用于 LDPC 码快速译码的改进多比特翻转算法简

为了提高RRWBF算法的译码速度,提出一种多比特翻转机制来加快RRWBF算法的收敛速度。但是,使用该多比特翻转机制的RRWBF算法时,译码过程中出现与单比特翻转类似的循环翻转现象,影响其译码性能。为此,进一步提出一种循环翻转消除机制来破坏多比特翻转译码过程中产生的循环翻转,进而提高其译码性能。仿真结果显示,与单比特翻转算法相比,提出的基于循环翻转消除的多比特RRWBF算法以较小的译码性能损失换来译码速度的较大提升。     

基于多/单比特切换机制的LDPC码两级WBF算法

为了提高低密度奇偶校验(LDPC)码的加权比特翻转(WBF)译码算法的译码速度和性能,文章提出了一种具有多/单比特切换机制的两级WBF译码算法.译码首先在第一级解码器中进行多比特翻转译码,当发现循环翻转或最大翻转函数值小于零时,跳到第二级解码器中进行单比特翻转继续译码,从而消除多比特的循环翻转和实现多比特向单比特译码的...     

逼近最小和译码性能的并行多比特翻转译码算法研究

相比于最小和译码算法,LDPC码的另外一种译码算法——比特翻转译码算法实现更简单,但其性能有较大恶化。最近提出的有噪梯度下降比特翻转译码（NGDBF）算法性能相比简单的比特翻转算法性能有明显提高,但该算法一次翻转一个比特限制了其应用。结合并行加权比特翻转译码（PWBF）中翻转标记的思想,本文提出了一种NGDBF译码的改进算法——并行NGDBF译码及其自适应形式,克服了PWBF译码对行重/列重较小的LDPC码性能不佳的缺陷。仿真表明:并行NGDBF译码的性能优于相应的NGDBF译码,其自适应形式不仅性能逼近最小和译码,而且实现简单。      

LDPC码的改进迭代比特翻转译码算法

为提高低密度奇偶校验(LDPC)码的低复杂度硬判决译码算法的性能,提出了一种改进的比特翻转(BF)译码算法,在迭代时利用一个交替的门限模式对多个比特进行翻转,降低了每次迭代时比特被错误翻转的概率,从而有效提高了译码性能.仿真结果表明,与BF算法相比,该算法在保持低复杂度的基础上获得了更好的译码性能和更快的收敛速度.     

动态扰动辅助的串行抵消双比特翻转Polar译码算法

针对串行抵消翻转译码算法（Successive Cancellation Flip,SCF）受限于单比特翻转而性能提升有限问题,提出了一种双比特翻转译码算法（Successive Cancellation Flip with 2 Bits,SCF2）。针对SCP算法扰动方差初始值固定的问题,设计了一种扰动方差可随码长和码率变化的改进SCP算法。在此基础上,结合翻转和扰动机制,提出了一种动态扰动辅助的串行抵消双比特翻转（Dynamic Perturbation-Aided SCF2,DPA-SCF2）译码算法,并对其译码复杂度和性能进行了分析。仿真结果显示,相比于列表长度为4的循环冗余校验辅助串行抵消列表（Cyclic Redundancy Check Aided Successive Cancellation List,CA-SCL）译码算法,所提算法最大可获得约0.5 dB的性能增益。     

基于分布式奇偶校验码的低复杂度极化码SCLF译码算法

针对极化码串行抵消列表比特翻转(Successive Cancellation List Bit-Flip, SCLF)译码算法复杂度较高的问题,提出一种基于分布式奇偶校验码的低复杂度极化码SCLF译码(SCLF Decoding Algorithm for Low-Complexity Polar Codes Based on Distributed Parity Check Codes, DPC-SCLF)算法。与仅采用循环冗余校验(Cyclic Redundancy Check, CRC)码校验的SCLF译码算法不同,该算法首先利用极化信道偏序关系构造关键集,然后采用分布式奇偶校验(Parity Check, PC)码与CRC码结合的方式对错误比特进行检验、识别和翻转,提高了翻转精度,减少了重译码次数。此外,在译码时利用路径剪枝操作,提高了正确路径的竞争力,改善了误码性能,且利用提前终止译码进程操作,减少了译码比特数。仿真结果表明,与D-Post-SCLF译码算法和RCS-SCLF译码算法相比,所提出算法具有更低的译码复杂度且在中高信噪比下具有更好的误码性能。     

