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电视技术

基于PC-PEG算法构造的QC-LDPC码性能研究

杨张, 袁梅冷, 雷海军

Published Jan 1, 2013• 0 citations
OpenAlex

Abstract

针对PEG(Progressive EdgeGrowth)算法构造的LDPC码在保证局部围长最大时仍有较多数目的小环,提出利用PC(Polynomial of Cycle)标记将PEG算法进行改进为PC-PEG算法,并应用于准循环码(QC-LDPC)中。该方法在满足局部围长尽可能大的前提下,减少了小环数目,提高了译码性能。引入QC-LDPC码的特性,其中校验矩阵是一种分块的循环移位码,该特定结构在工程上可以实现部分并行译码,节省存储空间。实验结果表明,该方法与PEG算法相比具有较少的小环数目,而准循环结构的特点在保证译码性能相当的前提下实现了工程上的部分并行译码。

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构造围长较大的校验矩阵,是提高二进制和多进制QC-LDPC码译码性能的一种有效手段.本文提出一种不需要借助于任何计算机搜索步骤,能够直接构造出围长至少为8的QC-LDPC码的显式构造框架.该框架所构造的QC-LDPC码不仅满足围长至少为8的条件,而且还具有循环置换矩阵(CPM)尺寸可以连续变化的优点.该框架可以分为两个步骤:第一步是在无穷大CPM尺寸条件下利用确定性方法构造一个围长至少为8的校验矩阵;第二步是根据本文新发现的一个围长性质,从该校验矩阵的移位矩阵直接精确地计算出CPM尺寸连续变化的紧致下界.

Dianzi xuebao•Jan 1, 2012•0 citations
针对PEG(Progressive EdgeGrowth)算法构造的LDPC码在保证局部围长最大时仍有较多数目的小环,提出利用PC(Polynomial of Cycle)标记将PEG算法进行改进为PC-PEG算法,并应用于准循环码(QC-LDPC)中。该方法在满足局部围长尽可能大的前提下,减少了小环数目,提高了译码性能。引入QC-LDPC码的特性,其中校验矩阵是一种分块的循环移位码,该特定结构在工程上可以实现部分并行译码,节省存储空间。实验结果表明,该方法与PEG算法相比具有较少的小环数目,而准循环结构的特点在保证译码性能相当的前提下实现了工程上的部分并行译码。
针对高码率的准循环低密度奇偶校验码(QC—LDPC)提出了一种新的高效的log-BP部分并行译码结构,它通过矩阵分裂,将原监督矩阵分裂成多个小的矩阵,使原本的校验节点更新运算被拆分成多次处理,有效地降低了BP迭代运算的复杂度;通过组织不同小矩阵校验节点更新运算与变量节点更新运算的先后顺序,可以使不同小矩阵的校验节点更新运算与变量节点更新运算同时进行,从而提高译码器的译码速率。该方法既适用于非规则码,也适用于规则码。实验结果表明,与现有的log—BP译码方法相比,在相同的码速率下,校验节点更新单元(CNU)与变量节点更新单元(VNU)规模总量减小1/3;在相同的硬件资源下,译码速率提高1/3,另外该方法使CNU与VNu结构趋于对称,有利于设置更少的流水线级数,获得更好的时钟性能。
Since LDPC code based on progressive edge growth(PEG) algorithm construction still has many small cycles in the case of maximization of local girth,make use of polynomial cycle(PC) mark to improve PEG algorithm to be enhanced PC-PEG algorithm is proposed in this paper,and it is applied in QC-LDPC.This approach can reduce the number of small circles and improve the performance under the maximization of local girth.By using of QC-LDPC,the parity check matrix is still block based cyclic shift code,this special structure can realize parallel decoding in the engineering and save the storage memory.The experimental results demonstrate that the proposed method has smaller number of girth compared with PEG algorithm,and the special structure of cyclic shift ensures parallel decoding with the same decoding performance.
为了扩展QC—LDPC码的逐步边增加(Progressivee dge—growth,PEG)算法,在分析Kronecker积和PEG基本算法的基础上,结合校验矩阵节点的度分布要求,提出了一种QC—LDPC码的Kronecker积一PEG普适算法。该算法通过引入Kronecker积实现基矩阵的构造,同时确定循环移位矩阵,进一步根据变量节点和校验节点的度分布要求完成了QC-LDPC码的设计,分析并证明了该算法的环长至少为girth-8。对算法性能进行了仿真验证,结果表明,该算法在保持QC—LDPC码低密度特征和良好误码性能的同时具有普适性。
A modified construction method of LDPC (Low-density Parity-check) codes based on polynomial of cycles of PEG (Progressive-Edge-Growth) is proposed according to reaction on the performance of LDPC codes by polynomial of cycles based on PEG and connectivity of cycles. It can reduce the number of the shortest cycles, increase average local girth and improve connectivity of cycles while deleting short cycles by considering girth of check matrix, number of the shortest cycles and ACE (Approximate Cycle EMD), so that it can improve performance of decoding. At the same time, a construction method of QC-LDPC (quasi-cyclic-LDPC) codes based on ACE and polynomial of cycles of PEG is also proposed to deal with the complexity of implementation on hardware of unstructured codes. Simulation results show that the performance of this code is better than unstructured Mackay code and it is easier for implementation on hardware.
本文研究了准循环LDPC码的一致校验矩阵与其对应Tanner图环结构之间的关系,将局部平均围长优化算法引入优化构造算法中,提出了一种基于PEG算法的准循环扩展LDPC码构造的改进算法。在改进算法中,首先利用PEG算法产生基矩阵,然后基于平均围长最大准则选择循环移位置换矩阵对基矩阵进行准循环扩展,通过围长分布的优化,从而改善了迭代译码的性能。仿真结果表明,在码长相同、码率和度分布近似情况下,与文献[7]中基于PEG算法的准循环扩展构造的码字比较,改进算法构造的码字能够获得更加优异的性能。
构造围长较大的校验矩阵,是提高二进制和多进制QC-LDPC码译码性能的一种有效手段.本文提出一种不需要借助于任何计算机搜索步骤,能够直接构造出围长至少为8的QC-LDPC码的显式构造框架.该框架所构造的QC-LDPC码不仅满足围长至少为8的条件,而且还具有循环置换矩阵(CPM)尺寸可以连续变化的优点.该框架可以分为两个步骤:第一步是在无穷大CPM尺寸条件下利用确定性方法构造一个围长至少为8的校验矩阵;第二步是根据本文新发现的一个围长性质,从该校验矩阵的移位矩阵直接精确地计算出CPM尺寸连续变化的紧致下界.