Formal Definition
Let X represent the space of signals that can be transmitted, and Y the space of signals received, during a block of time over the channel. Let
be the conditional distribution function of Y given X. Treating the channel as a known statistic system, is an inherent fixed property of the communications channel (representing the nature of the noise in it). Then the joint distribution
of X and Y is completely determined by the channel and by the choice of
the marginal distribution of signals we choose to send over the channel. The joint distribution can be recovered by using the identity
Under these constraints, next maximize the amount of information, or the message, that one 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
Read more about this topic: Channel Capacity
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