On the Probabilistic Shaping and Geometric Shaping in Optical Communication Systems

We introduce and compare typical shaping schemes suitable for optical communications. The geometrically shaped-quadrature amplitude modulation (GS-QAM) formats are characterized by the non-equidistant spacing of constellation points, transmitted uniformly, and applied to improve system capacity. On the other hand, the well-known constant composition distribution matcher (CCDM) is applied for the generation of probabilistically shaped QAM (PS-QAM) formats. Mutual information (MI) is used as a metric to analyze the performances of regular/GS/PS-MQAM formats. In a linear amplified spontaneous emission noise limited region, it can be proved by the numerical simulation that MI performances of the GS-8/16QAM are always better than regular 8/16QAM and PS-8/16QAM; the largest shaping gains can be separately reached by PS-32QAM and GS-32QAM. We continue with the experimental demonstration on the 16QAM-based transmission system, and find that GS-16QAM generally has the best MI performance. We also find that the modulation-dependent nonlinear noises of the GS-8/16/32QAM are comparable to that of the regular 8/16/32QAM and generally lower than PS-8/16/32QAM. By using the enhanced Gaussian noise model, we observe that the GS-8/16QAM formats have better performances than regular 8/16QAM and PS-8/16QAM over multi-span transmission. Meanwhile, PS-32QAM formats provide superior performance over a relatively long transmission distance.