@inproceedings{23e0f0c646ac49a5996f829ee0a191b6,
title = "Mutual information and MMSE in Gaussian channels",
abstract = "Consider arbitrarily distributed input signals observed in additive Gaussian noise. A new fundamental relationship is found between the input-output mutual information and the minimum mean-square error (MMSE) of an estimate of the input given the output: The derivative of the mutual information (nats) with respect to the signal-to-noise ratio (SNR) is equal to half the MMSE. This identity holds for both scalar and vector signals, as well as for discrete- and continuous-time noncausal MMSE estimation (smoothing). A consequence of the result is a new relationship in continuous-time nonlinear filtering: Regardless of the input statistics, the causal MMSE achieved at snr is equal to the expected value of the noncausal MMSE achieved with a channel whose SNR is chosen uniformly distributed between 0 and snr.",
author = "Dongning Guo and Shlomo Shamai and Sergio Verd{\'u}",
year = "2004",
doi = "10.1109/ISIT.2004.1365386",
language = "English (US)",
isbn = "0780382803",
series = "IEEE International Symposium on Information Theory - Proceedings",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "347",
booktitle = "Proceedings - 2004 IEEE International Symposium on Information Theory",
address = "United States",
note = "2004 IEEE International Symposium on Information Theory, ISIT 2004 ; Conference date: 27-06-2004 Through 02-07-2004",
}