LDPC码的一种高效加权比特翻转译码算法

针对低密度奇偶校验(LDPC)码中加权比特翻转(WBF)译码算法在迭代过程中绝大多数情况都是进行单比特翻转,导致译码效率低并且可能会发生比特翻转"死循环"的现象,提出一种更为高效的加权比特翻转(EWBF)算法.该算法对翻转阈值进行了改进,使得每次迭代能够翻转多个比特,提高译码效率,并且能够避免译码过程出现的翻转"死循环"现象.仿真结果表明,所提译码算法与WBF算法、改进的WBF(MWBF)算法和IMWBF(Improved MWBF)算法相比,平均迭代次数分别降低51.6%~56.2%、49.6%~54.2%和48.1%~51.3%;而在译码性能方面,算法性能接近甚至优于IMWBF算法,当最大迭代次数设定为30次时,相比于IMWBF算法,在误码率为10-4时可获得0.92 dB的增益.     

用于图像传输的改进的LDPC码译码算法

为了改善改进的加权比特翻转(IWBF)算法的误比特率性能以及译码收敛速度,结合并行比特翻转算法的特性,提出了在IWBF算法的每次迭代中一次更新多个比特的标准,并将这种算法应用于图像传输中。仿真结果表明,改进的算法不但误码性能优于IWBF算法约0.5 dB,性能明显改善,译码收敛速度也大大提高,并能实现图像的快速高质量传输。     

LDPC-CRC-极化码级联码及其比特翻转译码算法

级联的LDPC-极化码被用于提升有限长度下极化码的译码性能,尽管在置信传播译码器下获得很大的性能提升,仍与最先进的CA-SCL译码器有着明显的性能差距.针对该问题,提出一个改进的LDPC-极化码级联码比特翻转译码算法,在传统的联合因子图置信传播译码算法译码失败后,通过每次对一个易错的信息比特进行比特翻转,在给定的翻转次...     

准循环LDPC码的两种典型快速译码算法研究

该文从译码速率、硬件实现的复杂度和误码率3个方面对比研究了两种典型的高速译码算法:Turbo型和积算法与并行加权比特翻转算法。以准循环LDPC码为对象,给出了Turbo型和积算法和并行加权比特翻转算法的实现时序、硬件复杂度以及误码率性能,其中,并行加权比特翻转算法的高效时序结构是首次给出的。计算机仿真结果表明,这两种算法都能够在迭代次数较少时取得良好的性能。     

Two Bit-Flipping Decoding Algorithms for Low-Density Parity-Check Codes

In this letter, a low complexity decoding algorithm for binary linear block codes is applied to low-density paritycheck (LDPC) codes and improvements are described, namely an extension to soft-decision decoding and a loop detection mechanism. For soft decoding, only one real-valued addition per code symbol is needed, while the remaining operations are only binary as in the hard decision case. The decoding performance is considerably increased by the loop detection. Simulation results are used to compare the performance with other known decoding strategies for LDPC codes, with the result that the presented algorithms offer excellent performances at smaller complexity.     

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.     

Novel modified min-sum decoding algorithm for low-density parity-check codes

The problem of improving the performance of min-sum decoding of low-density parity-check(LDPC)codes is considered in this paper.Based on rain-sum algorithm,a novel modified min-sum decoding algorithm for LDPC codes is proposed.The proposed algorithm modifies the variable node message in the iteration process by averaging the new message and previous message if their signs are different.Compared with the standard min-sum algorithm,the modification is achieved with only a small increase in complexity,but significantly improves decoding performance for both regular and irregular LDPC codes.Simulation results show that the performance of our modified decoding algorithm is very close to that of the standard sum-produet algorithm for moderate length LDPC codes.     

