Two-Stage Coded Modulation for Hurwitz Constellations in Fiber-Optical Communications

Abstract

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.