Four-dimensional signal constellations based on the checkerboard lattice $\boldsymbol{D}_4$ offer a packing gain over conventional QAM constellations per polarization. Due to the increased number of nearest neighbors such power-efficient 4D formats cannot be Gray-labeled and bit-interleaved coded modulation results in a considerable performance loss. Instead, a suited coded-modulation scheme must be tailored to the properties of the underlying signal lattice. We apply a low-complexity two-stage coded-modulation scheme for constellations based on the set of Hurwitz integers, an isomorphic representation of the $\boldsymbol{D}_4$ lattice. The proposed signaling scheme is evaluated in numerical simulations and fiber-optical system experiments. The performance is compared to a reference implementation using square QAM formats as proposed in the current 400ZR standardization activities. We demonstrate a 0.8 dB gain in required OSNR of the 512-ary Hurwitz constellation over dual-polarization 16-QAM (with 256 signal points in 4D) at the same symbol and bit rate. Additional numerical and experimental results show the potential for applications in the long-haul as well as the short-reach regime.

中文翻译：

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光纤通信中 Hurwitz 星座的两级编码调制

基于棋盘格的四维信号星座 $\boldsymbol{D}_4$ 提供一个 包装增益每个极化的传统 QAM 星座。由于最近邻居数量的增加，这种节能的 4D 格式无法进行灰度标记，比特交错编码调制会导致相当大的性能损失。取而代之的是，必须根据底层信号格的特性调整合适的编码调制方案。我们基于 Hurwitz 整数集对星座应用低复杂度的两级编码调制方案，这是$\boldsymbol{D}_4$格子。所提出的信号方案在数值模拟和光纤系统实验中进行了评估。将性能与当前 400ZR 标准化活动中提议的使用方形 QAM 格式的参考实现进行比较。我们证明了 512 进制 Hurwitz 星座在相同符号和比特率的双极化 16-QAM（4D 中有 256 个信号点）所需的 OSNR 增益为 0.8 dB。额外的数值和实验结果显示了在长途和短距离范围内的应用潜力。