{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,28]],"date-time":"2026-03-28T06:30:28Z","timestamp":1774679428986,"version":"3.50.1"},"reference-count":33,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2020,7,11]],"date-time":"2020-07-11T00:00:00Z","timestamp":1594425600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100010663","name":"H2020 European Research Council","doi-asserted-by":"publisher","award":["757791"],"award-info":[{"award-number":["757791"]}],"id":[{"id":"10.13039\/100010663","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Probabilistic amplitude shaping (PAS) is a coded modulation strategy in which constellation shaping and channel coding are combined. PAS has attracted considerable attention in both wireless and optical communications. Achievable information rates (AIRs) of PAS have been investigated in the literature using Gallager\u2019s error exponent approach. In particular, it has been shown that PAS achieves the capacity of the additive white Gaussian noise channel (B\u00f6cherer, 2018). In this work, we revisit the capacity-achieving property of PAS and derive AIRs using weak typicality. Our objective is to provide alternative proofs based on random sign-coding arguments that are as constructive as possible. Accordingly, in our proofs, only some signs of the channel inputs are drawn from a random code, while the remaining signs and amplitudes are produced constructively. We consider both symbol-metric and bit-metric decoding.<\/jats:p>","DOI":"10.3390\/e22070762","type":"journal-article","created":{"date-parts":[[2020,7,14]],"date-time":"2020-07-14T04:46:01Z","timestamp":1594701961000},"page":"762","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Achievable Information Rates for Probabilistic Amplitude Shaping: An Alternative Approach via Random Sign-Coding Arguments"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8551-2851","authenticated-orcid":false,"given":"Yunus Can","family":"G\u00fcltekin","sequence":"first","affiliation":[{"name":"Information and Communication Theory Lab, Signal Processing Systems Group, Department of Electrical Engineering, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2172-3051","authenticated-orcid":false,"given":"Alex","family":"Alvarado","sequence":"additional","affiliation":[{"name":"Information and Communication Theory Lab, Signal Processing Systems Group, Department of Electrical Engineering, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7316-3471","authenticated-orcid":false,"given":"Frans M. J.","family":"Willems","sequence":"additional","affiliation":[{"name":"Information and Communication Theory Lab, Signal Processing Systems Group, Department of Electrical Engineering, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,7,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1109\/TIT.1977.1055718","article-title":"A new multilevel coding method using error-correcting codes","volume":"23","author":"Imai","year":"1977","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1361","DOI":"10.1109\/18.771140","article-title":"Multilevel codes: Theoretical concepts and practical design rules","volume":"45","author":"Wachsmann","year":"1999","journal-title":"IEEE Trans. Inf. 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