| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [1] Univ Campinas UNICAMP, Inst Math Stat & Sci Comp IMECC, BR-13083859 Campinas, SP - Brazil
[2] Univ Campinas UNICAMP, Sch Elect & Comp Engn FEEC, BR-13083852 Campinas, SP - Brazil
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | IEEE TRANSACTIONS ON INFORMATION THEORY; v. 67, n. 12, p. 7925-7939, DEC 2021. |
| Web of Science Citations: | 0 |
| Abstract | |
We present a new systematic approach to constructing spherical codes in dimensions 2(k), based on Hopf foliations. Using the fact that a sphere S2n-1 is foliated by manifolds S-cos eta(n-1) x S-sin eta(n-1), eta is an element of {[}0, pi/2], we distribute points in dimension 2(k) via a recursive algorithm from a basic construction in R-4. 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(n log n). We also propose a sub-optimal decoding procedure, which does not require storing the codebook and has time complexity O(n log n). (AU) | |
| FAPESP's process: | 18/21391-1 - Gauge theory and algebraic geometry |
| Grantee: | Marcos Benevenuto Jardim |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 16/05126-0 - Construction of spherical codes using the Hopf fibration |
| Grantee: | Henrique Koji Miyamoto |
| Support Opportunities: | Scholarships in Brazil - Scientific Initiation |
| FAPESP's process: | 17/20007-0 - Gauge theory and geometric structures in dimension 7 |
| Grantee: | Henrique Nogueira de Sá Earp |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 13/25977-7 - Security and reliability of Information: theory and practice |
| Grantee: | Marcelo Firer |
| Support Opportunities: | Research Projects - Thematic Grants |