Description
Slepian group-orbit code whose codewords are constructed from an arbitrary unit vector in two possible variants. Variant 1 consists of codewords that are permutations of the vector's coordinates, while Variant 2 consists of such permutations and all possible sign changes of the vector's components.
Rate
Number of codewords cannot increase exponentially with dimension \(n\) [3]
Decoding
Efficient maximum-likelihood decoder determining the Voronoi region of an error word.
Notes
See [4; Ch. 4] for more details and tables of optimal codes.
Parent
- Slepian group-orbit code — Permutations and sign changes can be implemented on vectors by orthogonal matrices, so permutation spherical codes are Slepian group-orbit codes.
Children
References
- [1]
- D. Slepian, “Permutation modulation”, Proceedings of the IEEE 53, 228 (1965) DOI
- [2]
- I. Ingemarsson, “Optimized permutation modulation”, IEEE Transactions on Information Theory 36, 1098 (1990) DOI
- [3]
- H. Landau, “How does a porcupine separate its quills?”, IEEE Transactions on Information Theory 17, 157 (1971) DOI
- [4]
- T. Ericson, and V. Zinoviev, eds. Codes on Euclidean spheres. Elsevier, 2001.
Page edit log
- Victor V. Albert (2022-11-03) — most recent
Cite as:
“Permutation spherical code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/permutation_spherical