{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:06:57Z","timestamp":1760148417233,"version":"build-2065373602"},"reference-count":47,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2023,4,30]],"date-time":"2023-04-30T00:00:00Z","timestamp":1682812800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This paper studies the secrecy capacity of an n-dimensional Gaussian wiretap channel under a peak power constraint. This work determines the largest peak power constraint R\u00afn, such that an input distribution uniformly distributed on a single sphere is optimal; this regime is termed the low-amplitude regime. The asymptotic value of R\u00afn as n goes to infinity is completely characterized as a function of noise variance at both receivers. Moreover, the secrecy capacity is also characterized in a form amenable to computation. Several numerical examples are provided, such as the example of the secrecy-capacity-achieving distribution beyond the low-amplitude regime. Furthermore, for the scalar case (n=1), we show that the secrecy-capacity-achieving input distribution is discrete with finitely many points at most at the order of R2\u03c312, where \u03c312 is the variance of the Gaussian noise over the legitimate channel.<\/jats:p>","DOI":"10.3390\/e25050741","type":"journal-article","created":{"date-parts":[[2023,5,1]],"date-time":"2023-05-01T12:14:08Z","timestamp":1682943248000},"page":"741","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Amplitude Constrained Vector Gaussian Wiretap Channel: Properties of the Secrecy-Capacity-Achieving Input Distribution"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7445-7634","authenticated-orcid":false,"given":"Antonino","family":"Favano","sequence":"first","affiliation":[{"name":"Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, 20133 Milano, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4052-2092","authenticated-orcid":false,"given":"Luca","family":"Barletta","sequence":"additional","affiliation":[{"name":"Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, 20133 Milano, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0625-5306","authenticated-orcid":false,"given":"Alex","family":"Dytso","sequence":"additional","affiliation":[{"name":"Qualcomm, Bridgewater, NJ 08807, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,30]]},"reference":[{"key":"ref_1","unstructured":"Favano, A., Barletta, L., and Dytso, A. 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