{"issue":"2","article_type":"original","quality_controlled":"1","date_updated":"2024-07-16T11:06:14Z","title":"Multiple packing: Lower bounds via error exponents","corr_author":"1","abstract":[{"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.","lang":"eng"}],"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).","volume":70,"publication":"IEEE Transactions on Information Theory","publisher":"IEEE","citation":{"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>.","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>","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>"},"arxiv":1,"publication_status":"published","external_id":{"arxiv":["2211.04408"]},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2211.04408","open_access":"1"}],"day":"01","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2024-02-01T00:00:00Z","oa_version":"Preprint","author":[{"id":"2ce5da42-b2ea-11eb-bba5-9f264e9d002c","full_name":"Zhang, Yihan","last_name":"Zhang","orcid":"0000-0002-6465-6258","first_name":"Yihan"},{"last_name":"Vatedka","first_name":"Shashank","full_name":"Vatedka, Shashank"}],"type":"journal_article","_id":"14665","intvolume":"        70","language":[{"iso":"eng"}],"page":"1008-1039","date_created":"2023-12-10T23:01:00Z","doi":"10.1109/TIT.2023.3334032","oa":1,"department":[{"_id":"MaMo"}],"scopus_import":"1","year":"2024","month":"02","publication_identifier":{"eissn":["1557-9654"],"issn":["0018-9448"]},"article_processing_charge":"No"}