Constructive Spherical Codes on Layers of Flat Tori

A new class of spherical codes is constructed by selecting a finite subset of flat tori from a foliation of the unit sphere S 2L-1 ⊂ R 2L and designing a structured codebook on each torus layer. The resulting spherical code can be the image of a lattice restricted to a specific box in R L in each la...

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Veröffentlicht in:	IEEE transactions on information theory 2013-10, Vol.59 (10), p.6655-6663
Hauptverfasser:	Torezzan, Cristiano, Costa, Sueli I. R., Vaishampayan, Vinay A.
Format:	Artikel
Sprache:	eng
Schlagworte:	Applied sciences Asymptotic methods Codes Coding theory Coding, codes Decoding Educational institutions Equations Exact sciences and technology Flat torus Gaussian channel Generators group codes Information theory Information, signal and communications theory Lattices Signal and communications theory spherical codes Telecommunications and information theory Vectors
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Beschreibung
Zusammenfassung:	A new class of spherical codes is constructed by selecting a finite subset of flat tori from a foliation of the unit sphere S 2L-1 ⊂ R 2L and designing a structured codebook on each torus layer. The resulting spherical code can be the image of a lattice restricted to a specific box in R L in each layer. Group structure and homogeneity, useful for efficient storage and decoding, are inherited from the underlying lattice codebook. A systematic method for constructing such codes are presented as well some examples of constructions. Upper and lower bounds on the performance, the asymptotic packing density and a method for decoding are derived.
ISSN:	0018-9448 1557-9654
DOI:	10.1109/TIT.2013.2272931