Canonical coordinates and the geometry of inference, rate, and capacity

Author

Scharf, Louis L. ; Mullis, Clifford T.

Author_Institution

Dept. of Electr. & Comput. Eng., Colorado Univ., Boulder, CO, USA

Volume

48

Issue

3

fYear

2000

fDate

3/1/2000 12:00:00 AM

Firstpage

824

Lastpage

831

Abstract

Canonical correlations measure the cosines of principal angles between random vectors. These cosines multiplicatively decompose concentration ellipses for second-order filtering and additively decompose the information rate for the Gaussian channel. More over, they establish a geometrical connection between error covariance, error rate, information rate, and principal angles. There is a limit to how small these angles can be made, and this limit determines the channel capacity

Keywords

Gaussian channels; channel capacity; correlation methods; covariance matrices; filtering theory; Gaussian channel; canonical coordinates; capacity; channel capacity; concentration ellipse decomposition; cosines; covariance matrix; error covariance; error rate; inference geometry; information rate; principal angles; random vectors; second-order filtering; second-order inference; Channel capacity; Coordinate measuring machines; Error analysis; Estimation theory; Gaussian channels; Geometry; Helium; Information filtering; Information filters; Information rates;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.824676

Filename

824676