基于EXIT图的Turbo均衡LDPC码性能分析及优化研究

EXIT图是用来分析级联系统中外信息迭代交换的重要工具,本文将Brink的基于EXIT图的优化MIMO信道LDPC码的思想推广到用于Turbo均衡的LDPC码性能分析及码结构设计优化中。文章首先给出了基于互信息的接收机具体分析模型,接着分别讨论了接收机分析模型中两个单元的EXIT曲线:线性MMSE均衡器和VND(variable node decoder)的联合EXIT曲线,CND(check node variable)的EXIT曲线的详细计算步骤。进一步以获得的EXIT曲线为基础,提出了用于Tur- bo均衡的LDPC码的码结构优化算法,EQVAC-EXIT(EQVAC:equalizer VND and CND)算法,算法能够自动地进行码集噪声门限值计算及优化次数分布对的搜索。最后的数值仿真结果表明,(3,6)正则码及优化得到的非正则码的噪声门限值距离Narayanan的结果仅相差0．03dB左右,优化得到的边的次数分布及节点的次数分布与Narayanan的结果相比也很接近。     

基于EXIT图和自适应微粒群算法的度分布对优化方法

综合EXIT图法和自适应微粒群优化(APSO)算法的优点,该文提出了一种基于EXIT图和APSO算法的非正则LDPC码度分布对优化方法。该方法设计了衡量EXIT曲线匹配程度的全局代价函数,并运用APSO算法对度分布对进行快速迭代优化,迭代过程中不需要固定CND曲线,可以获得EXIT曲线更加匹配的优化度分布对,以及更高的噪声门限。仿真结果表明,该方法在码结构优化方面有着很好的性能,且优化速度较高斯逼近法有了较大提高。     

基于EXIT曲线图的IRA码译码方法研究

基于IRA码迭代译码器结构,研究了EXIT曲线图性能分析方法。利用此方法求出几种码率IRA码的收敛门限值,并与高斯近似和密度进化方法求得的结果进行比较分析,探讨EXIT曲线图的优点和应用技术。     

DVB-S2中IRA码EXIT曲线图分析方法研究

基于IRA码迭代译码器结构，丈中研究了EXIT曲线图性能分析方法。利用此方法求出DVB—S2中各种码率IRA码的收敛门限值，并与高斯近似和密度进化方法求得的结果进行比较分析，探讨了EXIT曲线图的优点和应用技术。     

纠删信道中LDPC码EXIT曲线匹配设计

基于单栓码和重复码EXIT图面积特性的分析,介绍了在二元纠删信道中,采用EXIT曲线匹配设计LDPC码度分布序列的最佳性:当内外码的EXIT曲线完全匹配时,所设计的度分布序列对应的速率能够达到信道容量;而当内外码EXIT曲线之间有间隔时,所设计的度分布序列对应的速率严格小于信道容量,并且间隔面积越大,所损失的速率越大.     

解码前传半双工中继信道下协作LDPC码设计

为逼近解码前传半双工中继信道容量,该文提出一种协作LDPC编码结构及度分布优化方法。与双层删除LDPC码不同,该结构将中继校验比特视为协作LDPC码的一部分,目的端利用从信源和中继接收的消息进行联合译码获得信源信息。为了分析协作LDPC码性能,拓展传统外信息转移(EXIT)图,推导了基于消息错误概率的双层EXIT图噪声门限分析方法。在此基础上,提出了协作LDPC码度分布优化方法,采用差分进化算法搜索了一组具有最大噪声门限的协作LDPC码。实验仿真证明,与双层删除LDPC码相比,协作LDPC码的性能得到了不同程度的改善。     

LDPC编码的BICM迭代系统中的映射方案研究

迭代BICM(BICM-ID)系统的性能与调制星座符号的映射方式有关,本文利用EXIT图的方法,分析了各种星座符号映射方案对LDPC编码的BICM-ID系统性能的影响.分析表明,已有的卷积码编码的BICM-ID系统的映射方式的优化设计准则不再适用于LDPC编码的BICM-ID系统,应按照迭代系统的EXIT特性曲线相匹配的原则,将映射的优化和码字的特点联合起来考虑.计算机仿真验证了这个结论.     

