Channel capacity Channel capacity of DMC is defined as the largest mutual information that can be transmitted over the channel in one use, maximized over all input probability assignments .
It is worth to observe that, whereas is a function of both the channel and the input probability assignment, C is a function only of the channel assignment! It is obvious that information can be transmitted at capacity, simply by using the appropriate input probability assignment. For the Symmetric Channel, misinformation:
, index is arbitrary, from 1 to D , as each row of contains same set of probabilities.
Capacity can be achieved by using inputs of equal probabilities, . For such channel:
and then,
. For the Binary Symmetric Channel :
and
It is worth to observe, that for such channel, if or , then, , capacity reaches the maximum value for the BSC, such channel is the noiseless one,
if , then , such channel is practically useless.
For the given models of input source (probability assignment) and BSC (bit error probability), rate of channel utilization can be calculated:
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