[{"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2211.04408","open_access":"1"}],"oa_version":"Preprint","_id":"14665","publication_status":"published","quality_controlled":"1","publication":"IEEE Transactions on Information Theory","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","article_type":"original","author":[{"last_name":"Zhang","first_name":"Yihan","id":"2ce5da42-b2ea-11eb-bba5-9f264e9d002c","full_name":"Zhang, Yihan","orcid":"0000-0002-6465-6258"},{"last_name":"Vatedka","full_name":"Vatedka, Shashank","first_name":"Shashank"}],"publisher":"IEEE","language":[{"iso":"eng"}],"day":"01","publication_identifier":{"issn":["0018-9448"],"eissn":["1557-9654"]},"page":"1008-1039","status":"public","external_id":{"arxiv":["2211.04408"],"isi":["001166812100008"]},"type":"journal_article","abstract":[{"lang":"eng","text":"We derive lower bounds on the maximal rates for multiple packings in high-dimensional Euclidean spaces. For any N > 0 and L ∈ Z ≥2 , a multiple packing is a set C of points in R n such that any point in R n lies in the intersection of at most L - 1 balls of radius √ nN around points in C . This is a natural generalization of the sphere packing problem. We study the multiple packing problem for both bounded point sets whose points have norm at most √ nP for some constant P > 0, and unbounded point sets whose points are allowed to be anywhere in R n . Given a well-known connection with coding theory, multiple packings can be viewed as the Euclidean analog of list-decodable codes, which are well-studied over finite fields. We derive the best known lower bounds on the optimal multiple packing density. This is accomplished by establishing an inequality which relates the list-decoding error exponent for additive white Gaussian noise channels, a quantity of average-case nature, to the list-decoding radius, a quantity of worst-case nature. We also derive novel bounds on the list-decoding error exponent for infinite constellations and closed-form expressions for the list-decoding error exponents for the power-constrained AWGN channel, which may be of independent interest beyond multiple packing."}],"isi":1,"scopus_import":"1","date_published":"2024-02-01T00:00:00Z","volume":70,"citation":{"mla":"Zhang, Yihan, and Shashank Vatedka. “Multiple Packing: Lower Bounds via Error Exponents.” <i>IEEE Transactions on Information Theory</i>, vol. 70, no. 2, IEEE, 2024, pp. 1008–39, doi:<a href=\"https://doi.org/10.1109/TIT.2023.3334032\">10.1109/TIT.2023.3334032</a>.","apa":"Zhang, Y., &#38; Vatedka, S. (2024). Multiple packing: Lower bounds via error exponents. <i>IEEE Transactions on Information Theory</i>. IEEE. <a href=\"https://doi.org/10.1109/TIT.2023.3334032\">https://doi.org/10.1109/TIT.2023.3334032</a>","chicago":"Zhang, Yihan, and Shashank Vatedka. “Multiple Packing: Lower Bounds via Error Exponents.” <i>IEEE Transactions on Information Theory</i>. IEEE, 2024. <a href=\"https://doi.org/10.1109/TIT.2023.3334032\">https://doi.org/10.1109/TIT.2023.3334032</a>.","short":"Y. Zhang, S. Vatedka, IEEE Transactions on Information Theory 70 (2024) 1008–1039.","ieee":"Y. Zhang and S. Vatedka, “Multiple packing: Lower bounds via error exponents,” <i>IEEE Transactions on Information Theory</i>, vol. 70, no. 2. IEEE, pp. 1008–1039, 2024.","ista":"Zhang Y, Vatedka S. 2024. Multiple packing: Lower bounds via error exponents. IEEE Transactions on Information Theory. 70(2), 1008–1039.","ama":"Zhang Y, Vatedka S. Multiple packing: Lower bounds via error exponents. <i>IEEE Transactions on Information Theory</i>. 2024;70(2):1008-1039. doi:<a href=\"https://doi.org/10.1109/TIT.2023.3334032\">10.1109/TIT.2023.3334032</a>"},"date_updated":"2025-09-04T11:32:49Z","department":[{"_id":"MaMo"}],"year":"2024","date_created":"2023-12-10T23:01:00Z","arxiv":1,"corr_author":"1","title":"Multiple packing: Lower bounds via error exponents","article_processing_charge":"No","doi":"10.1109/TIT.2023.3334032","acknowledgement":"The work of Yihan Zhang was supported by the European Union’s Horizon 2020 Research and Innovation Programme under Grant 682203-ERC-[Inf-Speed-Tradeoff]. The work of Shashank Vatedka was supported in part by the Core Research Grant from the Science and\r\nEngineering Research Board, India, under Grant CRG/2022/004464; and in\r\npart by the Department of Science and Technology (DST), India, under Grant\r\nDST/INT/RUS/RSF/P-41/2020 (TPN No. 65025).","issue":"2","oa":1,"intvolume":"        70","month":"02"}]