Challenges in bit-pattered magnetic recording (BPMR) include two-dimensional (2D) inter-symbol interference (ISI) constituted by both one-dimensional ISI and inter-track interference (ITI), and media noise arising from island position jitter (PJ) and island size fluctuations (SF) in both the down-track and cross-track directions. A LDPC code optimization approach is proposed for BPMR channel with media noise, where a reduced-complexity 2D detector based on the iterative row-column soft detection feedback with Gaussian approximation (IRCSDF-GA) detector is employed. Also, the threshold of the proposed LDPC codes is calculated for different percentage of media noise in BPMR. Simulations results show that about 0.3 dB performance gain can be achieved when BPMR is only suffered from the PJ.