Sphere packing bounds in the Grassmann and Stiefel manifolds

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 analysed. 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.