{"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/on-the-capacity-of-the-peak-power-constrained","title":"On the Capacity of the Peak Power Constrained Vector Gaussian Channel: An Estimation Theoretic Perspective","arxiv_id":"1804.08524","date":"2018-04-23","proceeding":null,"authors":["Alex Dytso","Mert Al","H. Vincent Poor","Shlomo Shamai"],"abstract":"This paper studies the capacity of an $n$-dimensional vector Gaussian noise channel subject to the constraint that an input must lie in the ball of radius $R$ centered at the origin. It is known that in this setting the optimizing input distribution is supported on a finite number of concentric spheres. However, the number, the positions and the probabilities of the spheres are generally unknown. This paper characterizes necessary and sufficient conditions on the constraint $R$ such that the input distribution supported on a single sphere is optimal. The maximum $\\bar{R}_n$, such that using only a single sphere is optimal, is shown to be a solution of an integral equation. Moreover, it is shown that $\\bar{R}_n$ scales as $\\sqrt{n}$ and the exact limit of $\\frac{\\bar{R}_n}{\\sqrt{n}}$ is found.","url_abs":"http://arxiv.org/abs/1804.08524v1","url_pdf":"http://arxiv.org/pdf/1804.08524v1.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":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"on-the-capacity-of-the-peak-power-constrained","repo_url":"https://github.com/almert/peak-power","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}