基于联合判决消息传递机制的LDPC码译码算法研究

采用消息传递算法(Message passing algorithm)对LDPC码进行译码时,变量消息的振荡会引起错误的发生.本文以(600.300)非规则LDPC码仿真实验为例分析了不同译码效果下判决消息均值的分布特点,并结合环的特点,分析了译码产生错误判决的原因.研究了"纠删"型消息传递机制和联合判决迭代停止准则,针对判决消息出现振荡情况,提出以"纠删"方式处理变量消息的更新,并结合变量节点判决消息均值分布趋势与伴随式结果确定迭代终止条件.在此基础上,提出一种新的LDPC码译码算法.仿真分析表明,新的译码算法能够在减少迭代次数和降低译码复杂度的同时,有效提高译码的纠错性能.     

多元LDPC码分层译码算法及其在QPSK调制下的应用

文章将二元LDPC码对数域的分层译码算法成功运用在多元LDPC码的译码过程当中。仿真结果表明,在理想加性高斯白噪声信道环境下,QPSK调制时,多元LDPC码分层译码算法的性能明显优于传统的对数域译码算法,因此它可以有效提升消息传递算法的收敛速度,减少译码延时。     

多径衰落信道下LDPC码初始译码消息研究

LDPC码初始译码消息是LDPC码密度演进研究的必要条件。本文简述了LDPC码的相关基础知识．重点研究了Rician衰落信道及Rayleigh信道下LDPC码的初始译码消息的概率密度．给出了译码消息的对称性和稳定性的表达，探讨了BP和BP_based两种译码方法的初始消息的概率密度形式，对于不同信道参数和译码算法下的初始消息的概率聚集函数（PMF：Probability Mass Function）进行了比较。     

卷积LDPC码在瑞利信道下的性能分析

本文研究了卷积LDPC码在瑞利衰落信道下的译码性能,给出了瑞利信道下,卷积LDPC码的译码算法,在同等条件下对比了卷积LDPC码在高斯信道和瑞利衰落信道下的译码性能。     

Rice信道下LDPC码密度进化的研究

应用低密度奇偶校验(LDPC)码译码消息的密度进化可以得到码集的噪声门限,依此评价不同译码算法的性能,并可以用来优化非正则LDPC码的次数分布对。该文首先以Rice信道下正则LDPC码为例,讨论了不同量化阶数及步长时BP,BP-based 和offset BP-based 3种译码算法的DDE(Discrete Density Evolution)分析,接着在offset BP-based译码算法的DDE分析基础上,采用差分进化方法对Rice信道下非正则LDPC码的次数分布对进行了优化,得出了相应的噪声门限。最后,给出了Rice信道下码率为1/2的优化非正则LDPC码的概率聚集函数(PMF)进化曲线。     

LDPC编译码算法分析

低密度奇偶校验(LDPC)码是一种线性分组码,其纠错能力可以接近香农极限。针对LDPC码的编译码问题,分析了校验矩阵的构造方法。给出了LDPC码的编码算法以及算法的实现结构。分析了基于软判决的置信传播(BP)译码算法,并给出了可以进一步降低计算复杂度的简化译码方法。通过仿真对比了不同的译码算法在高斯信道下的译码性能。     

基于串行消息传递机制的QC-LDPC码快速译码算法研究

针对准循环LDPC(QC-LDPC)码基于洪水消息传递机制译码算法的不足,该文提出了一种快速的分组串行译码算法。该算法通过将LDPC码的校验节点(或变量节点)按一定规则划分成若干个子集,在每一轮迭代过程中,依次对各个子集中的校验节点(或变量节点)并行地进行消息更新,提高了译码速度。同时根据分组规则,提出了一种有效的分组方法,并通过分析发现基于循环置换阵的准循环LDPC码非常适合采用这种分组译码算法进行译码。通过对不同消息传递机制下准循环LDPC码译码算法性能的仿真比较,验证了在复杂度不增加的情况下,该译码算法在继承了串行译码算法性能优异和迭代收敛快等优点的同时,极大地提高了准循环LDPC码的译码速度。分析表明,分组串行译码算法译码速度至少为串行译码算法的p倍(p为准循环LDPC码校验矩阵中循环置换阵的行数或列数)。     

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。     

多元LDPC码与二元LDPC码的性能比较

介绍了一种基于有限域构造的多元准循环LDPC码的编码方法,译码采用基于快速傅立叶变换的和积算法.通过对多元LDPC码与二元LDPC码在高斯和衰落信道下的性能仿真比较,发现调制方式为BPSK时,二元LDPC码的性能在高斯信道和独立瑞利衰落信道下好于多元LDPC码,在相关衰落信道中则是多元LDPC码表现更佳;而当调制方式为16-QAM时,多元LDPC码在不同信道环境中的性能均好于谱效率相同的二元LDPC码.     

