Lower bounds for multiple packing Zhang, Yihan ; https://orcid.org/0000-0002-6465-6258 Vatedka, Shashank 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. IEEE 2022 info:eu-repo/semantics/conferenceObject doc-type:conferenceObject text http://purl.org/coar/resource_type/c_5794 https://research-explorer.ista.ac.at/record/12015 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> eng info:eu-repo/semantics/altIdentifier/doi/10.1109/ISIT50566.2022.9834443 info:eu-repo/semantics/altIdentifier/issn/2157-8095 info:eu-repo/semantics/altIdentifier/isbn/9781665421591 info:eu-repo/semantics/altIdentifier/wos/001254261903042 info:eu-repo/semantics/closedAccess