— As the capacity of the two-dimensional coherent optical memory (2D-COM) increases, the bit error rate (BER) performance of the system is degraded due to increased twodimensional inter-symbol interference (2D-ISI) and noise. To improve the system performance under these adverse effects and to increase the capacity, in this paper, we devise an iterative softinput soft-output equalization method which is optimized in minimum mean square error (MMSE) sense called iterative softMMSE (ISISO-MMSE) equalization by considering the nonlinearity inherent in the channel. We evaluate the performance of ISISO-MMSE by using numerical experiments under different amount of 2D-ISI and optical noise. Simulation results suggest that ISMME is a good candidate for ultra-high capacity 2D-COM.