一种低译码复杂度的Turbo架构LDPC码

针对低密度奇偶校验(LDPC)码较大的译码复杂度和RAM占用,该文提出了一种低译码复杂度的Turbo架构LDPC码并行交织级联Gallager码 (Parallel Interleaved Concatenated Gallager Code,PICGC)。该文给出了PICGC的设计方法和编译码算法,并分析比较了PICGC译码器与LDPC译码器所需的RAM存储量,推导出RAM节省比的上界。理论分析和仿真结果表明,PICGC以纠错性能略微降低为代价,有效地降低译码复杂度和RAM存储量,且译码时延并未增加,是一种有效且易于实现的信道编码方案。     

光通信系统中一种新颖的随机交织型级联码方案

基于LDPC码,提出一种新颖的随机交织型级联码(RICC,random interleaved concatenatedcode)方案。在编码阶段,根据LDPC码中不同度数的变量节点采用不同纠错能力的BCH外码,分别进行保护的思想进行集分割编码;在译码阶段,采用硬判决辅助软判决的联合迭代译码。不同于传统的单极型和交织型级联方式,它是一种根据LDPC码变量节点(VN)度数来决定交织深度,因而交织方式是随机的。仿真结果分析表明,在误比特率(BER)为10-8时,四集合分割的RICC-4P的净编码增益(NCG)比无分割的单级型级联码提高了0.15dB,比ITU-T G.709和G.975.1标准中的RS(255,239)、RS(255,239)+CSOC(n/k=7/6,J=8)级联码和开销为25%的正交级联BCH码的NCG分别提高了3.0、1.5和0.4dB,其纠错性能的提升得益于采用集分割保护和硬判决辅助软判决的联合迭代译码。     

LDPC码的不可检测译码错误分析

纠错性能良好的LDPC码同时具有良好的检错性能。本文介绍了LDPC码的不可检测译码错误概率上限，讨论了不可检测译码错误与码参数的关系，提出对于特定构造的LDPC码，在基于AWGN信道传输和置信传播迭代译码时，可以应用迭代过程中连续消息的密度进化来分析不可检测译码错误概率，并给出了一些短码长高码率情况下的仿真结果。     

一种改进的自纠正最小和LDPC码的译码算法

低密度奇偶校验(LDPC)码是一类具有优良纠错能力的差错控制编码,可以逼近香农极限.目前LDPC码正在进入越来越多的工程应用中,高效的译码算法具有重要的价值.在研究已知的LDPC码译码算法的基础上,提出了一种改进的简化译码算法,称为加约束的自纠正最小和(CSCMS)算法,该算法的计算复杂度与最小和(MS)译码算法相当,性能却提升了0.2 dB左右,与其他几种改进的简化译码算法相比,性能提升约0.1 dB,并且译码的平均迭代次数也有所降低.     

一种改进的LDPC码译码算法

文中提出了一种改进的基于加权错误校验的LDPC码比特反转算法,该算法不需要软信息,译码时采用了设定判决门限的方法,减少了译码过程中的迭代次数和译码复杂度.仿真结果表明:对于高Girth、低码率的LDPC码,该算法达到了比多种利用软信息的比特反转算法更少的迭代次数和更优异的性能.     

一种BCH码编译码器的设计与实现

二元BCH码具有良好的代数结构和纠错能力,是应用最为广泛的码类之一。在此介绍了BCH（255,223）的编译码算法和硬件实现方法,针对二元BCH码提出了一种适合硬件模块化设计的BM迭代译码算法,并基于Xilinx公司的xc5vlx110t实现了BCH（255,223）纠错编译码。仿真结果表明,采用此方法实现的编译码器具有速度快、构造简单、性能稳定以及结构灵活的优点。目前该编译码器已成功用于某数字电台系统中。     

BCH-Turbo编码的设计与仿真实现

本文针对Turbo码在低信噪比下迭代次数多、译码时延长问题,在分析了Turbo码的编译码原理和算法基础上,提出一种可以有效降低平均迭代次数、减少译码时延的基于BCH迭代停止准则的Turbo码迭代译码的设计方案。本方案采用BCH码作为Turbo迭代译码的停止准则。并对每一个分量译码器结果都进行判断。可提前停止迭代。通过Monte Carlo仿真表明在AWGN信道下,误码率有所降低。Turbo码译码的平均迭代次数与交叉熵准则相比有明显下降。本文还分析了BCH码编码效率和分组长度的选择对系统性能的影响。     

基于DTMB中LDPC码与BCH码的乘积码构造

中国地面数字电视传输(DTMB)标准中的级联码能够有效降低低密度奇偶校验(Low-Density Parity-Check,LDPC)码的误码平层以获得极低的误比特率。基于DTMB标准中LDPC码与BCH码提出了一种性能优越的乘积码构造方案。构造的乘积码不仅性能优于级联码而且编译码复杂度与级联码相当,代价是较大的译码延时与较大的存储量。仿真结果表明,在码率相同且误比特率为1×10-7时,与级联码相比,构造的码长最长的乘积码可获得约0.12 dB的编码增益。     

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...     

DVB-S2标准IRA-LDPC译码算法研究与改进

首先对DVB-S2标准LDPC码编码原理、IRA码以及校验矩阵的特征进行了分析,接着对该标准中LDPC码的Tanner图参数进行了总结,然后对不同的译码算法从性能和复杂度方面进行了比较,并且对不同迭代次数时LDPC码的判决信息的分布进行了分析,最后对各种译码算法的性能和复杂度进行了总结.仿真结果表明,SPA译码算法性能最优但是复杂度最大,MinSum算法的复杂度最低但是性能最差,而改进的MinSum算法则在复杂度和性能方面是前面两种算法的折中,对实际工程的应用有较强的借鉴作用.     

