Counting short cycles of QC‐LDPC codes in base graph

Abstract

AbstractThe performance of quasi‐cyclic low‐density parity‐check codes is closely tied to the number of short cycles. Here, a method is proposed to accurately count short cycles within the base matrix. By searching for all distinct and non‐redundant cyclic paths and combining the number of cycles from each path, the total number of short cycles is obtained. These results demonstrate that the complexity of our algorithm is independent of the code length and directly proportional to the number of edges in the base graph. Moreover, as the lifting degree of the codes increases, the proposed algorithm achieves faster cycle counting.