Consider this setting:


$Y=X+N$


where $N$ is a Gaussian standard random variable and $X$ is another arbitrarily distributed r.v. You can think of this $X$ as a message being transmitted over an AWGN channel the output of which is the r.v. $Y$. I am wondering if anybody can introduce me some good resources on the connection between $MMSE = E[(X- E[X|Y])^2]$ and mutualinput-output information, namely $I(X:Y)= E[log \frac {p\_{X,Y}}{p\_X p\_Y}]$ 



Minimum Mean Square Error (MMSE) and Mutual Information (I)
This must be extremely relevant


"Mutual Information and Minimum Mean-square Error in Gaussian Channels" by Dongning Guo, Shlomo Shamai (Shitz), and Sergio Verdu 


<http://arxiv.org/pdf/cs/0412108>


