I. Introduction
The practical design of optical submarine communication cables has to carefully consider the cable weight and size, so that limits the accommodated fiber count. As a consequence, multi-core fibers (MCFs) are able to further increase the capacity thanks to space division multiplexing (SDM). Illustration of the MCFs-based submarine cable across the sea is given in Fig. 1. Due to the power supply to the cable repeaters is fed by the voltage difference between shores, the submarine cable is also optical power limited. Under these two limitations, SDM linearly scale the capacity with using more spatial paths, so that outperforms the SMF link whose capacity approximately complies with the logarithmic relationship to optical power. The power saving of submarine cables has been theoretically proved to be efficient by SDM using the MCFs ribbon [1]. On the other hand, fiber nonlinearity can not be neglected even for the power limited submarine cable because the transmission distance is over several thousands of kilometers. The reduced power density by SDM results in less fiber nonlinearity, which in return boosts the upper bound of power supply.