几类QC-LDPC码的构造设计

发布时间：2018-04-30 15:24

  本文选题：QC-LDPC码 + 序列构造　； 参考：《扬州大学》2017年硕士论文

【摘要】：随着信息技术的高速发展,人们对信息传输的要求越来越高,推动着现代编码理论的研究。作为一类具有逼近Shannon极限性质的优异码,低密度奇偶校验(LDPC)码近二十年来一直是信道编码研究的热点,在诸多领域发挥着不可替代的作用。LDPC码是一类特殊的线性分组码,其校验矩阵具有稀疏性,因而有优良的译码性能。其研究方向包括校验矩阵的构造、编译码算法的优化以及性能分析。准循环低密度奇偶校验(QC-LDPC)码作为一类重要的LDPC码,校验矩阵具有准循环性,不需要占用大量的存储空间,编译码复杂度较低,因此对信道编码研究有重要意义。论文主要给出了两大类QC-LDPC码的校验矩阵构造方式。第一类源自范德蒙德矩阵,以一个给定序列为基础,先构造出相应的母矩阵,之后用循环置换矩阵扩张构造出围长最小为6的校验矩阵,得到QC-LDPC码。随后对矩阵元素进行降幂处理,得到码长更加灵活方便的校验矩阵,同时去除了其中长度为6的环。最后在保证扩张矩阵阶数较小的情况下给出逐步最小值算法,还将计算结果与Fossorier在2004年给出的构造进行比较。在行数为2和行、列数均为3情况下,得到的扩张矩阵阶数较小。行数为3,列数为7或8两者相同。在母矩阵较小的情况下,利用我们提出的算法得到的扩张矩阵阶数接近Fossorier用计算机穷举搜索得到的极限值。第二类基于前人对欧氏几何(EG)LDPC码的研究,为提高校验矩阵围长提供了一种新颖的方法。将长度为6的环的存在条件与欧式几何结合,在避免欧式几何中出现三个点两两相连的基础上,给出两种围长至少为8的EG-LDPC码,(6,9,2,3)码与(8,12,2,4)码。随后将一种长度为8的环的不存在条件与欧式几何结合,在欧式几何中避免出现四个点首尾相连且固定行重与列重小于4,给出一种围长至少为10的EG-LDPC码,(8,12,2,3)码。最后经循环置换矩阵扩展,得到对应码长的QC-LDPC码。同目前对EG-LDPC已有研究相比,此类方法为构造高围长校验矩阵提供一种简单有效的方法。最后用比特翻转算法对第一类逐步最小值算法构造的QC-LDPC码和第二类围长至少为8的QC-LDPC码进行仿真分析。仿真结果表明,两类QC-LDPC码均具有良好的译码性能。
[Abstract]:With the rapid development of information technology, the demand for information transmission is becoming higher and higher, which promotes the research of modern coding theory. As a class of excellent codes with approximation to the limit of Shannon, low density parity check (LDPC) code has been a hot spot in the research of channel coding for nearly twenty years, and plays an irreplaceable role in many fields,.L DPC code is a special class of linear block codes. The check matrix has sparsity, so it has excellent decoding performance. The research direction includes the construction of the check matrix, the optimization of the coding and decoding algorithm and the performance analysis. The quasi cyclic low density parity check (QC-LDPC) code is a class of heavy required LDPC codes, and the check matrix is quasi cyclic and does not need to be used. Taking up a large amount of storage space and low compiling and coding complexity, it is of great significance to study the channel coding. This paper mainly gives the construction methods of the check matrix of two kinds of QC-LDPC codes. The first class is derived from the Van Redmond matrix, based on a given sequence, the corresponding matrix is constructed first, and then the construction of the matrix is constructed by cyclic substitution matrix. The QC-LDPC code is obtained with the minimum circumference of 6. Then the matrix element is reduced to a more flexible and convenient checksum matrix, and a ring with a length of 6 is removed. Finally, a gradual minimum value algorithm is given under the condition that the order of the expansion matrix is small, and the calculation results are given in 2004. The construction is compared. With the row number 2 and the row, and the row number is 3, the order of the expansion matrix is smaller. The number of rows is 3, the number of columns is 7 or 8. In the case of the smaller mother matrix, the order of the expansion matrix obtained by the algorithm proposed by us is close to the limit value of the Fossorier calculation machine. The second classes are based on the limit value. Previous studies on Euclidean geometry (EG) LDPC code provide a novel method for improving the length of check matrix. Combining the existence condition of the ring with the length of 6 and the Euclidean geometry, on the basis of avoiding the appearance of three points and 22 connections in the Euclidean geometry, two kinds of EG-LDPC codes, (6,9,2,3) codes and (8,12,2,4) codes are given, and then the (6,9,2,3) code and (8,12,2,4) codes are given. The non existence condition of a ring with a length of 8 is combined with the Euclidean geometry. In the Euclidean geometry, four points are avoided and the fixed row weight and the column weight are less than 4. A EG-LDPC code, (8,12,2,3) code with a peri length of at least 10, is given. Finally, the QC-LDPC code of the corresponding code length is obtained by the extension of the cyclic permutation matrix. In comparison, this method provides a simple and effective method for constructing the high peri length parity check matrix. Finally, the bit flipping algorithm is used to simulate the QC-LDPC code of the first class step minimum value algorithm and the second class of QC-LDPC codes with a circumference of at least 8. The simulation results show that the two classes of QC-LDPC codes have good decoding performance.

【学位授予单位】：扬州大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O157.4
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本文编号：1825092