Protograph based quasi-cyclic LDPC coding for ultra-high density magnetic recording channels

In this paper, protograph-based quasi-cyclic (QC) low-density parity-check (LDPC) codes are proposed for the efficient structure coding of LDPC codes in 2-D intersymbol interference (ISI) ultrahigh density magnetic recording channels, such as bit-patterned magnetic recording and 2-D magnetic recording, where a reduced-complexity 2-D detector based on the iterative row–column soft detection feedback with Gaussian approximation is employed instead of the full 2-D Bahl–Cocke–Jelinek–Raviv detector. The proposed protograph-based codes, whose base matrices are constructed according to the degree sequences for 2-D-ISI channels, have a low-complexity QC encoder structure with a readily parallelizable protograph decoder structure. Simulation results show that the proposed protograph-based QC-LDPC codes outperform the random LDPC codes optimized for additive white Gaussian noise channels. Furthermore, the performance of the QC codes is similar to that exhibited by ISI-optimized random LDPC codes designed for 2-D-ISI channels, while retaining the implementational benefits.