---
res:
bibo_abstract:
- We derive lower bounds on the maximal rates for multiple packings in high-dimensional
Euclidean spaces. For any N > 0 and L ∈ Z ≥2 , a multiple packing is a set C of
points in R n such that any point in R n lies in the intersection of at most L
- 1 balls of radius √ nN around points in C . This is a natural generalization
of the sphere packing problem. We study the multiple packing problem for both
bounded point sets whose points have norm at most √ nP for some constant P > 0,
and unbounded point sets whose points are allowed to be anywhere in R n . Given
a well-known connection with coding theory, multiple packings can be viewed as
the Euclidean analog of list-decodable codes, which are well-studied over finite
fields. We derive the best known lower bounds on the optimal multiple packing
density. This is accomplished by establishing an inequality which relates the
list-decoding error exponent for additive white Gaussian noise channels, a quantity
of average-case nature, to the list-decoding radius, a quantity of worst-case
nature. We also derive novel bounds on the list-decoding error exponent for infinite
constellations and closed-form expressions for the list-decoding error exponents
for the power-constrained AWGN channel, which may be of independent interest beyond
multiple packing.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Yihan
foaf_name: Zhang, Yihan
foaf_surname: Zhang
foaf_workInfoHomepage: http://www.librecat.org/personId=2ce5da42-b2ea-11eb-bba5-9f264e9d002c
orcid: 0000-0002-6465-6258
- foaf_Person:
foaf_givenName: Shashank
foaf_name: Vatedka, Shashank
foaf_surname: Vatedka
bibo_doi: 10.1109/TIT.2023.3334032
bibo_issue: '2'
bibo_volume: 70
dct_date: 2024^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/0018-9448
- http://id.crossref.org/issn/1557-9654
dct_language: eng
dct_publisher: IEEE@
dct_title: 'Multiple packing: Lower bounds via error exponents@'
...