一种AWGN信道下非规则LDPC码的优化方法

提出了一种加性高斯噪声（AWGN）信道下非规则低密度奇偶校验（LDPC）码的优化方法。利用LDPC码迭代译码算法下变量节点与校验节点的EXIT曲线之间的面积反映码的收敛阈值与香农限的差距这一特点,设计表示两条EXIT曲线之间面积的函数F,该函数可以衡量非规则LDPC码的性能,F值越小,LDPC码的收敛阈值就越接近香农限。仿真显示,合理设计变量节点和校验节点,减小函数F的值,能够提高非规则LDPC码的性能。     

具有快速译码收敛速度的LDPC码设计

为了提高非规则LDPC码译码的收敛速度,提出了一种具有快速收敛速度的LDPC码构造算法。该算法在原有非规则LDPC码的基础上,通过对校验矩阵进行列重排,来提升信息比特译码的可靠性,以此降低迭代次数,提高收敛速度。仿真实验表明,采用该算法设计的LDPC码,在采用基于变量节点的分层置信度传播（VL-BP）译码算法下,平均迭代次数有明显的降低。另外,对于置信度传播（BP）译码算法和VL-BP译码算法来说,设计的LDPC码具有更优的误码性能。     

两种级联空时格码方案的EXIT分析

级联空时格码方案可以有效地提高空时格码系统的性能。研究了两种级联空时格码方案:PC-STTC和ST-Turbo-TC。由于两种级联方案都使用了迭代译码方法,而外信息转移(EXIT)图是分析迭代译码性能的有利工具,主要分析比较了PC-STTC和ST-Turbo-TC的EXIT性能,比较了不同信噪比和编码多项式对于译码外信息转移特性的影响。研究结果显示,PC-STTC方案比ST-Turbo-TC方案有着更好的迭代收敛性能,同时给出了BER仿真图证明了EXIT图的分析结论。     

基于EXIT图的正则LDPC码性能分析研究

EXIT（EXtrinsic Information Transfer）图分析方法可以看作密度进化技术的一种简化,具有实现简单的优点,并且在不同的信道、调制方案以及检测器中都可以使用。在详细阐述了EXIT图分析方法的基础上,给出了基于EXIT图的正则LDPC码的门限判决算法,进一步通过计算机仿真分别给出了变量节点译码器和校验节点译码器的EXIT曲线,以及不同的信道信噪比下（3,6）正则LDPC码EXIT图的变化规律,直观地对迭代译码过程中的互信息变化进行了描述分析。     

基于差分进化的非规则LDPC码优化设

为优化非规则低密度奇偶校验(LDPC)码的度分布,引入差分进化(DE)极值搜索算法,根据差分进化后的最佳成员矢量,确定非规则LDPC码变量点的度分布。基于期望码率和变量点的度分布调整校验点的度分布,获得期望码率下的LDPC码。为提高优化搜索效率,改进差分进化停止准则,从而有效控制进化迭代次数。在此基础上,设计一组加性高斯白噪声(AWGN)信道下的非规则LDPC码。实验结果表明,该方法的译码复杂度低,设计的LDPC码具有较高的噪声门限。     

改进型LLR BP译码算法研究

短低密度校验(LDPC)码的Tanner图中通常存在环路,变量节点之间的信息不再相互独立,导致LLR BP算法译码性能的下降。针对上述问题,提出一种改进型LLR BP译码算法,推导出有环时变量节点的真实信息,利用最小均方误差准则计算出有记忆的变量节点信息的权值,通过调整变量节点信息的迭代过程降低变量节点之间信息的相关性。仿真结果表明,改进型LLR BP算法具有比LLR BP算法、归一化BP算法及偏移量BP算法更好的LDPC译码性能。     

一种LDPC码的译码停止准则

提出了一种实用的LDPC码译码停止准则,利用信息节点的对数概率似然比(LLR)来控制迭代次数,避开了设置停止准则门限,可以很快判断出译码情况,较其他方法省去了大量繁杂的计算。     