LDPC码的优化设计

通过码结构优化设计,可以得到性能接近香农限的LDPC好码,其关键是寻找好的次数分布对。本文阐述了几种有效分析LDPC码性能的方法：密度演进分析,高斯近似分析及基于EXIT图的方法,在此基础上给出了LDPC码优化设计的过程。LDPC码结构设计的研究对提高码的性能和进一步推动LDPC码的实际应用有着重要的意义。     

LDPC编码的空时BICM系统中的一种优化设计方案

本文基于外附信息转移(EXIT)图的系统优化设计思想,提出了一种级联预编码器的低密度奇偶校验码(LDPC)编码的空时比特交织编码调制(BICM-MIMO)系统设计方案.该方案在调制器的前端级联一个码率为1的累加器作为预编码器,在相邻的比特之间引入相关性,从而使得联合检测器的EXIT曲线发生变化,与空时MIMO系统下优化LDPC码的译码器EXIT曲线相匹配,并使两条曲线相交于EXIT图的右上角.和已有系统设计方案相比,该方案可提高系统的译码性能并能降低误码的错误平层(error floor).     

有限平面LDPC码的停止集

有限平面LDPC码是一类重要的有结构的LDPC码,在利用和积算法(SPA)等迭代译码方法进行译码时表现出卓越的纠错性能。众所周知,次优的迭代译码不是最大似然译码,因而如何对迭代译码的性能进行理论分析一直是LDPC码的核心问题之一。近几年来,Tanner图上的停止集(stopping set)和停止距离(stopping distance)由于其在迭代译码性能分析中的重要作用而引起人们的重视。该文通过分析有限平面LDPC码的停止集和停止距离,从理论上证明了有限平面LDPC码的最小停止集一定是最小重量码字的支撑,从而对有限平面LDPC码在迭代译码下的良好性能给出了理论解释。     

Extrinsic information transfer functions: model and erasure channel properties

Extrinsic information transfer (EXIT) charts are a tool for predicting the convergence behavior of iterative processors for a variety of communication problems. A model is introduced that applies to decoding problems, including the iterative decoding of parallel concatenated (turbo) codes, serially concatenated codes, low-density parity-check (LDPC) codes, and repeat-accumulate (RA) codes. EXIT functions are defined using the model, and several properties of such functions are proved for erasure channels. One property expresses the area under an EXIT function in terms of a conditional entropy. A useful consequence of this result is that the design of capacity-approaching codes reduces to a curve-fitting problem for all the aforementioned codes. A second property relates the EXIT function of a code to its Helleseth-Klove-Levenshtein information functions, and thereby to the support weights of its subcodes. The relation is via a refinement of information functions called split information functions, and via a refinement of support weights called split support weights. Split information functions are used to prove a third property that relates the EXIT function of a linear code to the EXIT function of its dual.     

Simple and Accurate Design of Low-Density Parity-Check Codes for Multi-Input Multi-Output Systems

In this paper we design an irregular low-density parity-check (LDPC) code for multiple-input multiple-output (MIMO) systems, using a simple extrinsic information transfer (EXIT) chart method. The MIMO systems considered are the optimal maximum a posteriori probability (MAP) detector and the suboptimal minimum mean square error soft-interference cancellation (MMSE-SIC) detector. The MIMO detector and the LDPC decoder exchange soft information and form a turbo iterative receiver. The EXIT charts are used to obtain the edge degree distribution of the irregular LDPC code which is optimized for the MIMO detector. It is shown that the performance of the designed LDPC code is better than that of conventional LDPC code which was optimized for either the Additive White Gaussian Noise (AWGN) channel or the MIMO channel without an explicit consideration of the given detector structure.     

Design of Irregular LDPC Codes for BIAWGN Channels with SNR Mismatch

Belief propagation (BP) algorithm for decoding lowdensity parity-check (LDPC) codes over a binary input additive white Gaussian noise (BIAWGN) channel requires the knowledge of the signal-to-noise ratio (SNR) at the receiver to achieve its ultimate performance. An erroneous estimation or the absence of a perfect knowledge of the SNR at the decoder is referred to as ?SNR mismatch?. SNR mismatch can significantly degrade the performance of LDPC codes decoded by the BP algorithm. In this paper, using extrinsic information transfer (EXIT) charts, we design irregular LDPC codes that perform better (have a lower SNR threshold) in the presence of mismatch compared to the conventionally designed irregular LDPC codes that are optimized for zero mismatch. Considering that min-sum (MS) algorithm is the limit of BP with infinite SNR over-estimation, the EXIT functions generated in this work can also be used for the efficient analysis and design of LDPC codes under the MS algorithm.     

Threshold of LDPC-coded BICM for Rayleigh fading

We analyze the threshold and convergence of LDPC coded bit interleaved coded modulation over Rayleigh fading channels. We compute the system threshold using the discretized density evolution and the extrinsic information transfer (EXIT) chart, and verify its effectiveness by simulation. Simulated detector output pdf is used to compute the variable node EXIT curve. It is shown that the convergence SNR observed from the transfer curves matches the density evolution threshold perfectly, and the EXIT chart actually provides a more computational efficient approach to estimate the threshold. An irregular code design example using the EXIT chart is given.     

