Three-dimensional constellation design based on centroid-corrected geometric shaping with optimized average Hamming distance

In this paper, a novel (to our knowledge) three-dimensional (3D) constellation design based on centroid-corrected geometric shaping (CCGS) with optimized average Hamming distance (OAHD) is proposed, referred to as 3D-CCGS-OAHD. This scheme employs a centroid-correction technique to optimize the constellation point distribution and ensure a balanced geometry for higher constellation figure of merit (CFM). Meanwhile, a simulated annealing (SA) algorithm is used to minimize the average Hamming distance (AHD) between adjacent constellation points and explore a better bit-to-symbol mapping strategy superior to Gray mapping to improve the bit error rate (BER) performance. The 3D-CCGS-OAHD scheme was successfully demonstrated over a 2 km 7-core fiber. Results show that the 3D-CCGS constellation achieves a sensitivity gain of 0.84 dB compared to the traditional 3D constellation under Gray mapping. In addition, the 3D-CCGS-OAHD scheme achieves a gain of 1.29 dB compared to the traditional 3D constellation. The experiment results demonstrate that the proposed scheme is suitable for short-distance optical communication systems and has promising research prospects.