Finite-length extrinsic information transfer analysis and design of protograph lowdensity parity-check codes for ultra-highdensity magnetic recording channels

The authors study the performance of protograph low-density parity-check (LDPC) codes over two-dimensional (2D) intersymbol interference (ISI) channels in this study. To begin with, the authors propose a modified version of finitelength (FL) extrinsic information transfer (EXIT) algorithm so as to facilitate the convergence analysis of protograph codes. Exploiting the FL-EXIT analyses, the authors observe that the protograph codes optimised for 1D ISI channels, e.g. the 1DISI protograph code, cannot maintain their advantages in the 2D-ISI scenarios. To address this problem, the authors develop a simple design scheme for constructing a family of rate-compatible improved protograph (RCIP) codes particularly for 2D-ISI channels, which not only outperform the 1D-ISI protograph code, but also are superior to the regular column-weight-3 code and optimised irregular LDPC codes in terms of the convergence speed and error performance. More importantly, such RCIP codes benefit from relatively lower error-floor as well as linear encoding and fast decoding. Thanks to these advantages, the proposed RCIP codes stand out as better alternatives in comparison with other error-correction codes for ultra-high-density data storage systems.