The ABCs of linear block codes

The basic principles of block codes are presented with illustrations to visualize the concepts of vector spaces and subspaces. Intuitive explanations of goals, capabilities, and limitations of codes are offered. An important subclass of block codes called cyclic codes is examined. Their algebraic structure is described and looked at the very popular BCH and R-S cyclic codes. In addition, the newest techniques, turbo codes and LDPC codes, that use iterative decoding to obtain performance exceedingly close to theoretical limitations.     

Construction of Quasi-Cyclic LDPC Codes for AWGN and Binary Erasure Channels: A Finite Field Approach

In the late 1950s and early 1960s, finite fields were successfully used to construct linear block codes, especially cyclic codes, with large minimum distances for hard-decision algebraic decoding, such as Bose-Chaudhuri-Hocquenghem (BCH) and Reed-Solomon (RS) codes. This paper shows that finite fields can also be successfully used to construct algebraic low-density parity-check (LDPC) codes for iterative soft-decision decoding. Methods of construction are presented. LDPC codes constructed by these methods are quasi-cyclic (QC) and they perform very well over the additive white Gaussian noise (AWGN), binary random, and burst erasure channels with iterative decoding in terms of bit-error probability, block-error probability, error-floor, and rate of decoding convergence, collectively. Particularly, they have low error floors. Since the codes are QC, they can be encoded using simple shift registers with linear complexity.     

基于LDPC码的BICM-OFDM系统性能分析

论文构造了一种简化的以LDPC码(低密度校验码)为分量码的BICM-OFDM无线通信系统,通过仿真分别与基于Turbo码、BCH码的BICM-OFDM系统相比较,验证了简化的BICM-LDPC-OFDM系统在衰落信道具有更好的性能。     

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。     

The renaissance of Gallager's low-density parity-check codes

LDPC codes were invented in 1960 by R. Gallager. They were largely ignored until the discovery of turbo codes in 1993. Since then, LDPC codes have experienced a renaissance and are now one of the most intensely studied areas in coding. In this article we review the basic structure of LDPC codes and the iterative algorithms that are used to decode them. We also briefly consider the state of the art of LDPC design.     

基于多重置换阵的满秩结构化LDPC码构造方法

 在多重置换阵的基础上,提出一种适用基于网络编码的协作中继策略的结构化LDPC码构造方法.首先定义了多重置换阵的概念,提出并证明了该方阵在秩和消元等方面的重要性质;给出具体的构造步骤,构造了列重为3和围长至少为6的满秩LDPC码;分析了该LDPC码的生成矩阵,具有稀疏和结构化的特点,适用基于网络编码的协作中继系统中进行联合网络编码和迭代译码.仿真结果表明,在相同码长、2/3码率和准循环矩阵 Y 结构条件下,相比阵列LDPC码、近似双对角形式的LDPC码和三对角形式的LDPC码,新构造的LDPC码具有相对较好的译码性能.     

LDPC block and convolutional codes based on circulant matrices

A class of algebraically structured quasi-cyclic (QC) low-density parity-check (LDPC) codes and their convolutional counterparts is presented. The QC codes are described by sparse parity-check matrices comprised of blocks of circulant matrices. The sparse parity-check representation allows for practical graph-based iterative message-passing decoding. Based on the algebraic structure, bounds on the girth and minimum distance of the codes are found, and several possible encoding techniques are described. The performance of the QC LDPC block codes compares favorably with that of randomly constructed LDPC codes for short to moderate block lengths. The performance of the LDPC convolutional codes is superior to that of the QC codes on which they are based; this performance is the limiting performance obtained by increasing the circulant size of the base QC code. Finally, a continuous decoding procedure for the LDPC convolutional codes is described.     

半双工中继信道下联合LDPC码设计

为了提高解码前传半双工中继通信系统的编码增益,提出了一种联合LDPC码编码结构及其度分布优化方法。该结构视信源和中继子码为联合LDPC码的一部分,目的端根据从信源和中继接收的消息进行联合译码,同时获得信源和中继的信息。为了分析联合LDPC码的渐进性能,推导了AWGN信道下联合LDPC码的高斯近似密度进化算法。结合译码收敛条件和度分布约束关系,提出联合LDPC码的度分布优化问题。仿真结果表明：联合LDPC码的渐进性能及误码性能优于BE-LDPC码和独立处理（SP）码。     

Toward low LDPC-code floors: a case study

While LDPC codes have been widely acclaimed in recent years for their near-capacity performance, they have not found their way into many important applications. For some cases, this is due to their increased decoding complexity relative to the classical coding techniques. For other cases, this is due to their inability to reach very low bit error rates (e.g., 10?12) at low signal-to-noise ratios (SNRs), a consequence of the errorrate floor phenomenon associated with iterative LDPC decoders. In the present paper, we make strides in the low-floor problem by identifying the weaknesses of the code under study and applying compensatory counter-measures. These counter-measures include: modifying the code itself, modifying the decoder, or adding a properly designed outer algebraic code. Our results demonstrate that each of these techniques can successfully lower an LDPC code?s floor, and that, for the code under study, an outer BCH code appears to be particularly effective. All of our results are based on FPGA decoder simulations and so they are reliable and repeatable.