Zhu Kun, Yang Hongwen
School of Information and Communication, Beijing University of Posts and Telecommunications, Beijing 100876, China.
Sensors (Basel). 2022 Sep 27;22(19):7335. doi: 10.3390/s22197335.
By connecting multiple short, local low-density parity-check (LDPC) codes with a global parity check, the globally coupled (GC) LDPC code can attain high performances with low complexities. The typical design of a local code is a quasi-cyclic (QC) LDPC for which the code length is proportional to the size of circulant permutation matrix (CPM). The greatest common divisor (GCD)-based full-length row multiplier (FLRM) matrix is constrained by a lower bound of CPM size to avoid six length cycles. In this paper, we find a new lower bound for the CPM size and propose an algorithm to determine the minimum CPM size and the corresponding FLRM matrix. Based on the new lower bound, two methods are proposed to construct the GC-QC-LDPC code of grith 8 based on the GCD based FLRM matrix. With the proposed algorithm, the CPM size can be 45% less than that given by sufficient condition of girth 8. Compared with the conventional GC-LDPC construction, the codes constructed with the proposed method have improved performance and are more flexible in code length and code rate design.
通过将多个短的局部低密度奇偶校验（LDPC）码与全局奇偶校验相结合，全局耦合（GC）LDPC码能够以低复杂度实现高性能。局部码的典型设计是准循环（QC）LDPC码，其码长与循环置换矩阵（CPM）的大小成正比。基于最大公因数（GCD）的全长行乘法器（FLRM）矩阵受CPM大小下限的约束，以避免出现长度为6的循环。在本文中，我们找到了CPM大小的一个新下限，并提出了一种算法来确定最小CPM大小和相应的FLRM矩阵。基于新下限，提出了两种基于GCD的FLRM矩阵构造围长为8的GC-QC-LDPC码的方法。使用所提出的算法，CPM大小可比围长为8的充分条件所给出的大小减少45%。与传统的GC-LDPC构造相比，用所提出的方法构造的码具有更好的性能，并且在码长和码率设计上更灵活。
