How small should the error probability be? Out of NN transmitted bits, on
the average
N
p
e
N
p
e
bits will be received in error. Do note the phrase "on the
average" here: Errors occur randomly because of the noise
introduced by the channel, and we can only predict the
probability of occurrence. Since bits are transmitted at a rate
RR, errors occur
at an average frequency of
R
p
e
R
p
e
. Suppose the error probability is an impressively small number
like
10-6
10
-6
. Data on a computer network like Ethernet is transmitted at a
rate
R=10 Mbps
R
10
Mbps
, which means that errors would occur roughly 100 per second.
This error rate is very high, requiring a much smaller
p
e
p
e
to achieve a more acceptable average occurrence rate for errors
occurring. Because Ethernet is a wireline channel, which means
the channel noise is small and the attenuation low, obtaining
very small error probabilities is not difficult. We do have some
tricks up our sleeves, however, that can essentially reduce the
error rate to zero without resorting to
expending a large amount of energy at the transmitter. We need
to understand digital channels and Shannon's Noisy
Channel Coding theorem.
