Channel capacity

In electrical engineering, computer science and information theory, channel capacity is the tight upper bound on the rate at which information can be reliably transmitted over a communications channel.

By the noisy-channel coding theorem, the channel capacity of a given channel is the limiting information rate (in units of information per unit time) that can be achieved with arbitrarily small error probability.

Information theory, developed by Claude E. Shannon during World War II, defines the notion of channel capacity and provides a mathematical model by which one can compute it. The key result states that the capacity of the channel, as defined above, is given by the maximum of the mutual information between the input and output of the channel, where the maximization is with respect to the input distribution.

The notion of channel capacity has been central to the development of modern wireline and wireless communication systems, with the advent of novel error correction coding mechanisms that have resulted in achieving performance very close to the limits promised by channel capacity.

Let ${\displaystyle X}$ and ${\displaystyle Y}$ be the random variables representing the input and output of the channel, respectively. Let ${\displaystyle p_{Y|X}(y|x)}$ be the conditional distribution function of ${\displaystyle Y}$ given ${\displaystyle X}$, which is an inherent fixed property of the communications channel. Then the choice of the marginal distribution ${\displaystyle p_{X}(x)}$ completely determines the joint distribution ${\displaystyle p_{X,Y}(x,y)}$ due to the identity

...
Wikipedia