{"publisher":"IEEE","publication":"IEEE Transactions on Information Theory","oa_version":"Preprint","month":"07","day":"01","issue":"7","title":"Multiple packing: Lower bounds via infinite constellations","language":[{"iso":"eng"}],"acknowledgement":"YZ thanks Jiajin Li for making the observation given by Equation (23). He also would like to thank Nir Ailon and Ely Porat for several helpful conversations throughout this project, and Alexander Barg for insightful comments on the manuscript.\r\nYZ has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 682203-ERC-[Inf-Speed-Tradeoff]. The work of SV was supported by a seed grant from IIT Hyderabad and the start-up research grant from the Science and Engineering Research Board, India (SRG/2020/000910).","quality_controlled":"1","date_created":"2023-04-16T22:01:09Z","abstract":[{"text":"We study the problem of high-dimensional multiple packing in Euclidean space. Multiple packing is a natural generalization of sphere packing and is defined as follows. Let 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 . 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 for finite fields. In this paper, we derive the best known lower bounds on the optimal density of list-decodable infinite constellations for constant L under a stronger notion called average-radius multiple packing. To this end, we apply tools from high-dimensional geometry and large deviation theory.","lang":"eng"}],"external_id":{"isi":["001017307000023"],"arxiv":["2211.04407"]},"date_published":"2023-07-01T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2023","doi":"10.1109/TIT.2023.3260950","volume":69,"intvolume":"        69","department":[{"_id":"MaMo"}],"type":"journal_article","date_updated":"2023-12-13T11:16:46Z","scopus_import":"1","_id":"12838","citation":{"mla":"Zhang, Yihan, and Shashank Vatedka. “Multiple Packing: Lower Bounds via Infinite Constellations.” <i>IEEE Transactions on Information Theory</i>, vol. 69, no. 7, IEEE, 2023, pp. 4513–27, doi:<a href=\"https://doi.org/10.1109/TIT.2023.3260950\">10.1109/TIT.2023.3260950</a>.","short":"Y. Zhang, S. Vatedka, IEEE Transactions on Information Theory 69 (2023) 4513–4527.","ama":"Zhang Y, Vatedka S. Multiple packing: Lower bounds via infinite constellations. <i>IEEE Transactions on Information Theory</i>. 2023;69(7):4513-4527. doi:<a href=\"https://doi.org/10.1109/TIT.2023.3260950\">10.1109/TIT.2023.3260950</a>","chicago":"Zhang, Yihan, and Shashank Vatedka. “Multiple Packing: Lower Bounds via Infinite Constellations.” <i>IEEE Transactions on Information Theory</i>. IEEE, 2023. <a href=\"https://doi.org/10.1109/TIT.2023.3260950\">https://doi.org/10.1109/TIT.2023.3260950</a>.","ieee":"Y. Zhang and S. Vatedka, “Multiple packing: Lower bounds via infinite constellations,” <i>IEEE Transactions on Information Theory</i>, vol. 69, no. 7. IEEE, pp. 4513–4527, 2023.","apa":"Zhang, Y., &#38; Vatedka, S. (2023). Multiple packing: Lower bounds via infinite constellations. <i>IEEE Transactions on Information Theory</i>. IEEE. <a href=\"https://doi.org/10.1109/TIT.2023.3260950\">https://doi.org/10.1109/TIT.2023.3260950</a>","ista":"Zhang Y, Vatedka S. 2023. Multiple packing: Lower bounds via infinite constellations. IEEE Transactions on Information Theory. 69(7), 4513–4527."},"publication_identifier":{"issn":["0018-9448"],"eissn":["1557-9654"]},"oa":1,"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2211.04407","open_access":"1"}],"isi":1,"status":"public","publication_status":"published","author":[{"last_name":"Zhang","id":"2ce5da42-b2ea-11eb-bba5-9f264e9d002c","first_name":"Yihan","full_name":"Zhang, Yihan","orcid":"0000-0002-6465-6258"},{"last_name":"Vatedka","first_name":"Shashank","full_name":"Vatedka, Shashank"}],"article_processing_charge":"No","article_type":"original","page":"4513-4527"}