PEG GLDPC码设计与性能分析

针对深空通信中高信道编码增益的需求,设计了一种新颖的基于按边增长(Progressive edge-growth,PEG)算法的广义低密度奇偶校验(Generalized LDPC,GLDPC)码.基于稀疏矩阵的二分图,首先改进了PEG算法用以构造规则LDPC,然后用BCH码作子码替换LDPC中的单奇偶校验码来构造PEG-GLDPC,最后重点研究了PEG-GLDPC的译码算法,提出一种联合BCH比特栅格译码与置信传播(Belief propagation,BP)算法的迭代译码机制.AWGN信道下的仿真结果表明,PEG-GLDPC译码性能优于LDPC以及传统GLDPC,适用于深空通信等低信噪比通信系统.     

基于软比特域的LT码修正震荡迭代算法

LT码的BP译码算法复杂度较高,在译码时由于Tanner图短环的出现易产生震荡效应。为此,提出一种软比特域迭代译码算法。将双曲正切函数进行变换和量化处理,得到(-1,1)区间的软比特域,并将变量节点信息更新算法变换到软比特域中进行计算。为解决LT码中短环的存在导致某些变量节点的外信息出现震荡效应的问题,给出一种新的震荡判断准则,只有当变量节点在连续2次迭代时符号发生反转,且软比特域值均高于阈值时判定为出现震荡。仿真结果表明,简化软比特域震荡迭代译码算法约比传统BP算法降低75%的运算量,并在误码率性能上逼近BP算法。     

利用HMM信源残留冗余的LDPC译码算法

提出一种基于二阶HMM（隐马尔可夫）信源和LDPC的联合信源信道译码算法。在迭代过程中,利用信源序列中的冗余信息校正LDPC译码的迭代软信息,提高LDPC码的纠错性能,加快迭代收敛速度。AWGN信道的仿真结果证实了该联合信源信道解码算法性能优越。     

累积码EXIT曲线的高效数值求法

累积码作为非规则RA码的分量码之一,除了在纠删信道上具有显式的EXIT函数之外,在一般信道上其EXIT曲线均由仿真获得。由仿真获得累积码EXIT曲线不但增加了非规则RA码的设计复杂度,而且使得整个设计过程无法实时完成。首先证明对于累积码而言,串行和积算法与BCJR算法是等价的;在此基础上,证明了累积码在串行和积译码时,与译码中间变量相关的互信息具有平稳特性;利用该平稳特性,推导了累积码EXIT函数的隐式表达式,从而给出一种求解累积码EXIT曲线的高效数值算法。采用该方法获得的EXIT曲线与仿真结果一致,能够显著降低非规则RA码的设计复杂度,并使非规则RA码的设计实时化。     

EXIT analysis of M-algorithm based MIMO detectors and LDPC code design optimization

This paper investigates joint design and optimization of both low density parity check (LDPC) codes and M-algorithm based detectors including iterative tree search (ITS) and soft-output M-algorithm (SOMA) in multiple-input multiple-output (MIMO) systems via the tool of extrinsic information transfer (EXIT) charts. First, we present EXIT analysis for ITS and SOMA. We indicate that the extrinsic information transfer curves of ITS obtained by Monte Carlo simulations based on output log-likelihood rations are not true EXIT curves, and the explanation for such a phenomenon is given, while for SOMA, the true EXIT curves can be computed, enabling the code design. Then, we propose a new design rule and method for LDPC code degree profile optimization in MIMO systems. The algorithm can make the EXIT curves of the inner decoder and outer decoder match each other properly, and can easily attain the desired code with the target rate. Also, it can transform the optimization problem into a linear one, which is computationally simple. The significance of the proposed optimization approach is validated by the simulation results that the optimized codes perform much better than standard non-optimized ones when used together with SOMA detector.     

