In this letter, a method for the construction of polar codes based on the mutual information approximation (MIA) is proposed for the 4Tb/in2 two-dimensional inter-symbol interference (2D-ISI) channels, such as the bit-patterned magnetic recording (BPMR) and two-dimensional magnetic recording (TDMR). The basic idea is to exploit the MIA between the input and output of a 2D detector to establish a log-likelihood ratio (LLR) distribution model based on the MIA results, which compensates the gap caused by the 2D ISI channel. Consequently, the polar codes obtained by the optimization techniques previously developed for the additive white Gaussian noise (AWGN) channels can also have satisfactory performances over 2D-ISI channels. Simulated results show that the proposed polar codes can outperform the polar codes constructed by the traditional methods over 4Tb/in2 2D-ISI channels.

When the track density of two-dimensional magnetic recording (TDMR) systems is increased, intertrack interference (ITI) inevitably grows, resulting in the extreme degradation of an overall system performance. In this work, we present coding, writing, and reading techniques which allow TDMR systems with multi-readers to overcome severe ITI. A rate-5/6 two-dimensional (2D) modulation code is adopted to protect middle-track data from ITI based on cross-track data dependence. Since the rate-5/6 2D modulation code greatly improves the reliability of the middle-track, there is a bit-error rate gap between middle-track and sidetracks. Therefore, we propose the different track width writing technique to optimize the reliability of all three data tracks. In addition, we also evaluate the TDMR system performance using an user areal density capability (UADC) as a main key parameter. Here, an areal density capability (ADC) can be measured by finding the bit-error rate of the system with sweeping track and linear densities. The UADC is then obtained by removing redundancy from the ADC. Simulation results show that a system with our proposed techniques gains the UADC of about 4.66% over the conventional TDMR systems.