High-Cardinality Geometrical Constellation Shaping for the Nonlinear Fibre Channel

TL;DR

This paper introduces analytical methods for optimizing high-cardinality, geometrically shaped constellations in optical fiber communications, achieving near-capacity performance with significantly reduced design time.

Contribution

It develops analytical derivatives of information metrics for constellation optimization, enabling efficient design of high-dimensional, high-cardinality constellations for nonlinear fiber channels.

Findings

Achieves near-capacity constellations with up to 8192 points.

Reduces design computation time from days to minutes.

Provides optimized constellations for linear and nonlinear channels.

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 \ac{MI} and \ac{GMI} are critical to the optimisation of geometrically-shaped constellations. It presents the analytical derivative of the achievable information rate metrics with respect to the input constellation. 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, with generalised mutual information (GMI) within 0.06 bit/2Dsymbol of additive white Gaussian noise channel (AWGN) capacity, are presented. Additionally, a design algorithm reducing the design computation time from days to minutes is introduced, allowing the presentation of optimised constellations for both linear AWGN and nonlinear fibre channels for a wide range of signal-to-noise ratios.