Page "Information theory" Paragraph 72

Here X represents the space of messages transmitted, and Y the space of messages received during a unit time over our channel.

Let be the conditional probability distribution function of Y given X.

We will consider to be an inherent fixed property of our communications channel ( representing the nature of the noise of our channel ).

Then the joint distribution of X and Y is completely determined by our channel and by our choice of, the marginal distribution of messages we choose to send over the channel.

Under these constraints, we would like to maximize the rate of information, or the signal, we can communicate over the channel.

The appropriate measure for this is the mutual information, and this maximum mutual information is called the channel capacity and is given by: