In information theory, the Kraft–McMillan theorem establishes that any directly decodable coding scheme for coding a message to identify one value x i out of a set of possibilities X can be seen as representing an implicit probability distribution q ( x i ) = 2 − − ℓ ℓ i over X, where ℓ ℓ i is the length of the code for x i in bits. Therefore, relative entropy can be interpreted as the expected extra message-length per datum that must be communicated if a code that is optimal for a given (wrong) distribution Q is used, compared to using a code based on the true distribution P : it is the excess entropy.