  In the present paper, a simplified two-dimensional magnetic recording (TDMR)
channel model is proposed in order to capture the qualitative features of
writing and read-back processes of TDMR systems.The proposed channel model
incorporates the effects of both linear interference from adjacent bit-cells
and signal-dependent noise due to irregular grain boundaries between adjacent
bit-cells. The simplicity of the proposed model enables us to derive the closed
form of the conditional PDF representing the probabilistic nature of the
channel. The conditional PDF is Gaussian distributed and is parameterized by a
signal-dependent covariance matrix. Based on this conditional PDF, a Monte
Carlo method for approximating the symmetric mutual information of this channel
is developed. The symmetric mutual information is closely related to the areal
density limit for TDMR systems. The numerical results suggest that we may need
low-rate coding, e.g., 2/3 or 1/2, when the jitter-like noise becomes dominant.
