Title :
Functional properties of MMSE
Author :
Wu, Yihong ; Verdú, Sergio
Author_Institution :
Dept. of Electr. Eng., Princeton Univ., Princeton, NJ, USA
Abstract :
We show that the minimum mean-square error (MMSE) of estimating the input based on the channel output is a concave functional of the input-output joint distribution, and its various regularity properties are explored. In particular, the MMSE in Gaussian channels is shown to be weakly continuous in the input distribution and Lipschitz continuous with respect to the quadratic Wasserstein distance for peak-limited inputs. Regularity properties of mutual information are also obtained and some connections with rate-distortion theory are also drawn.
Keywords :
Gaussian channels; channel estimation; least mean squares methods; Gaussian channels; MMSE; channel estimation; channel input-output joint distribution; minimum mean square error; quadratic Wasserstein distance; Additives; Channel capacity; Data processing; Distributed computing; Gaussian channels; Gaussian noise; Mean square error methods; Mutual information; Rate-distortion; Signal to noise ratio;
Conference_Titel :
Information Theory Proceedings (ISIT), 2010 IEEE International Symposium on
Conference_Location :
Austin, TX
Print_ISBN :
978-1-4244-7890-3
Electronic_ISBN :
978-1-4244-7891-0
DOI :
10.1109/ISIT.2010.5513606
