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WOLFRAM|DEMONSTRATIONS PROJECT

Probability in a Communication Channel

​
P(A)
0.6
P(X|A)
0.9
P(Y|A)
0.9
P(A) = 0.6
P(B) = 0.4
P(X)P(B)P(Y|A)+P(A)P(X|A) = 0.58
P(Y)P(A)P(X|B)+P(B)P(Y|B) = 0.42
P(A|X)
P(A)P(X|A)
P(X)
= 0.93
P(B|Y)
P(B)P(Y|B)
P(Y)
= 0.86
P(B|X)
P(B)P(X|B)
P(X)
= 0.07
P(A|Y)
P(A)P(Y|A)
P(Y)
= 0.14
In a binary communication system, the symbols 0 and 1 are sent through a channel, but noise can switch 1 to 0 or vice versa with certain probabilities. The error can be estimated by Bayes' rule.
Let
A
be the event of sending 0 (represented by
A0
) and
B
be the event of sending 1 (represented by
B0
), with corresponding probabilities
P(A)
and
P(B)
. On the receiving side,
X
and
Y
are the events of receiving 0 or 1. Represented by
X←0
and
Y←1
,
P(X|A)
is the probability of receiving 1 given that 0 was sent,
P(Y|B)
is the probability of receiving 1 given that 1 was sent,
P(A|X)
is the conditional probability of
A
given
X
, and so on.
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