conference paper published yes Yihan Zhang author 2ce5da42-b2ea-11eb-bba5-9f264e9d002c0000-0002-6465-6258 Shashank Vatedka author MaMo department ISIT: International Symposium on Information Theory 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. IEEE2022Espoo, Finland eng 2157-8095 9781665421591 00125426190304210.1109/ISIT50566.2022.9834443 20223085-3090 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> 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. 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> 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>. Zhang Y, Vatedka S. 2022. Lower bounds for multiple packing. 2022 IEEE International Symposium on Information Theory. ISIT: International Symposium on Information Theory vol. 2022, 3085–3090. Y. Zhang, S. Vatedka, in:, 2022 IEEE International Symposium on Information Theory, IEEE, 2022, pp. 3085–3090. 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>. 120152022-09-04T22:02:05Z2025-09-10T09:44:24Z