Sphere packing bounds in the Grassmann and Stiefel manifolds

Details Sphere packing bounds in the Grassmann and Stiefel manifolds Sphere packing bounds in the Grassmann and Stiefel manifolds

2003-08-12

arxiv.org/abs/math/0308110v4

IEEE Transactions on Information Theory, vol 51, no 10, (2005), 3445-3456

Mathematics

Metric Geometry

Replaced with final version, 11 pages

Scientific paper

10.1109/TIT.2005.855594

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.

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