is the number of bits which would have to be transmitted to identify X from N equally likely possibilities, less the relative entropy of the product distribution P U ( X ) P ( Y ) from the true joint distribution P ( X , Y ) — i.e. less the expected number of bits saved which would have had to be sent if the value of X were coded according to the uniform distribution P U ( X ) rather than the conditional distribution P ( X | Y ) of X given Y.