Sphere-packing bounds in the Grassmann and Stiefel manifolds

Authors:
O. Henkel
Affiliations:
Fraunhofer German-Sino Lab for Mobile Commun. MCI, Berlin
Venue:
IEEE Transactions on Information Theory
Year:
2005

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Abstract

Applying the Riemann geometric machinery of volume estimates in terms of curvature, bounds for the minimal distance of packings/codes in the Grassmann and Stiefel manifolds will be derived and analyzed. In the context of space-time block codes this leads to a monotonically increasing minimal distance lower bound as a function of the block length. This advocates large block lengths for the code design