Signal Processing for Near 10 Tbit/in$^{2}$ Density in Two-Dimensional Magnetic Recording (TDMR)

Two-dimensional magnetic recording (TDMR) is a new magnetic recording paradigm that aims to record one bit of information in one or a few grains, with the goal of achieving a recording density of nearly 10 Tbit/in$^{2}$. In addition to the usual noise, a TDMR channel experiences the problem that some bits are never recorded because of the randomness of grain size and location. Thus, it is believed that a key component of a TDMR channel is two-dimensional (2-D) signal processing along with a strong error correction code. In this study, the TDMR channel is investigated based on a random Voronoi grain model and a signal processing architecture is proposed. Here, a 2-D linear minimum mean squared error (LMMSE) equalizer and a low-density parity-check (LDPC) code are employed and the effects of unwritten bits are modeled by a Gaussian mixture model. In numerical simulations, the proposed architecture shows the feasibility of user bit densities near 10 Tbit/in$^{2}$ for media with a 20 ${\rm Tgrains/in}^{2}$ grain density.