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。     

构造接近香农极限的低密度校验码

低密度校验(LDPC)码的性能优劣在很大程度上取决于该码的最小环长(Girth)和最小码距。本文采用几何构造方法构造最小环长为8的LDPC码,联合随机搜索算法改善其码重分布,所构造的LDPC码在码长为4k、编码效率为0.95时,距离香农极限仅1.1dB。     

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。     

低复杂度的LDPC码联合编译码构造方法研究

LDPC码因为其具有接近香农限的译码性能和适合高速译码的并行结构,已经成为纠错编码领域的研究热点。LDPC码校验矩阵的构造是基于稀疏的随机图,所以该类码字编码和译码的硬件实现比较复杂。以单位阵的循环移位阵为基本单元,构造LDPC码的校验矩阵,降低了LDPC码在和积算法下的译码复杂度。同时考虑到LDPC码的编码复杂度,给出了一种可以简化编码的结构。针对该方案构造的LDPC码,提出了消除其二分图上的短圈的方法。通过大量的仿真和计算分析,本文比较了这种LDPC码和随机构造的LDPC码在误码率性能,圈长分布以及最小码间距估计上的差异。     

基于稀疏二进制序列的低密度奇偶校验码

通过对低密度奇偶校验(LDPC)码构造的研究,提出了一种利用稀疏二进制序列构造规则LDPC码的新颖而简单的方法。在构造中,还提出了奇偶校验矩阵里元素‘1’的分布矩阵的概念。为了确保码Tanner图的最小圈长为8,利用了序列的周期自相关函数和周期互相关函数。通过仿真表明构造的新码在和积算法下进行迭代解码性能优异。由于产生的LDPC码本身固有的准循环结构,还能得到较低的编码复杂度。     

一种优化Girth分布的准循环LDPC码设计方法研究

在准循环LDPC码的构造中,校验矩阵拥有尽可能好的girth分布对于改善码的性能有着重要的意义。该文提出了构造准循环LDPC码的GirthOpt-DE算法,优化设计以获得具有好girth分布的移位参数矩阵为目标。仿真结果表明,该文方法得到的准循环LDPC码在BER性能和最小距离上均要优于固定生成函数的准循环LDPC码,Arrary码和Tanner码,并且使用上更为灵活,可以指定码长,码率及尽可能好的girth分布。     

一种优化LDPC码环分布的改进算法

在下一代移动通信系统中,为了满足移动用户对高速、宽带数据传输业务不断增长和更高质量的要求,需要对现有物理层的关键技术作进一步的改进、完善和实用化,例如在信道编码方面,就采用了革命性的LDPC码。而PEG算法则是目前构造中短码长LDPC码最有效的算法之一。通过借鉴ACE算法,在对已有的结构优化设计算法深入理解的基础上,对PEG算法进行了改进,得到了一种可以进一步优化LDPC码环分布和最小距离的改进算法。仿真结果表明：由新算法构造出来的LDPC码的环分布和码重分布都明显优于PEG算法;其性能曲线在低信噪比时与原算法相差不大,而随着信噪比的增加可以有效地降低错误平层。     

一种估测LDPC码最小距离的方法

由于LDPC码具有译码复杂度低,纠错性能好等众多优点,WiMAX 802.16e标准已将 LDPC 码作为OFDMA物理层的一种信道编码方案.本文采用从最小距离和码重分布的角度来研究LDPC码的纠错性能,深入研究了估计LDPC码距离特性的ANC算法,并利用此算法估测出几组LDPC码的最小距离.结果验证了ANC算法的正确...     

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．     

大小兼容的阵列LDPC码设计的新方法

阵列LDPC码构造简单,又易于VLSI实现.文献[4]对其进行了改进,支持任意码长,称为大小兼容的阵列LDPC码(记为SC阵列LDPC码).对于SC阵列LDPC码,本文提出3种改进方法,方法1对文献[4]SC阵列LDPC码进行了完善,排除了因k不是L的因子而产生的错误.方法2、3研究了新的子矩阵排列方法.这些方法对码的距离特性和误码性能都有很大改善.不仅在AWGN信道,还在UWB CM3信道上,通过仿真,证明了其良好性能.     

