NDLI: Constructive spherical codes near the Shannon bound

Content Provider	Springer Nature Link
Author	Belfiore, Jean Claude Solé, Patrick
Copyright Year	2012
Abstract	Shannon gave a lower bound in 1959 on the binary rate of spherical codes of given minimum Euclidean distance ρ. Using nonconstructive codes over a finite alphabet, we give a lower bound that is weaker but very close for small values of ρ. The construction is based on the Yaglom map combined with some finite sphere packings obtained from nonconstructive codes for the Euclidean metric. Concatenating geometric codes meeting the TVZ bound with a Lee metric BCH code over GF(p), we obtain spherical codes that are polynomial time constructible. Their parameters outperform those obtained by Lachaud and Stern (IEEE Trans Inf Theory 40(4):1140–1146, 1994). At very high rate they are above 98% of the Shannon bound.
Ending Page	26
Page Count	10
Starting Page	17
File Format	PDF
ISSN	09251022
e-ISSN	15737586
Journal	Designs, Codes and Cryptography
Issue Number	1-3
Volume Number	66
Language	English
Publisher	Springer US
Publisher Date	2012-03-29
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Saddle point method Information and Communication, Circuits Data Structures, Cryptology and Information Theory Codes for the Euclidean metric Discrete Mathematics in Computer Science Data Encryption Coding and Information Theory Geometric methods (including applications of algebraic geometry) Applications of the theory of convex sets and geometry of numbers (covering radius, etc.) Spherical codes Combinatorics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Discrete Mathematics and Combinatorics Theoretical Computer Science Computer Science Applications

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