{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,25]],"date-time":"2026-09-25T16:19:52Z","timestamp":1790353192600,"version":"4.1.0"},"reference-count":22,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2017,12,22]],"date-time":"2017-12-22T00:00:00Z","timestamp":1513900800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1527387"],"award-info":[{"award-number":["1527387"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Agence Nationale pour la Recherche","award":["13-BS03-0008"],"award-info":[{"award-number":["13-BS03-0008"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This paper introduces an explicit covert communication code for binary-input asynchronous discrete memoryless channels based on binary polar codes, in which legitimate parties exploit uncertainty created by both the channel noise and the time of transmission to avoid detection by an adversary. The proposed code jointly ensures reliable communication for a legitimate receiver and low probability of detection with respect to the adversary, both observing noisy versions of the codewords. Binary polar codes are used to shape the weight distribution of codewords and ensure that the average weight decays as the block length grows. The performance of the proposed code is severely limited by the speed of polarization, which in turn controls the decay of the average codeword weight with the block length. Although the proposed construction falls largely short of achieving the performance of random codes, it inherits the low-complexity properties of polar codes.<\/jats:p>","DOI":"10.3390\/e20010003","type":"journal-article","created":{"date-parts":[[2017,12,22]],"date-time":"2017-12-22T05:50:19Z","timestamp":1513921819000},"page":"3","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Polar Codes for Covert Communications over Asynchronous Discrete Memoryless Channels"],"prefix":"10.3390","volume":"20","author":[{"given":"Guillaume","family":"Fr\u00e8che","sequence":"first","affiliation":[{"name":"UMI 2958 Georgia Tech-CNRS, 57070 Metz, France"},{"name":"School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA"},{"name":"CentraleSup\u00e9lec, 57070 Metz, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9315-9050","authenticated-orcid":false,"given":"Matthieu","family":"Bloch","sequence":"additional","affiliation":[{"name":"UMI 2958 Georgia Tech-CNRS, 57070 Metz, France"},{"name":"School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michel","family":"Barret","sequence":"additional","affiliation":[{"name":"UMI 2958 Georgia Tech-CNRS, 57070 Metz, France"},{"name":"CentraleSup\u00e9lec, 57070 Metz, France"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2017,12,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1921","DOI":"10.1109\/JSAC.2013.130923","article-title":"Limits of reliable communication with low probability of detection on AWGN channels","volume":"31","author":"Bash","year":"2013","journal-title":"IEEE J. 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