对LDPC码的LLRBP算法研究

在LDPC译码时,使用IJLRBP算法其校验节点的计算复杂度十分高,而且当LDPC码中有许多的短环时,译码性能也会降低。基于以上的这些问题提出了一个新的混合校验变量过程,通过调整校验节点的处理振幅和变量节点的信息相关性来降低计算复杂度,其仿真过程表明在译码性能和运算复杂度上与LLRBP算法都有较大的提高。     

Parallel Weighted Bit-Flipping Decoding

A parallel weighted bit-flipping (PWBF) decoding algorithm for low-density parity-check (LDPC) codes is proposed. Compared to the best known serial weighted bit-flipping decoding, the PWBF decoding converges significantly faster but with little performance penalty. For decoding of finite-geometry LDPC codes, we demonstrate through examples that the proposed PWBF decoding converges in about 5 iterations with performance very close to that of the standard belief-propagation decoding.     

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。     

基于低密度校验码编码的MIMO系统方案

该文采用数值仿真的方法探讨了MIMO系统中采用低密度校验(LDPC)码作为信道编码后的系统性能,针对LDPC码的置信度传播译码算法,提出了基于因子图(Factor graph)的联合迭代检测译码最大后验概率(MAP)算法,分析比较了发射端分别采用独立编码和联合编码对系统性能的影响,仿真结果表明,LDPC码可以充分利用MIMO系统中空间分集和时间分集性能提高系统的有效分集增益,并且联合迭代检测译码算法对这两种发射端编码结构的系统性能增益有较大差别。     

基于原型图的低码率LDPC码最小和译码算法改进方案

低密度奇偶校验(LDPC)码的译码硬件实现方案大多采用计算复杂度较低的修正最小和(NMS)算法,然而对于低码率LDPC码,由于校验节点度数低,NMS算法的修正误差较大,导致其译码性能和标准的置信传播(BP)算法相比有较大差异。该文针对基于原图构造的一类低码率LDPC码,提出了在NMS迭代译码中结合震荡抵消(OSC)处理和多系数(MF)修正技术的方案。结合低码率原型图LDPC码行重分布差异较大的特点,MF修正算法可以有效地减少计算误差,从而改善译码性能。另外低码率原型图LDPC码的收敛较慢,而OSC处理则可以较好地抑制正反馈信息,进一步提高NMS算法的性能增益。仿真结果表明,对于此类低码率LDPC码, MF-OSC-NMS算法可以达到接近BP算法的性能。OSC处理和MF修正技术硬件实现简单,与NMS算法相比几乎没有增加计算复杂度,因此MF-OSC-NMS算法是译码算法复杂度和性能之间一个较好的折中处理方案。     

On decoding of low-density parity-check codes over the binary erasure channel

This paper investigates decoding of low-density parity-check (LDPC) codes over the binary erasure channel (BEC). We study the iterative and maximum-likelihood (ML) decoding of LDPC codes on this channel. We derive bounds on the ML decoding of LDPC codes on the BEC. We then present an improved decoding algorithm. The proposed algorithm has almost the same complexity as the standard iterative decoding. However, it has better performance. Simulations show that we can decrease the error rate by several orders of magnitude using the proposed algorithm. We also provide some graph-theoretic properties of different decoding algorithms of LDPC codes over the BEC which we think are useful to better understand the LDPC decoding methods, in particular, for finite-length codes.     

Iterative decoding of one-step majority logic deductible codesbased on belief propagation

Previously, the belief propagation (BP) algorithm has received a lot of attention in the coding community, mostly due to its near-optimum decoding for low-density parity check (LDPC) codes and its connection to turbo decoding. In this paper, we investigate the performance achieved by the BP algorithm for decoding one-step majority logic decodable (OSMLD) codes. The BP algorithm is expressed in terms of likelihood ratios rather than probabilities, as conventionally presented. The proposed algorithm fits better the decoding of OSMLD codes with respect to its numerical stability due to the fact that the weights of their check sums are often much higher than that of the corresponding LDPC codes. Although it has been believed that OSMLD codes are far inferior to LDPC codes, we show that for medium code lengths (say between 200-1000 bits), the BP decoding of OSMLD codes can significantly outperform BP decoding of their equivalent LDPC codes. The reasons for this behavior are elaborated