BICM-compatible Rate Adaptive Geometric Constellation Shaping Using Optimized Many-to-one Labeling

In this paper, a rate adaptive geometric constellaion 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 in a many-to-one fashion such that the performance of the ‘dummy’ bits is sacrificed in favor of the performance of the data bits. The proposed GCS scheme is compared to a time-sharing hybrid (TH) QAM modulation and the now mainstream probabilistic amplitude shaping (PAS) scheme employing a Maxwell-Boltzmann probability mass function. 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.