@inproceedings{12015,
  abstract     = {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.},
  author       = {Zhang, Yihan and Vatedka, Shashank},
  booktitle    = {2022 IEEE International Symposium on Information Theory},
  isbn         = {9781665421591},
  issn         = {2157-8095},
  location     = {Espoo, Finland},
  pages        = {3085--3090},
  publisher    = {IEEE},
  title        = {{Lower bounds for multiple packing}},
  doi          = {10.1109/ISIT50566.2022.9834443},
  volume       = {2022},
  year         = {2022},
}