{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2023-12-18T07:46:45Z","type":"journal_article","doi":"10.1109/TIT.2023.3334032","oa_version":"Preprint","department":[{"_id":"MaMo"}],"publication_identifier":{"issn":["0018-9448"],"eissn":["1557-9654"]},"article_processing_charge":"No","citation":{"ista":"Zhang Y, Vatedka S. 2023. Multiple packing: Lower bounds via error exponents. IEEE Transactions on Information Theory.","mla":"Zhang, Yihan, and Shashank Vatedka. “Multiple Packing: Lower Bounds via Error Exponents.” <i>IEEE Transactions on Information Theory</i>, IEEE, 2023, doi:<a href=\"https://doi.org/10.1109/TIT.2023.3334032\">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, 2023. <a href=\"https://doi.org/10.1109/TIT.2023.3334032\">https://doi.org/10.1109/TIT.2023.3334032</a>.","apa":"Zhang, Y., &#38; Vatedka, S. (2023). 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>","ama":"Zhang Y, Vatedka S. Multiple packing: Lower bounds via error exponents. <i>IEEE Transactions on Information Theory</i>. 2023. doi:<a href=\"https://doi.org/10.1109/TIT.2023.3334032\">10.1109/TIT.2023.3334032</a>","short":"Y. Zhang, S. Vatedka, IEEE Transactions on Information Theory (2023).","ieee":"Y. Zhang and S. Vatedka, “Multiple packing: Lower bounds via error exponents,” <i>IEEE Transactions on Information Theory</i>. IEEE, 2023."},"title":"Multiple packing: Lower bounds via error exponents","scopus_import":"1","_id":"14665","article_type":"original","quality_controlled":"1","status":"public","date_published":"2023-11-16T00:00:00Z","year":"2023","external_id":{"arxiv":["2211.04408"]},"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"}],"publisher":"IEEE","oa":1,"publication_status":"epub_ahead","month":"11","date_created":"2023-12-10T23:01:00Z","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2211.04408"}],"language":[{"iso":"eng"}],"day":"16","publication":"IEEE Transactions on Information Theory","author":[{"orcid":"0000-0002-6465-6258","last_name":"Zhang","first_name":"Yihan","id":"2ce5da42-b2ea-11eb-bba5-9f264e9d002c","full_name":"Zhang, Yihan"},{"first_name":"Shashank","last_name":"Vatedka","full_name":"Vatedka, Shashank"}]}