In this paper, we estimate the Mutual Information Rate (MIR) for Two-Dimensional Magnetic Recording (TDMR) channel with input constraints by using the Generalized Belief Propagation (GBP) algorithm. The Voronoi channel model is considered in this paper. Since the main source of media noise in the TDMR channel is the boundary distortion of the bit area which is manifested in presence of transitions of the input data, the constraints utilized for TDMR systems limit the number of transitions in the input patterns. In , we showed that constrained coding can provide performance gain in the bit error rate (BER). However, BER is not a proper figure of merit to compare various input distributions for a fixed channel since the rate loss due to using constrained input is not accounted for. On the other hand, computing MIR for different input distributions can lead us to the limits of the channel capacity.