Abstract
As a general framework, partial geometries play an important role in constructing good low-density parity-check (LDPC) codes with low error-floors. Partial geometries from row–column constrained (RC-constrained) arrays of circulant permutation matrices (CPMs) have been determined by Q. Diao et al. In this paper, we study partial geometries from RC-constrained matrices based on group divisible designs (GDDs). From the combinational design perspective, it is shown that the existence of two classes of partial geometries is equivalent to the existence of balanced incomplete block designs (BIBDs) and transversal design (TDs), respectively. Therefore, relevant constructions of BIBDs and TDs are presented. Furthermore, we present a method for constructing LDPC codes with flexible code rate and length parameters by employing the resolvability of GDDs. Numerical results show that the proposed LDPC codes have good performance under iterative decoding over the additive white Gaussian noise (AWGN) channel.
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