A CLASS OF LDPC CODE’S CONSTRUCTION BASED ON AN ITERATIVE RANDOM METHOD

This letter gives a random construction for Low Density Parity Check （LDPC） codes, which uses an iterative algorithm to avoid short cycles in the Tanner graph. The construction method has great flexible choice in LDPC code＇s parameters including codelength, code rate, the least girth of the graph, the weight of column and row in the parity check matrix. The method can be applied to the irregular LDPC codes and strict regular LDPC codes. Systemic codes have many applications in digital communication, so this letter proposes a construction of the generator matrix of systemic LDPC codes from the parity check matrix. Simulations show that the method performs well with iterative decoding.     

Design of Quasi‐Cyclic Low‐Density Parity Check Codes with Large Girth

In this paper we propose a graph‐theoretic method based on linear congruence for constructing low‐density parity check (LDPC) codes. In this method, we design a connection graph with three kinds of special paths to ensure that the Tanner graph of the parity check matrix mapped from the connection graph is without short cycles. The new construction method results in a class of (3, ρ)‐regular quasi‐cyclic LDPC codes with a girth of 12. Based on the structure of the parity check matrix, the lower bound on the minimum distance of the codes is found. The simulation studies of several proposed LDPC codes demonstrate powerful bit‐error‐rate performance with iterative decoding in additive white Gaussian noise channels.     

A trellis-based method for removing cycles from bipartite graphs and construction of low density parity check codes

This letter presents a trellis-based iterative method for removing short cycles from bipartite graphs. This method can be used to improve the performance of low density parity check (LDPC) codes or to construct new LDPC codes.     

多元LDPC码与二元LDPC码的性能分析

为了比较多元LDPC码与二元LDPC码的性能,文章从校验矩阵、Tanner图、BP译码算法等方面将两者进行有效的分析,并结合具体的Monte Carlo仿真实验,得出多元LDPC码的性能确实优于等长度码长的二元LDPC码.     

一种低密度奇偶校验码的环数统计方法

对于Tanner图中给定码长的序列,LDPC码的短环对码的性能有重要影响.本文在分析LDPc码在Tanner图中的环在校验矩阵中的形状的基础上,提出了一种统计LDPC码中不同环长的环数的方法.首先对校验矩阵中一定数目的行组合中的环数进行统计,然后将所有行组合中的环数相加即得到校验矩阵中的环数.该方法可根据LDPC码的短环分布情况对其性能进行评估.应用提出的方法分别对MacKay的随机码和Fossorier的准循环码进行了环数统计.BER性能显示,尽管随机码环数特性比准循环码要差,但它的误码率性能比准循环码要好.     

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.     

一种π-旋转LDPC码的Min-Sum译码算法

π-旋转LDPC码结构规则,存储量少,易于硬件实现。给出一种新的π-旋转LDPC码编码、解码方法。根据校验矩阵的半规则化结构,给出校验矩阵行索引和列索引矩阵的构造方法。基于这种索引矩阵,给出一种运算量较少的编码、Min-Sum译码算法。这种编译码方法甚至不需要构造真正的H矩阵。     

基于高斯近似的IRA码构造算法研究

介绍了非规则重复累积码(IRA)的结构,对其Tanner图和校验矩阵进行了分析。IRA码的构造分为优化度分布和设计奇偶校验矩阵2部分。在AWGN信道下,对给定的噪声方差,采用高斯近似的方法优化度分布并得出优化结果。根据度分布和相应规则设计奇偶校验矩阵,给出了设计步骤。对设计出的码进行计算机仿真,结果表明这类码相对于计算机随机构造的LDPC码能带来性能上的提高,且随码长增加,码的性能有明显改善。     

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(Low Density 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。     

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。     

一种可快速编码的QC-LDPC码构造新方法

为解决LDPC码的编码复杂度问题,使其更易于硬件实现,提出了一种可快速编码的准循环LDPC码构造方法。该方法以基于循环置换矩阵的准循环LDPC码为基础,通过适当的打孔和行置换操作,使构造码的校验矩阵具有准双对角线结构,可利用校验矩阵直接进行快速编码,有效降低了LDPC码的编码复杂度。仿真结果表明,与IEEE 802.16e中的LDPC码相比,新方法构造的LDPC码在低编码复杂度的基础上获得了更好的纠错性能。     

