{"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 P, N > 0 and L∈Z≥2. A multiple packing is a set C of points in Bn(0–,nP−−−√) such that any point in ℝ n lies in the intersection of at most L – 1 balls of radius nN−−−√ around points in C. 1 In this paper, we derive two lower bounds on the largest possible density of a multiple packing. These bounds are obtained through a stronger notion called average-radius multiple packing. Specifically, we exactly pin down the asymptotics of (expurgated) Gaussian codes and (expurgated) spherical codes under average-radius multiple packing. To this end, we apply tools from high-dimensional geometry and large deviation theory. The bound for spherical codes matches the previous best known bound which was obtained for the standard (weaker) notion of multiple packing through a curious connection with error exponents [Bli99], [ZV21]. The bound for Gaussian codes suggests that they are strictly inferior to spherical codes.","lang":"eng"}],"status":"public","_id":"12015","page":"3085-3090","day":"03","author":[{"id":"2ce5da42-b2ea-11eb-bba5-9f264e9d002c","full_name":"Zhang, Yihan","last_name":"Zhang","first_name":"Yihan"},{"last_name":"Vatedka","full_name":"Vatedka, Shashank","first_name":"Shashank"}],"publisher":"IEEE","publication":"2022 IEEE International Symposium on Information Theory","department":[{"_id":"MaMo"}],"type":"conference","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","conference":{"name":"ISIT: Internation Symposium on Information Theory","end_date":"2022-07-01","start_date":"2022-06-26","location":"Espoo, Finland"},"date_created":"2022-09-04T22:02:05Z","date_updated":"2022-09-05T10:39:04Z","intvolume":"      2022","year":"2022","publication_identifier":{"isbn":["9781665421591"],"issn":["2157-8095"]},"volume":2022,"title":"Lower bounds for multiple packing","language":[{"iso":"eng"}],"scopus_import":"1","quality_controlled":"1","oa_version":"None","date_published":"2022-08-03T00:00:00Z","publication_status":"published","month":"08","doi":"10.1109/ISIT50566.2022.9834443","citation":{"ista":"Zhang Y, Vatedka S. 2022. Lower bounds for multiple packing. 2022 IEEE International Symposium on Information Theory. ISIT: Internation Symposium on Information Theory vol. 2022, 3085–3090.","mla":"Zhang, Yihan, and Shashank Vatedka. “Lower Bounds for Multiple Packing.” <i>2022 IEEE International Symposium on Information Theory</i>, vol. 2022, IEEE, 2022, pp. 3085–90, doi:<a href=\"https://doi.org/10.1109/ISIT50566.2022.9834443\">10.1109/ISIT50566.2022.9834443</a>.","short":"Y. Zhang, S. Vatedka, in:, 2022 IEEE International Symposium on Information Theory, IEEE, 2022, pp. 3085–3090.","chicago":"Zhang, Yihan, and Shashank Vatedka. “Lower Bounds for Multiple Packing.” In <i>2022 IEEE International Symposium on Information Theory</i>, 2022:3085–90. IEEE, 2022. <a href=\"https://doi.org/10.1109/ISIT50566.2022.9834443\">https://doi.org/10.1109/ISIT50566.2022.9834443</a>.","ama":"Zhang Y, Vatedka S. Lower bounds for multiple packing. In: <i>2022 IEEE International Symposium on Information Theory</i>. Vol 2022. IEEE; 2022:3085-3090. doi:<a href=\"https://doi.org/10.1109/ISIT50566.2022.9834443\">10.1109/ISIT50566.2022.9834443</a>","ieee":"Y. Zhang and S. Vatedka, “Lower bounds for multiple packing,” in <i>2022 IEEE International Symposium on Information Theory</i>, Espoo, Finland, 2022, vol. 2022, pp. 3085–3090.","apa":"Zhang, Y., &#38; Vatedka, S. (2022). Lower bounds for multiple packing. In <i>2022 IEEE International Symposium on Information Theory</i> (Vol. 2022, pp. 3085–3090). Espoo, Finland: IEEE. <a href=\"https://doi.org/10.1109/ISIT50566.2022.9834443\">https://doi.org/10.1109/ISIT50566.2022.9834443</a>"},"article_processing_charge":"No"}