Performance of low-density parity-check codes with linear minimum distance

This correspondence studies the performance of the iterative decoding of low-density parity-check (LDPC) code ensembles that have linear typical minimum distance and stopping set size. We first obtain a lower bound on the achievable rates of these ensembles over memoryless binary-input output-symmetric channels. We improve this bound for the binary erasure channel. We also introduce a method to construct the codes meeting the lower bound for the binary erasure channel. Then, we give upper bounds on the rate of LDPC codes with linear minimum distance when their right degree distribution is fixed. We compare these bounds to the previously derived upper bounds on the rate when there is no restriction on the code ensemble.     

High-Rate Quasi-Cyclic Low-Density Parity-Check Codes Derived From Finite Affine Planes

This paper shows that several attractive classes of quasi-cyclic (QC) low-density parity-check (LDPC) codes can be obtained from affine planes over finite fields. One class of these consists of duals of one-generator QC codes. Presented here for codes contained in this class are the exact minimum distance and a lower bound on the multiplicity of the minimum-weight codewords. Further, it is shown that the minimum Hamming distance of a code in this class is equal to its minimum additive white Gaussian noise (AWGN) pseudoweight. Also discussed is a class consisting of codes from circulant permutation matrices, and an explicit formula for the rank of the parity-check matrix is presented for these codes. Additionally, it is shown that each of these codes can be identified with a code constructed from a constacyclic maximum distance separable code of dimension 2. The construction is similar to the derivation of Reed-Solomon (RS)-based LDPC codes presented by Chen and Djurdjevic Experimental results show that a number of high rate QC-LDPC codes with excellent error performance are contained in these classes     

Upper bounds on the rate of LDPC codes as a function of minimum distance

New upper bounds on the rate of low-density parity-check (LDPC) codes as a function of the minimum distance of the code are derived. The bounds apply to regular LDPC codes, and sometimes also to right-regular LDPC codes. Their derivation is based on combinatorial arguments and linear programming. The new bounds improve upon the previous bounds due to Burshtein et al. It is proved that at least for high rates, regular LDPC codes with full-rank parity-check matrices have worse relative minimum distance than the one guaranteed by the Gilbert-Varshamov bound.     

Generalization of Tanner's minimum distance bounds for LDPC codes

Tanner derived minimum distance bounds of regular codes in terms of the eigenvalues of the adjacency matrix by using some graphical analysis on the associated graph of the code. In this letter, we generalize Tanner's results by deriving a bit-oriented bound and a parity-oriented bound on the minimum distances of both regular and block-wise irregular LDPC codes.     

On the stopping distance of finite geometry LDPC codes

In this letter, the stopping sets and stopping distance of finite geometry LDPC (FG-LDPC) codes are studied. It is known that FG-LDPC codes are majority-logic decodable and a lower bound on the minimum distance can be thus obtained. It is shown in this letter that this lower bound on the minimum distance of FG-LDPC codes is also a lower bound on the stopping distance of FG-LDPC codes, which implies that FG-LDPC codes have considerably large stopping distance. This may explain in one respect why some FG-LDPC codes perform well with iterative decoding in spite of having many cycles of length 4 in their Tanner graphs.     

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.     

A lattice-based systematic recursive construction of quasi-cyclic LDPC codes

This paper presents a low-complexity recursive and systematic method to construct good well-structured low-density parity-check (LDPC) codes. The method is based on a recursive application of a partial Kronecker product operation on a given gamma x q, q ges 3 a prime, integer lattice L(gamma x q). The (n - 1)- fold product of L(gamma x q) by itself, denoted Lⁿ(gamma x q), represents a regular quasi-cyclic (QC) LDPC code, denoted (see PDF), of high rate and girth 6. The minimum distance of (see PDF) is equal to that of the core code (see PDF) introduced by L(gamma x q). The support of the minimum weight codewords in (see PDF) are characterized by the support of the same type of codewords in (see PDF). From performance perspective the constructed codes compete with the pseudorandom LDPC codes.     

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.     

Codes for iterative decoding from partial geometries

This paper develops codes suitable for iterative decoding using the sum-product algorithm. By considering a large class of combinatorial structures, known as partial geometries, we are able to define classes of low-density parity-check (LDPC) codes, which include several previously known families of codes as special cases. The existing range of algebraic LDPC codes is limited, so the new families of codes obtained by generalizing to partial geometries significantly increase the range of choice of available code lengths and rates. We derive bounds on minimum distance, rank, and girth for all the codes from partial geometries, and present constructions and performance results for the classes of partial geometries which have not previously been proposed for use with iterative decoding. We show that these new codes can achieve improved error-correction performance over randomly constructed LDPC codes and, in some cases, achieve this with a significant decrease in decoding complexity.