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QC—LDPC码的普适Kronecker积-逐步边增加算法

李思佳, 毛玉泉, 曹祥玉, 裴鑫, 尹忠海

Published Jan 1, 2013• 0 citations
OpenAlex

Abstract

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。

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For a given base graph, the lifted graph can be obtained by a copy-and-permute procedure. If the permutation is cyclic, the lifted graph corresponds to a quasi-cyclic (QC) protograph low-density parity-check (LDPC) code. The girth of the QC protograph LDPC code is determined by the girth of the base graph and the permutation shifts. In this paper, we first derive a lower bound on the lifting degree to achieve a large girth lifted graph. Then, motivated by the cycle searching and girth maximizing features of the progressive edge-growth (PEG) algorithm, we introduce the permutation shifts determining (PSD) PEG algorithm, which can construct large girth base graph and determine the optimal permutation shifts, simultaneously. It is shown that the computational complexity of PSD-PEG algorithm is much lower than that of the PEG algorithm and the PEG-QC algorithm for the same codeword length. Furthermore, we show that the PSD-PEG algorithm can also be used to construct nonbinary QC protograph LDPC codes without low weight codes. Simulation results show that the binary and nonbinary QC protograph LDPC codes constructed by the PSD-PEG algorithm have good bit error rate performance and frame error rate performance over the additive white Gaussian noise channel.

IEEE Access•Jan 1, 2017•23 citations

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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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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.

Video Engineering•Jan 1, 2013•0 citations
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。
For a given base graph, the lifted graph can be obtained by a copy-and-permute procedure. If the permutation is cyclic, the lifted graph corresponds to a quasi-cyclic (QC) protograph low-density parity-check (LDPC) code. The girth of the QC protograph LDPC code is determined by the girth of the base graph and the permutation shifts. In this paper, we first derive a lower bound on the lifting degree to achieve a large girth lifted graph. Then, motivated by the cycle searching and girth maximizing features of the progressive edge-growth (PEG) algorithm, we introduce the permutation shifts determining (PSD) PEG algorithm, which can construct large girth base graph and determine the optimal permutation shifts, simultaneously. It is shown that the computational complexity of PSD-PEG algorithm is much lower than that of the PEG algorithm and the PEG-QC algorithm for the same codeword length. Furthermore, we show that the PSD-PEG algorithm can also be used to construct nonbinary QC protograph LDPC codes without low weight codes. Simulation results show that the binary and nonbinary QC protograph LDPC codes constructed by the PSD-PEG algorithm have good bit error rate performance and frame error rate performance over the additive white Gaussian noise channel.
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。
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。
The Progressive edge-growth (PEG) algorithm was proven to be a simple and effective approach in designing Low-density parity-check (LDPC) codes. However, the Tanner graph constructed with the PEG algorithm is non-structured, which leads to random distributions of the positions of 1's in the corresponding parity-check matrix. In this paper, an improved algorithm based on the PEG algorithm for constructing quasi-cyclic (QC) LDPC codes is proposed. The proposed algorithm can eliminate short cycles efficiently and gain low error-floors. What is more important, the proposed QC-LDPC codes construction method is hardware-friendly because of its quasi-cyclic structure. Our simulation results demonstrate that the codes constructed with the proposed algorithm has better performance than the PEG algorithm over the additive white Gaussian noise (AWGN) channel and Rayleigh flat fading channel.
围长（girth）较大的Qc-LDPC码，由于译码性能优良而且便于硬件实现，因此目前已经成为国际信道编码领域的一个研究热点。最近，J—WZhang在第四届多媒体信息网络与安全国际会议上提出了一种构造girth-8（3，L）QC-LDPC码的新方案，但是没有对围长特性和分块矩阵尺寸取值进行理论分析和论证。利用等价变换和最大公约数体系，本文得到了该方案的围长特性和分块矩阵尺寸取值的精确理论结果。此外，还利用最大公约数体系对该方案进行了扩展，得到一种新的围长为8的QC—LDPC码。新码的参数选取范围包含很多原方案不适用的参数选择范围。仿真结果说明，新码在和积译码算法下具有较优良的译码性能。
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.