Bit-patterned media recording (BPMR), heat (or microwave) assisted magnetic recording (HAMR) and shingled writing (SW)/two-dimensional magnetic recording (TDMR) have been primed to further increase the areal density of magnetic recording beyond 1Tb/in2[1-3]. However, with the reduction of the track pitch, inter-track interference (ITI) becomes a major impairment for these magnetic recording systems. ITI combined with the conventional (down-track) inter-symbol interference (ISI) forms a two-dimensional (2D) interference that severely degrades the performance of data detection in these systems.