Torus-layer spherical code (TLSC)[1]

Description

Code whose codewords are elements of a foliation of the \(2n-1\)-dimensional hypersphere \(S^{2n-1}\) using flat tori \(S^1\times S^1\cdots\times S^1\). Related constructions include the spherical codes by Hopf foliations (SCHF) [2].

Decoding

Efficiently decodable [1].

Parent

  • Slepian group-orbit code — Polyphase codewords can be implemented by acting on the all-ones initial vector by diagonal orthogonal matrices whose entries are the codeword components [3; Ch. 8]. TLSC codes are generalizations of polyphase codes to other initial vectors and are examples of abelian Slepian-group codes.

Child

References

[1]
C. Torezzan, S. I. R. Costa, and V. A. Vaishampayan, “Spherical codes on torus layers”, 2009 IEEE International Symposium on Information Theory (2009) DOI
[2]
H. K. Miyamoto, H. N. Sa Earp, and S. I. R. Costa, “Constructive spherical codes in 2\({}^{\text{k}}\) dimensions”, 2019 IEEE International Symposium on Information Theory (ISIT) (2019) DOI
[3]
T. Ericson, and V. Zinoviev, eds. Codes on Euclidean spheres. Elsevier, 2001.
Page edit log

Your contribution is welcome!

on github.com (edit & pull request)

edit on this site

Zoo Code ID: tlsc

Cite as:
“Torus-layer spherical code (TLSC)”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/tlsc
BibTeX:
@incollection{eczoo_tlsc, title={Torus-layer spherical code (TLSC)}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/tlsc} }
Share via:
Twitter | Mastodon |  | E-mail
Permanent link:
https://errorcorrectionzoo.org/c/tlsc

Cite as:

“Torus-layer spherical code (TLSC)”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/tlsc

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/classical/spherical/numerical/tlsc.yml.