A special class of quasi-cyclic low-density parity-check codes based on repetition codes and permutation matrices

We propose a new ensemble of binary low-density parity-check codes with paritycheck matrices based on repetition codes and permutation matrices. The proposed class of codes is a subensemble of quasi-cyclic codes. For the constructed ensemble, we obtain minimum distance estimates. We present simulation results for the proposed code constructions under the (Sum-Product) iterative decoding algorithm for transmission over an additive white Gaussian noise channel using binary phase-shift keying.     

有19-(4,f)型自同构的二元自对偶码

应用二元自对偶码可看成几个自对偶码的直和理论,研究了具有19-(4,f)型自同构、码长在100以内的的二元自对偶码。这种对偶码都可看成一个码长为4的收缩码和GF(2)n上一些偶重量多项式的直和。证明了码长大于80且小于100时,不存在19-(4,f)型的二元自对偶码。根据码长较短的自对偶码分别构造出了码长为76、78和80的二元自对偶码,并给出其生成矩阵。由码的等价得到了这几类码可能的分类情况。运行Matlab程序,证明了具有19-(4,2)型和19-(4,4)型的二元自对偶码在等价情况下都有11个,19-(4,0)型的二元自对偶码在等价情况下是不存在的。     

具有7-(8,0)型自同构的二元双偶极值码

把长度为56的具有7-(8,0)型自同构的二元双偶极值码看成二元域上的多项式,分解成一个收缩码和一个偶重量多项式的直和。利用已知的码长较短的编码构造出长度为56的具有7-(8,0)型自同构的二元双偶极值码,并给出可能的生成矩阵。由于该双偶极值码的最小距离为12,根据两个码等价的类型,对生成矩阵运行Matlab程序,证明了在等价情况下,当E1(σ)*的维数K=2时,不存在有7-(8,0)型自同构的二元双偶极值码;当E1(σ)*的维数K=4时,有7-(8,0)型自同构二元双偶极值码共75种。对长度为56到70的具有类似型自同构的双偶极值码进行相似讨论,得到了其生成矩阵和分类情况。至此,长度在50到70之间的二元双偶极值码的生成矩阵和分类情况得到完全解决。     

Decoding turbo-like codes via linear programming

We introduce a novel algorithm for decoding turbo-like codes based on linear programming. We prove that for the case of repeat-accumulate codes, under the binary symmetric channel with a certain constant threshold bound on the noise, the error probability of our algorithm is bounded by an inverse polynomial in the code length.Our linear program (LP) minimizes the distance between the received bits and binary variables representing the code bits. Our LP is based on a representation of the code where codewords are paths through a graph. Consequently, the LP bears a strong resemblance to the min-cost flow LP. The error bounds are based on an analysis of the probability, over the random noise of the channel, that the optimum solution to the LP is the path corresponding to the original transmitted codeword.     

A Note on the Stopping Redundancy of Linear Codes

In this paper, we study the stopping sets, stopping distance and stopping redundancy for binary linear codes. Stopping redundancy is a new concept proposed by Schwartz and Vardy recently for evaluating the performance of a linear code under iterative decoding over a binary erasure channel （BEC）. Since the exact value of stopping redundancy is difficult to obtain in general, good lower and upper bounds are important. We obtain a new general upper bound on the stopping redundancy of binary linear codes which improves the corresponding results of Schwartz and Vardy.     

On a new class of binary group codes

A new class of binary group error-correcting codes is formalized and defined. The codes are generated by irreducible and primitive polynomials over the binary field by an iterative procedure. A general formula for the number of corregible errors related to the lengthn of the code vectors is given. A method to obtain from a given code a class of subcodes is described. The encoding and decoding (error-detecting, error-correcting) procedures are extremely simple and use linear shift registers. A general formula describing the number of operations involved is given. This work has been supported by the National Science Fundation under grant numberGP-2122 and represents part of the doctoral dissertation.