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.