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The feasibility of two-dimensional magnetic recording (TDMR) at 4 Tb/in2 customer areal-density is investigated via numerical simulations. In addition to the coding overhead needed to correct possible errors in a TDMR channel, the overhead required to obtain accurate position and timing estimates is taken into account in determining achievable customer density. The TDMR channel model used for this investigation is based on a random Voronoi granular medium, a two-dimensional (2-D) Gaussian read sensitivity function with random position and timing offsets and additive white Gaussian noise (AWGN). Read channel signal processing consists of a 2-D linear minimum mean square error (LMMSE) equalizer, a Gaussian mixture model (GMM) based log likelihood ratio (LLR) extractor and a low-density parity-check (LDPC) decoder. This work suggests that reliable performance may be achieved on media with 14 × 1012 grains/in2 by TDMR at a net customer areal-density of 0.29 bits per grain, including the overhead required for the LDPC code and the position and the timing fields.