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. 2021 Mar 12;12:1666. doi: 10.1038/s41467-021-21793-1

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© The Author(s) 2021

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 9 — The retrieved 5-bit grayscale image encoded in a 32-level SPDPSK system sent through a free-space channel with various turbulence strengths. The blue pixels indicate the incorrect data received, and the error rate of each image is listed on the top.