EXIT-Chart-Based LDPC Code Design for 2D ISI Channels

Abstract

In this paper, optimization of low-density parity-check (LDPC) codes to approach the symmetric information rate (SIR) of two-dimensional (2-D) intersymbol interference (ISI) channels is proposed for high-density magnetic recording, such as bit-patterned magnetic recording (BPMR) and 2-D magnetic recording (TDMR). The code design makes use of the modified Extrinsic Information Transfer (EXIT) chart, where the optimal variable node degree is searched by selecting the best check node degree to fit the check node decoder (CND) EXIT curve to the EXIT curve of the variable node decoder (VND) curve combined with 2-D detector. Simulation results show that LDPC codes with code length 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> bits optimized for a 2-D ISI channel corresponding to 4 Tb/in <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> recording density can achieve bit error rate 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> at signal-to-noise ratio 0.33 dB away from the SIR. To our knowledge, this is the first capacity-approaching LDPC code successfully optimized for a 2-D ISI channel.