准循环多进制LDPC码构造

该文研究准循环多进制LDPC码的构造,给出多进制LDPC码的设计流程和构造方法.详细讨论了多进制LDPC码的性能影响因素,综合考虑了环长和环的连通性对性能的影响,研究了母矩阵扩展中偏移因子的选择以及GF(q)上非零元素替代.同时提出了次优解的搜索方法,以降低搜索复杂度.最后,将提出的方法用于不同阶数下LDPC码的构造.仿真结果表明,通过新方法构造得到的多进制LDPC码与二进制码相比,在BPSK调制方式下在误帧率10-4附近有0.2 dB的性能提升;在有限域阶数与调制阶数匹配的情况下,有更大的性能提升.与相近码长,相同码率的多进制循环码相比,该文构造得到的多进制LDPC码在误帧率10-4附近有0.25 dB的性能提升.     

Blind frame synchronization for error correcting codes having a sparse parity check matrix

We present in this letter a blind frame synchronization method based on a Maximum A Posteriori probability (MAP) approach. Applied to coded communication systems, this method is based on the calculation of the Log-likelihood Ratios (LLR) of the syndrome obtained according to the parity check matrix of the code. After presenting the proposed method, we compare it to an existing blind synchronization method previously introduced. Simulation results show that the proposed method outperforms the existing one and presents good performance when applied to codes having a sparse parity check matrix such as Low Density Parity Check (LDPC) codes and convolutional codes.     

基于欧氏几何的LDPC码构造方法

基于有限几何的低密度奇偶校验码(LDPC)是一种极具实用价值的码型。首先介绍了LD-PC码的原理和基本的构造方法,然后介绍了欧氏有限几何的概念,提出了一种构造欧氏有限几何LDPC码的方法,最后提出了对EG码字的改进方法。     

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。     

Low-density parity check codes for partial response channels

The goals of this article are twofold: (1) to provide a brief tutorial of the application of low-density parity check (LDPC) codes for partial response (PR) channels under the framework of turbo equalization and (2) to highlight the use of structured LDPC codes in PR systems. We begin by introducing LDPC codes, their graph representations and associated sum-product decoding algorithm, followed by describing the general framework of iterative equalization and decoding approach to combat ISI. We then present explicit constructions of structured LDPC codes, which facilitate efficient implementation of encoding and decoding and show simulation results.     

Low-density parity check codes and iterative decoding for long-haul optical communication systems

A forward-error correction (FEC) scheme based on low-density parity check (LDPC) codes and iterative decoding using belief propagation in code graphs is presented in this paper. We show that LDPC codes provide a significant system performance improvement with respect to the state-of-the-art FEC schemes employed in optical communications systems. We present a class of structured codes based on mutually orthogonal Latin rectangles. Such codes have high rates and can lend themselves to very low-complexity encoder/decoder implementations. The system performance is further improved by a code design that eliminates short cycles in a graph employed in iterative decoding.     

编码协作系统准循环重复累积码的联合设计与性能分析

重复累积(RA)码是一种特殊结构的低密度奇偶校验(LDPC)码,不仅具有LDPC码的优点,还能实现差分编码。针对LDPC编码协作系统编码复杂度高、时延长的问题,该文引入准循环RA(QC-RA)码,推导出信源节点和中继节点采用的QC-RA码对应的联合校验矩阵,基于公差构造方法设计该联合校验矩阵,并证明该方法设计的联合校验矩阵不存在围长为girth-4, girth-6的短环。理论分析和仿真结果表明,同等条件下该系统比相应点对点系统具有更优异的误码率性能。仿真结果同时表明,与采用一般构造QC-RA码或基于Z型构造QC-RA码相比,采用基于公差构造的联合设计QC-RA码的多信源多中继协作均可获得更高的编码增益。     

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。     

RS码与LDPC码的联合迭代译码

针对RS码与LDPC码的串行级联结构,提出了一种基于自适应置信传播(ABP)的联合迭代译码方法.译码时,LDPC码置信传播译码器输出的软信息作为RS码ABP译码器的输入;经过一定迭代译码后,RS码译码器输出的软信息又作为LDPC译码器的输入.软输入软输出的RS译码器与LDPC译码器之间经过多次信息传递,译码性能有很大提高.码长中等的LDPC码采用这种级联方案,可以有效克服短环的影响,消除错误平层.仿真结果显示:AWGN信道下这种基于ABP的RS码与LDPC码的联合迭代译码方案可以获得约0.8 dB的增益.