|
Consider a communication system. If a string of 0s and 1s are sent at a transmitter (signal) then one would expect the same string of 0s and 1s to arrive at the receiver (response). However, due to noise conditions, some 0s are mistakenly received as 1s and some 1s may be mistakenly received as 0s. Suppose the probability of wrongly classifying a 0 as 1 is p and the probability of wrongly classifying a 1 as 0 is q.
|
Process A
|
Output 0
|
Output 1
|
Total
|
|
Input 0
|
n(1- p )
|
np
|
n
|
|
Input 1
|
mq
|
m(1- q )
|
m
|
|
Total
|
n - np + mq
|
m + np - mq
|
n + m
|
How does one ensure transmission of digital signals with least error; i.e. a high Signal-to-Noise ratio?
How do we do it?
Our strategy is as follows:
This is a digital system where p and q must both be leveled and then reduced. That is, p and q must first be made approximately equal and then reduced. Consequently, any comparison of process performance must include leveling.
|
Process A
|
Output 0
|
Output 1
|
Total
|
|
Input 0
|
1 - p
|
p
|
1
|
|
Input 1
|
q
|
1 - q
|
1
|
|
Total
|
1 - p + q
|
1 - q + p
|
2
|
|
