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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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1 Answer 1

up vote 2 down vote accepted

Do the names Guo, Shamai and Verdu ring any bells? :)

Check out the following two papers by these guys. They are comprehensive and are probably just what the doctor ordered.

http://www.princeton.edu/~verdu/reprints/GuoShaVer.Apr2005.pdf

http://www.princeton.edu/~verdu/reprints/GuoWuShaVer2011.pdf

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This is excellent Sevekatr. I had seen these papers before, though. I am looking for a more detailed presentation of the topic. Maybe a textbook or so. –  Farshid May 29 '11 at 16:27
    
@Farshid - These are recent results, so I'm not sure if any textbook covers them. I feel that these papers are the best resource for these results as of now. –  svenkatr May 29 '11 at 17:52

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