# Minimum Mean Square Error (MMSE) and Mutual Information (I)

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 $I(X:Y)= E[log \frac {p_{X,Y}}{p_X p_Y}]$

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