DocumentCode
2946559
Title
Volume of geodesic balls in the complex Stiefel manifold
Author
Krishnamachari, Rajesh T. ; Varanasi, Mahesh K.
Author_Institution
Dept. of Electr. & Comput. Eng., Univ. of Colorado, Boulder, CO
fYear
2008
fDate
23-26 Sept. 2008
Firstpage
902
Lastpage
909
Abstract
Volume estimates of geodesic balls in Riemannian manifolds find many applications in coding and information theory. This paper computes the precise power series expansion of volume of small geodesic balls in a complex Stiefel manifold of arbitrary dimension. The volume result is employed to bound the minimum distance of codes over the manifold. An asymptotically tight characterization of the rate-distortion tradeoff for sources uniformly distributed over the surface is also provided.
Keywords
MIMO communication; channel coding; wireless channels; Riemannian manifolds; complex Stiefel manifold; geodesic balls volume; multiinput-multioutput channel; Channel state information; Computational geometry; Computational modeling; Feedback; Geophysics computing; Information theory; MIMO; Numerical simulation; Rate-distortion; Upper bound; Geodesic Ball Volume; Riemannian Geometry; Stiefel/Grassmann Manifold;
fLanguage
English
Publisher
ieee
Conference_Titel
Communication, Control, and Computing, 2008 46th Annual Allerton Conference on
Conference_Location
Urbana-Champaign, IL
Print_ISBN
978-1-4244-2925-7
Electronic_ISBN
978-1-4244-2926-4
Type
conf
DOI
10.1109/ALLERTON.2008.4797653
Filename
4797653
Link To Document