In this paper, a rate adaptive geometric constellation shaping (GCS) scheme which is fully backward-compatible with existing state of the art bit-interleaved coded modulation (BICM) systems is proposed and experimentally demonstrated. The system relies on optimization of the positions of the quadrature amplitude modulation (QAM) points on the I/Q plane for maximized achievable information rate, while maintaining quantization and fiber nonlinear noise robustness. Furthermore, `dummy' bits are multiplexed with coded bits before mapping to symbols. Rate adaptivity is achieved by tuning the ratio of coded and `dummy' bits, while maintaining a fixed forward error-correction block and a fixed modulation format size. The points' positions and their labeling are optimized using automatic differentiation. The proposed GCS scheme is compared to a time-sharing hybrid (TH) QAM modulation and the now mainstream probabilistic amplitude shaping (PAS) scheme. The TH without shaping is outperformed for all studied data rates in a simulated linear channel by up to 0.7 dB. In a linear channel, PAS is shown to outperform the proposed GCS scheme, while similar performances are reported for PAS and the proposed GCS in a simulated nonlinear fiber channel. The GCS scheme is experimentally demonstrated in a multi-span recirculating loop coherent optical fiber transmission system with a total distance of up to 3000 km. Near-continuous zero-error flexible throughput is reported as a function of the transmission distance. Up to 1-2 spans of increased reach gains are achieved at the same net data rate w.r.t. conventional QAM. At a given distance, up to 0.79 bits/2D symbol of gain w.r.t. conventional QAM is achieved. In the experiment, similar performance to PAS is demonstrated.

翻译：本文提出并实验验证了一种速率自适应几何星座整形（GCS）方案，该方案与现有最先进的比特交织编码调制（BICM）系统完全后向兼容。该方案通过优化I/Q平面上正交幅度调制（QAM）点的位置，在保持量化和光纤非线性噪声鲁棒性的同时最大化可达信息速率。此外，在映射到符号前，将"虚拟"比特与编码比特进行复用。通过调节编码比特与虚拟比特的比例实现速率自适应，同时保持固定的前向纠错码块和固定的调制格式尺寸。采用自动微分技术优化星座点位置及其标签分配。将所提GCS方案与时分混合（TH）QAM调制及当前主流的概率幅度整形（PAS）方案进行对比。在仿真线性信道中，所提方案在所有研究数据速率下均优于无整形TH方案（性能提升最高达0.7 dB）。在线性信道条件下，PAS方案性能优于所提GCS方案，而在仿真非线性光纤信道中，PAS与所提GCS方案性能相当。通过总距离达3000 km的多跨距循环相干光传输系统实验验证了该GCS方案。实验结果表明，近连续零错误灵活吞吐量随传输距离变化。与传统QAM相比，在相同净数据速率下可实现1-2个跨距的传输距离增益提升。在给定距离下，相对于传统QAM可获得高达0.79 bits/2D符号的增益。实验证明该方案与PAS方案性能相当。