Bounds on packings of spheres in the Grassmann manifold

Correction to "Bounds on Packings of Spheres in the Grassmann Manifold"

Bounds on Packings of Spheres in the Grassmann Manifolds

We derive the Varshamov{Gilbert and Hamming bounds for packings of spheres (codes) in the Grassmann manifolds over R and C. The distance between two k-planes is deened as (p; q) = (sin 2 1 + +sin 2 k) 1=2 , where i ; 1 i k, are the principal angles between p and q.

Quantization Bounds on Grassmann Manifolds and Applications to MIMO Systems

This paper considers the quantization problem on the Grassmann manifold with dimension n and p. The unique contribution is the derivation of a closed-form formula for the volume of a metric ball in the Grassmann manifold when the radius is sufficiently small. This volume formula holds for Grassmann manifolds with arbitrary dimension n and p, while previous results are only valid for either p = ...

On Orthogonal Space-Time Block Codes and Packings on the Grassmann Manifold

We show that orthogonal space-time block codes may be identified with packings on the Grassmann manifold. We describe a general criterion for packings on the Grassmann manifold that yield coherent space-time constellations with the same code properties that make orthogonal space-time block codes so favorable. As an example, we point out that the rate 3/4 orthogonal space-time block code motivat...

Volume-minimizing Foliations on Spheres

The volume of a k-dimensional foliation F in a Riemannian manifold Mn is defined as the mass of image of the Gauss map, which is a map from M to the Grassmann bundle of k-planes in the tangent bundle. Generalizing the construction by Gluck and Ziller in [4], “singular” foliations by 3-spheres are constructed on round spheres S, as well as a singular foliation by 7-spheres on S, which minimize v...