于随机构造的规则LDPC码．     

几种LDPC码的最小汉明距离的计算

本文提出一种计算LDPC码的真实最小汉明距离的方法．该方法能够用来计算多种LDPC码方案的真实最小汉明距离，比如准循环LDPC码、pi-旋转LDPC码等．该方法是通过计算码的环长间接地找到LDPC码最小距离，由于计算环长的计算量要远比直接计算最小汉明距离来得低，因而该算法能够在有限时间内找到LDPC码的真实最小距离．通过仿真表明，用目前主流的个人计算机利用该方法找出一个有最小距离24的码率为1／4的准循环LDPC码最小距离大概需要花77分钟。     

一种具有最小距离下界的正则LDPC码的构造

主要提出一种新的计算规则LDPC(low-density parity-check)码的最小距离下界的方法。该方法是基于LDPC码的每个变量节点的独立树进行构造LDPC码。与随机构造的LDPC码和用PEG方法构造的方法比较,这个新的构造方法得到了更大的围长和最小距离下界。在AWGN信道中,在码长N=1 008和N=1 512时进行Matlab仿真,仿真结果表明随着信噪比的增加此方法构造的LDPC码有优异的误码率性能。     

构造短码长不规则LDPC码

在给定长度和度数分布对情况下,不规则短码长LDPC码的性能差别很大。本文给出了一种低复杂度的基于树的贪婪搜索算法(GTS),此算法通过调整校验矩阵中环的分布情况,尽量减少短长度环,获得最大的平均最小环,从而构造性能很好的短码长不规则LDPC码。     

基于循环移位矩阵的LDPC码构造方法研究

论文提出了一种将矩阵分块并以单位阵的循环移位阵为基本单元构造LDPC码的校验矩阵的方法,降低了LDPC码在和积算法下的译码复杂度。同时,基于这种循环移位矩阵构造的类下三角结构可以减小编码复杂度。仿真和分析结果表明,这种LDPC码相对于随机构造的LDPC码在环长分布、最小汉明距离以及误码率性能方面也具有优越性。     

不含短环的(n,3,k)LDPC码的几何构造方法

该文基于不含短环的(n,2, k)规则低密度奇偶校验(LDPC)码,提出了一种最短环长为8的(n,3, k)规则LDPC码的几何构造方法,该方法简单直观而有效。仿真结果显示,在AWGN信道中其具有明显优于随机构造的规则LDPC码的性能。     

一种基于伪循环MDS码的准循环LDPC码构造方法

该文提出了一种利用两个信息符号的伪循环最大距离可分(MDS)码,构造围长为6的准循环低密度奇偶校验(LDPC)码的方法。在GF(q)中,它通过直接计算长为q+1的伪循环MDS码生成多项式,构造准循环LDPC码的校验矩阵。其主要利用了含两个信息符号的伪循环MDS码字特殊的循环性,及任意两个码字间距离不小于q的特点,使所构造的准循环LDPC码保证无4环。仿真结果表明,基于伪循环MDS码的准循环LDPC码在高斯信道下,能获得较好的误码性能。     

基于一些PBIBD的低密度校验码的构造

本文构造了两类部分平衡不完全区组设计.并利用它们构造了一类低密度校验码(LDPC码),其最小环长至少为6,码率的选取具有很大的灵活性,而且可以具有拟循环结构.计算机仿真结果表明这种方法构造的LDPC码,在加性高斯白噪声信道中BPSK调制下用和积迭代译码性能很好.     

基于移位矩阵优化的LDPC码构造

环的存在对准循环LDPC（Low Density Parity Code）码的译码效率造成很大影响,拥有尽可能好的girth分布的校验矩阵对于码的性能改善有着重要的意义。首先对准循环LDPC码校验矩阵的girth分布进行分析,然后在母矩阵和移位矩阵之间设定一个合理的约束关系,使得构造后的校验矩阵最小环长及平均最小环长追求最大化,最后提出了一种易于实现的具有高girth的QC-LDPC（Quasi cyclic-Low Density Parity Code）码构造方法。仿真结果表明,该方法尽量减少码中的短循环,能构造实用化的好码。     

一类环长至少为10的准循环LDPC码

为扩展性能优良、易于工程实现的LDPC码的构造方法,提出了一类环长至少为10的准循环低密度奇偶校验(quasi-cyclic low-density parity-check, QC-LDPC)码的构造方法。该方法首先基于基矩阵和 准则[11]构造出环长至少为10的校验矩阵;然后,利用掩蔽矩阵对得到的校验矩阵进行变换;最终,构造出满秩的准循环LDPC码。理论分析和仿真结果表明,该类QC-LDPC码字构造灵活,在AWGN信道下具有优异的性能。     

低密度奇偶校验码的girth集及其性能分析

girth性质研究已经成为当前LDPC码的研究重点之一,本文在找到一种基于递归的LDPC码girth搜索方法的基础上,提出LDPC码的girth长度与纠错性能之间没有必然关系,并通过IEEE Std 802.16e格式的LDPC码进行了仿真验证;此外.本文指出,girth集影响LDPC码的纠错性能,在girth长度、码长等其他参数相同的情况下,纠错能力随girth集的变小而增强。     

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.     

