Title :
Volume of geodesic balls in the real Stiefel manifold
Author :
Krishnamachari, Rajesh T. ; Varanasi, Mahesh K.
Author_Institution :
Dept. of Electr. & Comput., Colorado Univ., Boulder, CO
Abstract :
Volume estimates of balls in Riemannian manifolds find many applications in information theory such as in the determination of the rate-distortion trade off for the quantization of a source randomly distributed over such surfaces. This paper computes the precise power series expansion of volume of small geodesic balls in a real Stiefel manifold of arbitrary dimension. An application of the result obtained is also demonstrated.
Keywords :
differential geometry; information theory; series (mathematics); Riemannian manifolds; differential geometry; geodesic ball volume estimation; information theory; power series expansion; rate-distortion trade-off; real Stiefel manifold; source quantization; Algebra; Equations; Feedback; Geometry; Geophysics computing; Hilbert space; Information theory; MIMO; Quantization; Rate-distortion; Geodesic Ball Volume; Real Stiefel Manifold; Riemannian Geometry;
Conference_Titel :
Information Sciences and Systems, 2008. CISS 2008. 42nd Annual Conference on
Conference_Location :
Princeton, NJ
Print_ISBN :
978-1-4244-2246-3
Electronic_ISBN :
978-1-4244-2247-0
DOI :
10.1109/CISS.2008.4558560
