# Asymptotically dense spherical codes - Part h Wrapped spherical codes

@article{Hamkins1997AsymptoticallyDS, title={Asymptotically dense spherical codes - Part h Wrapped spherical codes}, author={Jon Hamkins and Kenneth Zeger}, journal={IEEE Trans. Inf. Theory}, year={1997}, volume={43}, pages={1774-1785} }

A new class of spherical codes called wrapped spherical codes is constructed by "wrapping" any sphere packing /spl Lambda/ in Euclidean space onto a finite subset of the unit sphere in one higher dimension. The mapping preserves much of the structure of /spl Lambda/, and unlike previously proposed maps, the density of the wrapped spherical codes approaches the density of /spl Lambda/ as the minimum distance approaches zero. We show that this implies that the asymptotically maximum spherical…

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## 47 Citations

Asymptotically dense spherical codes - Part II: Laminated spherical codes

- Mathematics, Computer ScienceIEEE Trans. Inf. Theory
- 1997

The three-dimensional laminated spherical code is asymptotically optimal, in the sense that its density approaches the Fejes Toth (1959) upper bound as the minimum distance approaches zero.

Spherical codes on torus layers

- Mathematics, Computer Science2009 IEEE International Symposium on Information Theory
- 2009

The torus layer spherical codes presented here exhibit good performance when compared to the well known apple-peeling, wrapped and laminated codes.

Constructive Spherical Codes on Layers of Flat Tori

- Physics, Computer ScienceIEEE Transactions on Information Theory
- 2013

A new class of spherical codes is constructed by selecting a finite subset of flat tori from a foliation of the unit sphere R2L and designing a structured codebook on each torus layer, which can be the image of a lattice restricted to a specific box in RL in each layer.

Structured spherical codes with asymptotically optimal distance distributions

- Mathematics, Computer Science2017 IEEE International Symposium on Information Theory (ISIT)
- 2017

It is shown that the distance spectrum of cyclic group codes achieves optimality in the sense of matching the random spherical code distance distribution bound as the block length grows large.

Flat tori, lattices and spherical codes

- Mathematics, Computer Science2013 Information Theory and Applications Workshop (ITA)
- 2013

The foliation of a sphere in an even number of dimensions by flat tori can be used to construct discrete spherical codes and also homogeneous curves for transmitting a continuous alphabet source over…

Asymptotic bounds for spherical codes

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- 2019

The main purpose of this article consists in extending the classical strategy of inventing explicit constructions of "good codes" and comparing new classes of codes with earlier ones to domain of spherical codes.

Gaussian source coding with spherical codes

- Mathematics, Computer ScienceIEEE Trans. Inf. Theory
- 2002

A wrapped Leech lattice shape quantizer is used to demonstrate a signal-to-quantization-noise ratio within 1 dB of the distortion-rate function for rates above 1 bit per sample, and an improvement over existing techniques of similar complexity.

Constructive spherical codes in 2k dimensions

- Computer Science, Mathematics2019 IEEE International Symposium on Information Theory (ISIT)
- 2019

This work presents a new approach to construct spherical codes in 2k dimensions, based on Hopf foliations, which outperforms some current constructive methods in several smalldistance regimes and constitutes a compromise between optimality and computational effort.

A heuristic approach for designing cyclic group codes

- Mathematics, Computer ScienceInt. Trans. Oper. Res.
- 2016

The obtained results assure that the heuristic approach have performance comparable to a brute-force search technique with the advantage of having low complexity, allowing for designing codes with a large number of points in higher dimensions.

Space frequency codes from spherical codes

- Mathematics, Computer ScienceProceedings. International Symposium on Information Theory, 2005. ISIT 2005.
- 2005

A new design method for high rate, fully diverse ('spherical') space frequency codes for MIMO-OFDM systems is proposed, which works for arbitrary numbers of antennas and subcarriers. The construction…

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