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].
Notes
See [3; Sec. 5.2] for an exposition.
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 [4; 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]
- S. I. R. Costa et al., Lattices Applied to Coding for Reliable and Secure Communications (Springer International Publishing, 2017) DOI
- [4]
- T. Ericson, and V. Zinoviev, eds. Codes on Euclidean spheres. Elsevier, 2001.
Page edit log
- Victor V. Albert (2022-11-23) — most recent
Cite as:
“Torus-layer spherical code (TLSC)”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/tlsc