---
_id: '12015'
abstract:
- lang: eng
  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.
article_processing_charge: No
author:
- first_name: Yihan
  full_name: Zhang, Yihan
  id: 2ce5da42-b2ea-11eb-bba5-9f264e9d002c
  last_name: Zhang
  orcid: 0000-0002-6465-6258
- first_name: Shashank
  full_name: Vatedka, Shashank
  last_name: Vatedka
citation:
  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>'
  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>'
  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>.
  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.
  ista: '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.'
  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.
conference:
  end_date: 2022-07-01
  location: Espoo, Finland
  name: 'ISIT: International Symposium on Information Theory'
  start_date: 2022-06-26
date_created: 2022-09-04T22:02:05Z
date_published: 2022-08-03T00:00:00Z
date_updated: 2025-09-10T09:44:24Z
day: '03'
department:
- _id: MaMo
doi: 10.1109/ISIT50566.2022.9834443
external_id:
  isi:
  - '001254261903042'
intvolume: '      2022'
isi: 1
language:
- iso: eng
month: '08'
oa_version: None
page: 3085-3090
publication: 2022 IEEE International Symposium on Information Theory
publication_identifier:
  isbn:
  - '9781665421591'
  issn:
  - 2157-8095
publication_status: published
publisher: IEEE
quality_controlled: '1'
scopus_import: '1'
status: public
title: Lower bounds for multiple packing
type: conference
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 2022
year: '2022'
...