On Disjoint Difference Sets and Their Associated QC-LDPC Codes with Large Girth

The disjoint difference set (DDS) has been utilized in recent years to construct quasi-cyclic (QC) low-density parity-check (LDPC) codes without small cycles. However, the existing DDS-based QC-LDPC codes have no all-zero circulants, which limits the decoding performance of such codes to some extent. In this paper, two new types of DDS-based QC-LDPC codes are proposed, which contain all-zero circulants and possess girth at least eight and girth at least ten, respectively. Numerical simulations show that the new codes have good performance in AWGN channels. Besides, a new result on existence for DDSs and two novel deterministic constructions for DDSs are put forward.