By Topic

MMSE Dimension

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Yihong Wu ; Dept. of Electr. Eng., Princeton Univ., Princeton, NJ, USA ; Verdu, S.

If N is standard Gaussian, the minimum mean square error (MMSE) of estimating a random variable X based on √(snr) X + N vanishes at least as fast as 1/snr as snr → ∞. We define the MMSE dimension of X as the limit as snr → ∞ of the product of snr and the MMSE. MMSE dimension is also shown to be the asymptotic ratio of nonlinear MMSE to linear MMSE. For discrete, absolutely continuous or mixed distribution we show that MMSE dimension equals Rényi's information dimension. However, for a class of self-similar singular X (e.g., Cantor dis tribution), we show that the product of snr and MMSE oscillates around information dimension periodically in snr (dB). We also show that these results extend considerably beyond Gaussian noise under various technical conditions.

Published in:

Information Theory, IEEE Transactions on  (Volume:57 ,  Issue: 8 )