Fault-tolerant four-dimensional constellation for coherent optical transmission systems

We propose a 4 -dimensional 2-ary amplitude ring -switched modulation format with 64 symbols, which is denoted as 4D-2A-RS64 encoded over two polarization tributaries to improve the transmission performance over long -haul optical fibers in the presence of the non-linear Kerr effect. At a spectral efficiency of 6 bits per 4D, simulation results show that this format outperforms the polarization division multiplexed (PDM) 8QAM-star modulation as well as the 4D-2A-8PSK over links without inline dispersion management. We evaluate the performance for a WDM transmission of 11 x 90 similar to Gbaud channels over a multi -span SSMF link. For an achievable information rate of 4.8bit/s/Hz, the maximum transmission distance is improved by 10.6% (400 km) and 4% (160 km) compared to PDM-8QAM-star and 4D-2A-8PSK respectively. The achieved gains are composed of a linear part and a non-linear part, respectively from the improved Euclidean -distance distribution and the constant power property of the 4D modulation. The geometric shaping of the proposed scheme is easy to implement and is robust to Mach-Zehnder modulator (MZM) imbalances and quantization errors stemming from the finite digital -to -analog converter (DAC) resolution. This robustness is compared to the one of other geometric -shaped non -linearity tolerant 4D schemes such as the 4D-2A-8PSK and the 4D-64PRS that can be both outperformed by our scheme in severe conditions.