Doubly Generalized LDPC Codes over the AWGN Channel

In this paper, the design of doubly generalized low-density parity-check (DGLDPC) codes is proposed. This approach generalizes the structure of LDPC codes at both check and variable nodes. The performance of DGLDPC codes over the AWGN channel is analyzed using EXIT charts. Combined with differential evolution optimization, this analysis provides thresholds for DGLDPC codes that are better than that of LDPC and GLDPC codes with the same maximum variable degree. These theoretical thresholds are verified via simulations. Furthermore DGLDPC codes exhibit a lower error floor compared with their LDPC and GLDPC counterparts.     

Does the Performance of LDPC Codes Depend on the Channel?

In this letter, we discuss the performance of low-density parity-check (LDPC) codes on memoryless channels. Using a recently proposed analysis technique based on extrinsic information transfer (EXIT) charts, we present an interpretation of the known fact that the bit-error rate (BER) performance of an ensemble of LDPC codes shows little dependence on the specific memoryless channel. This result has been partially observed in the literature for symmetric channels and is here extended to asymmetric channels. We conjecture and demonstrate that the performance of an ensemble of LDPC codes depends primarily and solely on the mutual information (MI) between the input and the output of the channel. As a validation of this conjecture, we compare the performance of a few LDPC codes with various rates for five representative memoryless (both symmetric and asymmetric) channels, obtaining results in excellent agreement with the EXIT chart-based prediction     

Bandwidth-Efficient Modulation Codes Based on Nonbinary Irregular Repeat–Accumulate Codes

Using nonbinary low-density parity-check (LDPC) codes with random-coset mapping, Bennatan and Burshtein constructed bandwidth-efficient modulation codes with remarkable performance under belief propagation (BP) decoding. However, due to the random nature of LDPC codes, most of the good LDPC codes found in the literature do not have a simple encoding structure. Thus, the encoding complexity of those LDPC codes can be as high as O(N ²), where N is the codeword length. To reduce the encoding complexity, in this paper, nonbinary irregular repeat-accumulate (IRA) codes with time-varying characteristic and random-coset mapping are proposed for bandwidth-efficient modulation schemes. The time-varying characteristic and random-coset mapping result in both permutation-invariance and symmetry properties, respectively, in the densities of decoder messages. The permutation-invariance and symmetry properties of the proposed codes enable the approximations of densities of decoder messages using Gaussian distributions. Under the Gaussian approximation, extrinsic information transfer (EXIT) charts for nonbinary IRA codes are developed and several codes of different spectral efficiencies are designed based on EXIT charts. In addition, by proper selection of nonuniform signal constellations, the constructed codes are inherently capable of obtaining shaping gains, even without separate shaping codes. Simulation results indicate that the proposed codes not only have simple encoding schemes, but also have remarkable performance that is even better than that constructed using nonbinary LDPC codes.     

Serial concatenation of LDPC codes and differential modulations

In this paper, we consider serially concatenated schemes with outer novel and efficient low-density parity-check (LDPC) codes and inner modulations effective against channel impairments. With a pragmatic approach, we show how to design LDPC codes tailored for simple and robust modulation formats, such as differentially encoded (DE) modulations. The LDPC codes are optimized through the use of a recently proposed analysis technique based on extrinsic information transfer (EXIT) charts. In particular, we optimize, through a "clever" random walk in the parametric space, the degree distributions of the outer LDPC codes, obtaining significant insights on the impact of such distributions on the performance of the proposed concatenated schemes. The optimization is carried out for transmission over both the additive white Gaussian noise channel and a noncoherent channel. The performance predicted by the EXIT chart-based optimization is confirmed by results obtained via computer simulations, considering phase-shift keying and quadrature amplitude modulation at the transmitter side, and iterative demodulation/decoding at the receiver side. The significance of the proposed optimized design of LDPC-coded schemes with DE modulations is validated by the fact that standard nonoptimized LDPC codes perform poorly when used together with inner DE modulations.     

Decoding and Design of LDPC Codes for High-Order Modulations

A concatenated code model is proposed for high-order low-density parity-check (LDPC) coded modulations. A corresponding concatenated-code belief propagation (CCBP) decoding algorithm is derived for our proposed concatenated code. Moreover, the design of LDPC codes under the CCBP decoding is developed using extrinsic information transfer (EXIT) charts. Compared with other algorithms, the CCBP method provides an excellent parallel decoding process, and the EXIT-based design method offers highly accurate LDPC code ensembles. Simulation results show that the performance of the proposed CCBP algorithm is superior to that of the conventional belief propagation decoding within a wide range of modulation orders, and the EXIT-based method can design capacity-approaching LDPC codes for high-order modulations.