{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/high-cardinality-geometrical-constellation","title":"High-Cardinality Geometrical Constellation Shaping for the Nonlinear Fibre Channel","arxiv_id":"2205.04391","date":"2022-05-09","proceeding":null,"authors":["Eric Sillekens","Gabriele Liga","Domaniç Lavery","Polina Bayvel","Robert I. Killey"],"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.","url_abs":"https://arxiv.org/abs/2205.04391v2","url_pdf":"https://arxiv.org/pdf/2205.04391v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"high-cardinality-geometrical-constellation","repo_url":"https://github.com/esillekens/high-cardinality-geometric-shaping","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[{"slug":"high-cardinality-geometrically-shaped","name":"High-cardinality Geometrically Shaped Constellation for the AWGN channel and optical fibre channel","full_name":""}],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}