Sphere-packing bounds in the Grassmann and Stiefel manifolds

IEEE Transactions on Information Theory

Volumn 51, Issue 10, 2005, Pages 3445-3456

  Henkel, Oliver ^a  

^a FRAUNHOFER HEINRICH HERTZ INSTITUTE   (Germany)

Author keywords

Gilbert Varshamov Hamming bounds; Space time codes; Sphere packings; Stiefel Grassmann manifold

Indexed keywords

ENCODING (SYMBOLS); ESTIMATION; RAYLEIGH FADING; TRANSMITTERS; VECTORS;

GILBERT-VARSHAMOV/HAMMING BOUNDS; SPACE TIME BLOCK CODES; SPHERE PACKINGS; STIEFEL-GRASSMANN MANIFOLD;

BLOCK CODES;

EID: 26844444273     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2005.855594     Document Type: Article

References (17)

1. A. Barg and D. Nogin, "Bounds on packings of spheres in the Grassmann manifold" IEEE Trans. Inf. Theory, vol. 48, no. 9, pp. 2450-2454, Sep. 2002.
2. G. Han and J. Rosenthal, "Unitary Space Time Constellation Analysis: An Upper Bound for the Diversity" preprint, arXiv:math.CO/ 0401045, 2004.
3. B. Hochwald and T. Marzetta, "Capacity of a mobile multiple-antenna communication link in Rayleigh flat fading," IEEE Trans. Inf. Theory, vol. 45, no. 1, pp. 139-157, Jan. 1999.
4. B. Hochwald and T. Marzetta, "Unitary space-time modulation for multiple-antenna communications in Rayleigh flat fading," IEEE Trans. Inf. Theory, vol. 46, no. 2, pp. 543-565, Mar. 2000.
5. L. Zheng and D. N. C. Tse, "Communication on the Grassmann manifold: A geometric approach to the noncoherent multiple-antenna channel," IEEE Trans. Inf. Theory, vol. 48, no. 2, pp. 359-383, Feb. 2002.
6. V. Tarokh, H. Jafarkhani, and A. Calderbank, "Space-time block codes from orthogonal designs," IEEE Trans. Inf. Theory, vol. 45, no. 5, pp. 1456-1467, Jul. 1999.
7. H. Bölcskei, M. Borgmann, and A. Paulraj, "Space-frequency coded MIMO-OFDM with variable multiplexing-diversity tradeoff," IEEE Trans. Inf. Theory, submitted for publication.
8. H. Bölcskei and M. Borgmann, "Code design for noncoherent MIMO-OFDM systems," IEEE Trans. Inf. Theory, submitted for publication.
9. A. Edelman, T. Arias, and S. Smith, "The geometry of algorithms with orthogonality constraints," SIAM J. Matrix Anal. Appl., vol. 20, pp. 303-353, 1998.
10. W. Kühnel, Differential Geometry: Curves - Surfaces - Manifolds, ser. Student Mathematical Library. Providence, RI: AMS, 2002, vol. 16. German edition: Drferentialgeometrie: Kurven - Flächen - Mannigfaltigkeiten, Vieweg 1999.
11. J. Conway, R. Hardin, and N. Sloane, "Packing lines, planes, etc.: Packings in Grassmannian spaces," Exper. Math., vol. 5, pp. 139-159, 1996.
12. S. Gallot, D. Hulin, and J. Lafontaine, Riemannian Geometry, 2nd ed. Berlin, Germany: Springer, 1993.
13. X.-B. Liang and X.-G. Xia, "Unitary signal constellations for differential space-time modulation with two transmit antennas: Parametric codes, optimal designs, and bounds," IEEE Trans. Inf. Theory, vol. 48, no. 8, pp. 2291-2322, Aug. 2002.
14. M. Fozunbal, S. McLaughlin, and R. Schafer, "On performance limits of space-time codes: A sphere-packing bound approach," IEEE Trans. Inf. Theory, vol. 49, no. 10, pp. 2681-2687, Oct. 2003.
15. W. A. Poor, Differential Geometric Structures. New York: McGraw-Hill, 1981.
16. B. Hassibi, B. Hochwald, and T. Marzetta, "Space-time autocoding," IEEE Trans. Inf. Theory, vol. 47, no. 7, pp. 2761-2781, Nov. 2001.
17. J. Duistermaat and J. Kolk, Lie Groups. Berlin, Germany: Springer, 2000.