一种利用大衍数列构造多码率原模图QC-LDPC码的方法

针对准循环低密度奇偶校验(Quasi-Cyclic Low-Density Parity-Check,QC-LDPC)码存在码长码率不能灵活选择的问题,提出了一种基于大衍数列构造多码率的原模图QC-LDPC码的新颖方法,该方法利用计算机搜索算法得到原模图基矩阵,然后基于大衍数列的循环移位矩阵对原模图基矩阵进行循环扩展,以此得到校验矩阵.该方法构造的校验矩阵围长至少为6,只需要简单的移位寄存器就可以实现编码,并且具有良好的纠错性能.仿真结果表明,在误码率(BitError Rate,BER)为10-6时,所构造的码率为0.5的P-DY-QC-LDPC(4000,2000)码和码率为0.75的P-DY-QC-LDPC(4000,3000)码与同码率近似码长的其他码型相比较,其净编码增益均有一定提高.     

Quasi-Cyclic Low-Density Parity-Check Codes With Girth Larger Than 12

A quasi-cyclic (QC) low-density parity-check (LDPC) code can be viewed as the protograph code with circulant permutation matrices (or circulants). In this correspondence, we find all the subgraph patterns of protographs of QC LDPC codes having inevitable cycles of length 2i, i = 6, 7, 8, 9,10, i.e., the cycles that always exist regardless of the shift values of circulants. It is also derived that if the girth of the protograph is 2g, g > 2, its protograph code cannot have the inevitable cycles of length smaller than 6g. Based on these subgraph patterns, we propose new combinatorial construction methods of the protographs, whose protograph codes can have girth larger than or equal to 14 or 18. We also propose a couple of shift value assigning rules for circulants of a QC LDPC code guaranteeing the girth 14.     

一种具有较大围长的正则LDPC码构造方法

提出一种新的具有较大围长的正则LDPC码构造方法。首先介绍以矩阵分裂技术为基础的高围长正则LDPC码的构造方法,并在此基础上分析了设计围长时参数的选取方法。仿真表明,用这种方法构造的正则LDPC码围长可以达到12,并且在AWGN信道下的性能不差于相同参数、随机构造的LDPC码,在高信噪比时甚至优于相同参数的随机码。     

任意列重大围长QC-LDPC码的确定性构造

针对准循环低密度奇偶校验（Quasi-Cyclic Low-Density Parity-Check,QC-LDPC）码中准循环基矩阵的移位系数确定问题,提出基于等差数列的确定方法.该方法构造的校验矩阵围长为8,列重可任意选取,移位系数由简单的数学表达式确定,编码复杂度与码长呈线性关系,节省了编解码存储空间.研究结果表明,列重和围长是影响码字性能的重要因素.在加性高斯白噪声（Additive White Gauss Noise,AWGN）信道和置信传播（Belief Propagation,BP）译码算法下,该方法构造的码字在短码时可以获得与IEEE 802.11n、802.16e码相一致的性能,在长码时误比特率性能接近DVB-S2码.同时表明该方法对码长和码率参数的设计具有较好的灵活性.     

Systematic recursive construction of LDPC codes

This letter presents a systematic and recursive method to construct good low-density parity-check (LDPC) codes, especially those with high rate. The proposed method uses a parity check matrix of a quasi-cyclic LDPC code with given row and column weights as a core upon which the larger code is recursively constructed with extensive use of pseudorandom permutation matrices. This construction preserves the minimum distance and girth properties of the core matrix and can generate either regular, or irregular LDPC codes. The method provides a unique representation of the code in compact notation.     

High Rate APPS and Bi-APPS LDPC Codes Design with Low Error Floor and Large Girth

In this paper, two new methods to construct low-density parity-check (LDPC) codes with low error floor and large girth are proposed. The first one is APPS-LDPC codes based on Arithmetic Progression theory and cycle classification, whose girth is at least eight. Based on the designed APPS-LDPC codes, we further construct Bi-diagonal APPS-LDPC codes with column degree 4, whose circulant permutation matrix is combined by two shifted identity matrix. The designed APPS-LDPC code has 0.25 and 0.2 dB coding gain compared to partition-and-shift (PS)-LDPC code and progressive-edge-growth (PEG)-LDPC code. And the Bi-APPS-LDPC code has similar performance to T2 LDPC code in CCSDS standard, but its effective structure is more suitable for high throughput decoder implementation on FPGA. Both codes have less construction complexity than PS-LDPC code and PEG-LDPC code.     

Partially Coherent EGC Reception of Uncoded and LDPC-Coded Signals over Generalized Fading Channels

This paper studies the bit-error rate (BER) performance of partially coherent equal-gain combining reception of uncoded and low-density parity-check (LDPC)-coded binary and quaternary phase-shift keying signals over generalized ?? ? ?? fading channels. For the uncoded signal detection case the obtained numerical and simulation results illustrate the BER performance degradation due to the imperfect reference signal recovery, receiver unbalancing and fading. It is demonstrated that imperfect cophasing causes an irreducible BER performance. Furthermore, we design large girth quasi-cyclic LDPC code with high code rate, suitable for use in communications over generalized fading channels. The proposed LDPC code does not exhibit the error floor phenomena, in the region of interest, even in the presence of imperfect cophasing and receiver unbalances, and outperforms standard convolutional code of lower code rate in the observed impairments. The effects of number of iterations in decoding algorithm and codeword length on BER performance are also investigated.     

围长为8的QC-LDPC码的显式构造及其在CRT方法中的应用

对于任意码长PL(P≥3L2/4+L 1),利用完全确定的方式构造出一类围长为8的(4,L)QC-LDPC码。将这类码作为分量码,结合中国剩余定理(CRT)构造出一类围长至少为8且码长非常灵活的合成QC-LDPC码。在1/2码率和中等码长条件下的仿真结果表明,这种合成码在AWGN信道下具有优异的性能。