Constructive spherical codes by hopf foliations
| Autor: | Costa, Sueli Irene Rodrigues, Sá Earp, Henrique Nogueira de, 1981, Miyamoto, Henrique Koji, 1996 |
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| Přispěvatelé: | UNIVERSIDADE ESTADUAL DE CAMPINAS |
| Rok vydání: | 2021 |
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| Zdroj: | Repositório da Produção Científica e Intelectual da Unicamp Universidade Estadual de Campinas (UNICAMP) instacron:UNICAMP |
| Popis: | We present a new systematic approach to constructing spherical codes in dimensions 2k , based on Hopf foliations. Using the fact that a sphere S2n-1 is foliated by manifolds Sn-1cos r×Sn-1sin r , E [0,p/2] , we distribute points in dimension 2k via a recursive algorithm from a basic construction in R4 . Our procedure outperforms some current constructive methods in several small-distance regimes and constitutes a compromise between achieving a large number of codewords for a minimum given distance and effective constructiveness with low encoding computational cost. Bounds for the asymptotic density are derived and compared with other constructions. The encoding process has storage complexity O(n) and time complexity O(nlogn) . We also propose a sub-optimal decoding procedure, which does not require storing the codebook and has time complexity O(nlogn) FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESP CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQ Fechado |
| Databáze: | OpenAIRE |
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