D-GLDPC codes with 3-D single parity-check product codes as super check nodes

A doubly-generalized low-density parity-check (D-GLDPC) code is a low-density parity-check (LDPC) code, where both of the check nodes and variable nodes use linear block codes instead of repetition and single parity-check (SPC) codes. In this paper, we propose a class of D-GLDPC codes in which 3-dimensional (3-D) single parity-check product-codes (SPC-PCs) are used as super-check nodes (SCNs). We derive the extrinsic information transfer (EXIT) function of 3-D SPC-PCs used as SCNs, and analyze the performance of the proposed D-GLDPC codes over the additive white Gaussian noise (AWGN) channel with EXIT charts. Numerical analysis from EXIT charts shows that our proposed D-GLDPC codes can offer better decoding threshold than D-GLDPC codes with 2-D SPC-PCs as SCNs.