高阶调制系统下LDPC码优化设计

为了提高编码调制系统的整体编码增益,提出一种高阶调制系统下LDPC码的度分布优化方法.根据高阶调制符号中不同比特的误比特特性,将调制符号所经历信道建模为一组对称二进制输入加性高斯信道.在此基础上,推导了高阶调制系统下LDPC码高斯近似密度进化分析方法,并得到译码收敛条件.结合度分布约束关系及译码收敛条件,提出高阶调制系统下LDPC码的度分布优化问题及差分进化实现方法.仿真结果表明,设计的LDPC码在高阶调制系统中的渐进性能和误码性能优于基于比特优化映射的编码调制方案.     

Joint message-passing decoding of LDPC codes and partial-responsechannels

Ideas of message passing are applied to the problem of removing the effects of intersymbol interference (ISI) from partial-response channels. Both bit-based and state-based parallel message-passing algorithms are proposed. For a fixed number of iterations less than the block length, the bit-error rate of the state-based algorithm approaches a nonzero constant as the signal-to-noise ratio (SNR) approaches infinity. This limitation can be removed by using a precoder. It is well known that low-density parity-check (LDPC) codes can be decoded using a message-passing algorithm. Here, a single message-passing detector/decoder matched to the combination of a partial-response channel and an LDPC code is investigated     

Finite-length rate-compatible LDPC codes: a novel puncturing scheme - [transactions letters]

In this paper, we study rate-compatible puncturing of finite-length low-density parity-check (LDPC) codes. We present a novel rate-compatible puncturing scheme that is easy to implement. Our scheme uses the idea that the degradation in performance is reduced by selecting a puncturing pattern wherein the punctured bits are far apart from each other in the Tanner graph of the code. Although the puncturing scheme presented is tailored to regular codes, it is also directly applicable to irregular parent ensembles. By simulations, the proposed rate-compatible puncturing scheme is shown to be superior to the existing puncturing methods for both regular and irregular LDPC codes over the binary erasure channel (BEC) and the additive white Gaussian noise (AWGN) Channel.     

FPGA implementation of low complexity LDPC iterative decoder

Low-density parity-check (LDPC) codes, proposed by Gallager, emerged as a class of codes which can yield very good performance on the additive white Gaussian noise channel as well as on the binary symmetric channel. LDPC codes have gained lots of importance due to their capacity achieving property and excellent performance in the noisy channel. Belief propagation (BP) algorithm and its approximations, most notably min-sum, are popular iterative decoding algorithms used for LDPC and turbo codes. The trade-off between the hardware complexity and the decoding throughput is a critical factor in the implementation of the practical decoder. This article presents introduction to LDPC codes and its various decoding algorithms followed by realisation of LDPC decoder by using simplified message passing algorithm and partially parallel decoder architecture. Simplified message passing algorithm has been proposed for trade-off between low decoding complexity and decoder performance. It greatly reduces the routing and check node complexity of the decoder. Partially parallel decoder architecture possesses high speed and reduced complexity. The improved design of the decoder possesses a maximum symbol throughput of 92.95 Mbps and a maximum of 18 decoding iterations. The article presents implementation of 9216 bits, rate-1/2, (3, 6) LDPC decoder on Xilinx XC3D3400A device from Spartan-3A DSP family.     

Rate-compatible puncturing of low-density parity-check codes

In this correspondence, we consider puncturing of low-density parity-check (LDPC) codes for additive white Gaussian noise (AWGN) channels. We show that good puncturing patterns exist and that the puncturing can be performed in a rate-compatible fashion. Furthermore, rate-compatible puncturing results in a small loss of performance with respect to threshold, namely, the punctured code is good (in terms of threshold) across a range of rates when compared with the optimal codes for each rate. This allows one to implement a single "mother" encoder and decoder that is good across a wide range of rates.     

Efficient Puncturing Method for Rate-Compatible Low-Density Parity-Check Codes

In this paper, we propose an efficient puncturing method for LDPC codes. The proposed algorithm provides the order of variable nodes for puncturing based on the proposed cost function. The proposed cost function tries to maximize the minimum reliability among those provided from all check nodes. Also, it tries to allocate survived check nodes evenly to all punctured variable nodes. Furthermore, the proposed algorithm prevents the formation of a stopping set from the punctured variable nodes even when the amount of puncturing is quite large. Simulation results show that the proposed punctured LDPC codes perform better than existing punctured LDPC codes.     

