I. Introduction
With the advent of technologies like virtual reality, self-driving car diagnostics, and cloud computing, higher requirements are placed on exchanging and transmitting information [1]. To attain the improvement for high-capacity, high-speed, constellation shaping has become a focal point as it enables optical communication systems close to the Shannon limit. [2]. Geometric shaping can adjust constellation distribution based on the transmission channel characteristics, improving bandwidth utilization efficiency and symbol reception. By optimizing the geometric constellation distribution, geometric shaping can enhance the capacity of optical transmission systems and improve transmission distances [3]. Therefore, research on shaping geometric constellations is crucial to enhance optical fiber communication systems.