{"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/deep-learning-of-the-nonlinear-schrodinger","title":"Deep Learning of the Nonlinear Schrödinger Equation in Fiber-Optic Communications","arxiv_id":"1804.02799","date":"2018-04-09","proceeding":null,"authors":["Christian Häger","Henry D. Pfister"],"abstract":"An important problem in fiber-optic communications is to invert the nonlinear\nSchr\\\"odinger equation in real time to reverse the deterministic effects of the\nchannel. Interestingly, the popular split-step Fourier method (SSFM) leads to a\ncomputation graph that is reminiscent of a deep neural network. This\nobservation allows one to leverage tools from machine learning to reduce\ncomplexity. In particular, the main disadvantage of the SSFM is that its\ncomplexity using M steps is at least M times larger than a linear equalizer.\nThis is because the linear SSFM operator is a dense matrix. In previous work,\ntruncation methods such as frequency sampling, wavelets, or least-squares have\nbeen used to obtain \"cheaper\" operators that can be implemented using filters.\nHowever, a large number of filter taps are typically required to limit\ntruncation errors. For example, Ip and Kahn showed that for a 10 Gbaud signal\nand 2000 km optical link, a truncated SSFM with 25 steps would require 70-tap\nfilters in each step and 100 times more operations than linear equalization. We\nfind that, by jointly optimizing all filters with deep learning, the complexity\ncan be reduced significantly for similar accuracy. Using optimized 5-tap and\n3-tap filters in an alternating fashion, one requires only around 2-6 times the\ncomplexity of linear equalization, depending on the implementation.","url_abs":"http://arxiv.org/abs/1804.02799v1","url_pdf":"http://arxiv.org/pdf/1804.02799v1.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":"abstracts"},"code_links":[{"paper_slug":"deep-learning-of-the-nonlinear-schrodinger","repo_url":"https://github.com/chaeger/LDBP","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}