Construction of Quasi‐Cyclic LDPC Codes Based on Fundamental Theorem of Arithmetic

Quasi‐cyclic (QC) LDPC codes play an important role in 5G communications and have been chosen as the standard codes for 5Genhanced mobile broadband(eMBB) data channel. In this paper, we study the construction of QC LDPC codes based on an arbitrary given expansion factor (or lifting degree). First, we analyze the cycle structure of QC LDPC codes and give the necessary and sufficient condition for the existence of short cycles. Based on the fundamental theorem of arithmetic in number theory, we divide the integer factorization into three cases and present three classes of QC LDPC codes accordingly. Furthermore, a general construction method of QC LDPC codes with girth of at least 6 is proposed. Numerical results show that the constructed QC LDPC codes perform well over the AWGN channel when decoded with the iterative algorithms.