Accumulation of nonlinear interference noise in probabilistically shaped 64-quadrature amplitude modulation systems

Abstract. An efficient procedure is presented for evaluating the effects of modulation format on the accumulation of nonlinear interference noise (NLIN) in probabilistically shaped 28 Gbaud 64-quadrature amplitude modulation (QAM) wavelength division multiplexed (WDM) systems. The shaped symbol sequences are generated by the rate adaptive scheme concatenating a constant composition distribution matcher and a systematic forward error correction encoder. A shaping distribution based on the Maxwell–Boltzmann and the uniform distribution with the same net bit rate is considered. The NLIN variance is emulated using the accurate enhanced modulation-dependent Gaussian noise model. Accounting for the impact of higher-order standardized moments of the modulation, the dependence of NLIN variance on probabilistic shaping is determined using the proposed procedure. In addition, an increase in NLIN variance for shaping over uniform input is demonstrated. For a dual polarization (DP) fully loaded C-band WDM optical fiber system with a channel spacing of 37.5 GHz, probabilistic shaping leads to a reduction of 0.036 in the ratio of intrachannel and interchannel contributions to nonlinear noise over uniform 64-QAM for a 1500-km distance. Finally, for nine channels with DP probabilistically shaped 64-QAM input over 1500-km transmission, distributed amplification enables a reduction of 2.54 dB in the accumulation of normalized NLIN power compared to lumped amplification.