The mutual information of two random variables, X and Y, is defined to be

I(X,Y) = Sum(Pr(x,y).log(Pr(x,y)/(Pr(x).Pr(y))))

Where Sum() is the sum over the alphabets of both X and Y. Alternatively, the mutual information can be expressed more intuitively as


Where H(X) is the entropy of X and H(X|Y) is the conditional entropy of X on Y. This can be interpreted as as measure of the reduction in the uncertainty of X when we know the value of Y - in other words a measure of how much we learn about X by finding out the value of Y. The mutual information is symmetric, so we can equivalently write


which may be easier to evaluate in some cases.

The capacity of a noisy channel is defined to be the maximum value of the mutual information of the input and output variables with respect to input probability distribution.

Log in or registerto write something here or to contact authors.