# channel capacity

tight upper bound on the rate at which information can be transmitted over the channel reliably (with arbitrarily small error).

it is defined as

\begin{equation}
C = \sup_{p(x)} I(X;Y)
\end{equation}

where

- \(X\) is the input
- \(Y\) is the output
- \(p(x)\) is the probablity distribution of inputs

This should be read as the maximum mutual information between the input and output over all possible distributions of inputs.