The channel capacity of a communication channel, meaning a mathematical model that associates possible outputs with each input, is the supremum
of the rates at which information can be transmitted with arbitrarily small error.
For a discrete memoryless channel having input 
and output 
, it is
 |
where 
is the mutual information and the maximum is
taken over input statistical distributions 
.
For an additive white Gaussian noise channel constrained to bandwidth 
, average signal power 
, and average noise power 
, the Shannon-Hartley
theorem gives 
.
This operational channel capacity is distinct from the graph-theoretic Shannon
capacity, which describes zero-error communication.
