Doubly-generalized LDPC codes with SPC codes as super variable nodes

In this paper, we design and analyze three kinds of doubly-generalized low-density parity-check (D-GLDPC) codes. We employ single parity-check (SPC) codes as super variable nodes (SVNs) and two-dimensional (2-D) single parity-check product codes (SPC-PCs) as super check nodes (SCNs). Three kinds of different SPC codes as super variable nodes (SVNs) are used in the systematic (5) form, the cyclic (C) form and the anti-systematic (A) form. Because the minimum distance of SPC codes is 2, they can meet upper bound of D-GLDPC codes. The performance of the proposed D-GLDPC codes is investigated over the AWGN channel with the extrinsic information transfer (EXIT) charts. The SPC codes in different forms have an effect on stability bound of D-GLDPC codes and also make a difference in decoding threshold. Simulation results show that D-GLDPC codes with C-form SPC codes as SVNs have the best stability bound and the minimum decoding threshold, the second best is D-GLDPC codes with S-form SPC codes as SVNs, and the worse one is D-GLDPC codes with A-form SPC codes as SVNs.