Non-Binary Protograph-Based LDPC Codes for 2-D-ISI Magnetic Recording Channels

2-D inter-symbol-interference (2-D-ISI), consisting of ISI in the down track direction and inter-track interference along the cross-track direction, is a major factor that severely degrades the performance of ultra-high density magnetic recording systems. Due to its superior performance and the protograph structure which facilitates high-speed encoding and decoding, the protograph codes have shown a high potential to tackle 2-D-ISI. However, so far, no work has been reported on the design of non-binary protograph-based low-density parity-check (NP-LDPC) codes for 2-D-ISI channels. In this paper, we first propose a modified protograph extrinsic information transfer analysis. In conjunction with the asymptotic ensemble weight distribution analysis, they both serve as theoretical tools to analyze the performance of NP-LDPC codes designed for the 2-D-ISI channels. By further applying a fast search approach, we construct two types of NP-LDPC codes for 2-D-ISI channels. Both theoretical analyses and simulated results show that the proposed codes outperform the existing binary LDPC codes that optimized for 2-D-ISI channels as well as the non-binary quasi-cyclic LDPC code, at both low and high SNR regions.