TY - GEN
T1 - Functional properties of MMSE
AU - Wu, Yihong
AU - Verdú, Sergio
PY - 2010
Y1 - 2010
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=77955686195&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=77955686195&partnerID=8YFLogxK
U2 - 10.1109/ISIT.2010.5513606
DO - 10.1109/ISIT.2010.5513606
M3 - Conference contribution
AN - SCOPUS:77955686195
SN - 9781424469604
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 1453
EP - 1457
BT - 2010 IEEE International Symposium on Information Theory, ISIT 2010 - Proceedings
T2 - 2010 IEEE International Symposium on Information Theory, ISIT 2010
Y2 - 13 June 2010 through 18 June 2010
ER -