Efficient construction and encoding of QC-LDPC codes by cyclic lifting of protographs  

基于原型图循环提升的高效QC-LDPC码构造和编码(英文)

作　　者：梁原[1] 张树林[1] 顾品标[1] 吴乐南[1] 

机构地区：[1]东南大学信息科学与工程学院,南京210096

出　　处：《Journal of Southeast University(English Edition)》2015年第1期25-30,共6页东南大学学报（英文版）

基　　金：The National Key Technology R&D Program of China during the 12th Five-Year Plan Period(No.2012BAH15B00)

摘　　要：Quasi-cyclic low-density parity-check （QC-LDPC） codes can be constructed conveniently by cyclic lifting of protographs. For the purpose of eliminating short cycles in the Tanner graph to guarantee performance, first an algorithm to enumerate the harmful short cycles in the protograph is designed, and then a greedy algorithm is proposed to assign proper permutation shifts to the circulant permutation submatrices in the parity check matrix after lifting. Compared with the existing deterministic edge swapping （DES） algorithms, the proposed greedy algorithm adds more constraints in the assignment of permutation shifts to improve performance. Simulation results verify that it outperforms DES in reducing short cycles. In addition, it is proved that the parity check matrices of the cyclic lifted QC-LDPC codes can be transformed into block lower triangular ones when the lifting factor is a power of 2. Utilizing this property, the QC- LDPC codes can be encoded by preprocessing the base matrices, which reduces the encoding complexity to a large extent.通过原型图的循环提升可方便地构造准循环低密度奇偶校验(QC-LDPC)码.为了保证QC-LDPC码的性能,消除Tanner图中的短环,首先设计一种算法用于找出原型图中的有害短环,然后提出一种贪婪算法用于对提升后的校验矩阵中的单位循环位移子阵分配适合的循环位移量.与已有的DES算法相比,所提出的贪婪算法在分配循环位移量时施加了更多的限制条件来提升性能,仿真结果表明它比DES算法能消除更多的短环.当提升因子为2的整数次幂时,证明了所得QC-LDPC码的校验阵可转化成分块下三角阵的形式.利用该性质,由原型图循环提升得到的QC-LDPC码仅需对基矩阵做预处理就可以实现编码,极大地降低了QC-LDPC码的编码复杂度.

关 键 词：low-density parity-check （LDPC） codes quasi-cyclic LDPC codes cyclic lifting protograph LDPC codes 

分 类 号：TN911.21[电子电信—通信与信息系统]