Multi-dimensional Energy Limitation in Sphere Shaping for Nonlinear Interference Noise Mitigation

We propose Four-Dimensional (4D) energy limit enumerative sphere shaping (ESS) of
$M$
-QAM signaling to minimize rate loss and improve the transmission performance over non-linear WDM optical-fiber systems. Simulation results show that the proposed scheme outperforms the conventional ESS by 0.19 bit/4D-symbol in achievable information rate over a 205-km single-span link and a WDM transmission of five polarization-division-multiplexed channels with 400-Gbit/s net rate per channel. We also study the achieved performance over several shaping block lengths and show that the achieved gains do not scale well over multi-span systems.