Properties of optimum binary message-passing decoders

We consider a class of message-passing decoders for low-density parity-check (LDPC) codes whose messages are binary valued. We prove that if the channel is symmetric and all codewords are equally likely to be transmitted, an optimum decoding rule (in the sense of minimizing message error rate) should satisfy certain symmetry and isotropy conditions. Using this result, we prove that Gallager's Algorithm B achieves the optimum decoding threshold among all binary message-passing decoding algorithms for regular codes. For irregular codes, we argue that when the nodes of the message-passing decoder do not exploit knowledge of their decoding neighborhood, optimality of Gallager's Algorithm B is preserved. We also consider the problem of designing irregular LDPC codes and find a bound on the achievable rates with Gallager's Algorithm B. Using this bound, we study the case of low error-rate channels and analytically find good degree distributions for them.     

Analysis of sum-product decoding of low-density parity-check codesusing a Gaussian approximation

Density evolution is an algorithm for computing the capacity of low-density parity-check (LDPC) codes under message-passing decoding. For memoryless binary-input continuous-output additive white Gaussian noise (AWGN) channels and sum-product decoders, we use a Gaussian approximation for message densities under density evolution to simplify the analysis of the decoding algorithm. We convert the infinite-dimensional problem of iteratively calculating message densities, which is needed to find the exact threshold, to a one-dimensional problem of updating the means of the Gaussian densities. This simplification not only allows us to calculate the threshold quickly and to understand the behavior of the decoder better, but also makes it easier to design good irregular LDPC codes for AWGN channels. For various regular LDPC codes we have examined, thresholds can be estimated within 0.1 dB of the exact value. For rates between 0.5 and 0.9, codes designed using the Gaussian approximation perform within 0.02 dB of the best performing codes found so far by using density evolution when the maximum variable degree is 10. We show that by using the Gaussian approximation, we can visualize the sum-product decoding algorithm. We also show that the optimization of degree distributions can be understood and done graphically using the visualization     

Capacity Achieving LDPC Codes Through Puncturing

The performance of punctured low-definition parity-check (LDPC) codes under maximum-likelihood (ML) decoding is studied in this correspondence via deriving and analyzing their average weight distributions (AWDs) and the corresponding asymptotic growth rate of the AWDs. In particular, it is proved that capacity-achieving codes of any rate and for any memoryless binary-input output-symmetric (MBIOS) channel under ML decoding can be constructed by puncturing some original LDPC code with small enough rate. Moreover, it is shown that the gap to capacity of all the punctured codes can be the same as the original code with a small enough rate. Conditions under which puncturing results in no rate loss with asymptotically high probability are also given in the process. These results show high potential for puncturing to be used in designing capacity-achieving codes, and in rate-compatible coding under any MBIOS channel.      

Design methods for irregular repeat-accumulate codes

We optimize the random-like ensemble of irregular repeat-accumulate (IRA) codes for binary-input symmetric channels in the large block-length limit. Our optimization technique is based on approximating the evolution of the densities (DE) of the messages exchanged by the belief-propagation (BP) message-passing decoder by a one-dimensional dynamical system. In this way, the code ensemble optimization can be solved by linear programming. We propose four such DE approximation methods, and compare the performance of the obtained code ensembles over the binary-symmetric channel (BSC) and the binary-antipodal input additive white Gaussian noise channel (BIAWGNC). Our results clearly identify the best among the proposed methods and show that the IRA codes obtained by these methods are competitive with respect to the best known irregular low-density parity-check (LDPC) codes. In view of this and the very simple encoding structure of IRA codes, they emerge as attractive design choices.     

Results on Punctured Low-Density Parity-Check Codes and Improved Iterative Decoding Techniques

This paper first introduces an improved decoding algorithm for low-density parity-check (LDPC) codes over binary-input-output-symmetric memoryless channels. Then some fundamental properties of punctured LDPC codes are presented. It is proved that for any ensemble of LDPC codes, there exists a puncturing threshold. It is then proved that for any rates R₁ and R₂ satisfying 012<1, there exists an ensemble of LDPC codes with the following property. The ensemble can be punctured from rate R₁ to R₂ resulting in asymptotically good codes for all rates R₁lesRlesR₂. Specifically, this implies that rates arbitrarily close to one are achievable via puncturing. Bounds on the performance of punctured LDPC codes are also presented. It is also shown that punctured LDPC codes are as good as ordinary LDPC codes. For BEC and arbitrary positive numbers R₁2<1, the existence of the sequences of punctured LDPC codes that are capacity-achieving for all rates R₁ lesRlesR₂ is shown. Based on the above observations, a method is proposed to design good punctured LDPC codes over a broad range of rates. Finally, it is shown that the results of this paper may be used for the proof of the existence of the capacity-achieving LDPC codes over binary-input-output-symmetric memoryless channels