Abstract

This paper presents design methods for highly efficient optimisation of geometrically shaped constellations to maximise data throughput in optical communications. It describes methods to analytically calculate the information-theoretical loss and the gradient of this loss as a function of the input constellation shape. The gradients of the mutual information (MI) and generalised mutual information (GMI) are critical to the optimisation of geometrically-shaped constellations. The analytically derived gradients of the achievable information rate metrics with respect to the input constellation are presented. The proposed method allows for improved design of higher cardinality and higher-dimensional constellations for optimising both linear and nonlinear fibre transmission throughput. Near-capacity achieving constellations with up to 8192 points for both 2 and 4 dimensions are presented. In the best case, a GMI value within 0.06 b/2Dsymbol of the additive white Gaussian noise channel (AWGN) capacity was achieved. Additionally, a design algorithm reducing the design computation time from days to minutes is introduced, allowing for the design of optimised constellations for both linear AWGN and nonlinear fibre channels over a wide range of signal-to-noise ratio values.

Orthant-symmetric four-dimensional geometric shaping for fiber-optic channels via a nonlinear interference model

Bin Chen, Wei Ling, Yi Lei, Zhiwei Liang, and Xuwei Xue
Opt. Express 31(10) 16985-17002 (2023)

2048-QAM transmission at 15 GBd over 100 km using geometric constellation shaping

Yuta Wakayama, Thomas Gerard, Eric Sillekens, Lídia Galdino, Domaniç Lavery, Robert I. Killey, and Polina Bayvel
Opt. Express 29(12) 18743-18759 (2021)

Discrete multitone transmission for underwater optical wireless communication system using probabilistic constellation shaping to approach channel capacity limit

Xiaojian Hong, Chao Fei, Guowu Zhang, Ji Du, and Sailing He
Opt. Lett. 44(3) 558-561 (2019)

Geometric shaping optimization of 64-APSK constellation in discrete nonlinear frequency division multiplexing systems

Junda Chen, Yizhao Chen, Yuxiang Duan, Xuefeng Wang, Li Wang, Tianhao Tong, Yating Xiang, Can Zhao, Deming Liu, and Ming Tang
Opt. Lett. 46(14) 3368-3371 (2021)

On the optimum signal constellation design for high-speed optical transport networks

Tao Liu and Ivan B. Djordjevic
Opt. Express 20(18) 20396-20406 (2012)