Similarly,
is the probability of error, given a ???0??? was transmitted. The overall error probability Pe involves the
weighted sum of the above conditional probabilities.
(8.8)
8.2 MONTE CARLO METHOD
In this section, we will present an error estimation technique known as the Monte Carlo method. Let
us consider the probability of error, given a 0 was transmitted, and denote this value as P0.
(8.9) P0 3
`
vth
f0(v) dv
Pe p(1) # P(eZ1) p(0) # P(eZ0)
P(eZ0) P(eZ1)
P(eZ0) 3
`
vth
f0(v) dv P(eZ1) 3
vth
`
f1(v) dv
P(b1 Q b2) 1 a
s2(Q^
) 3
`
`
[G(Y )]2 # fY (y) dy Q2
s2(Q^
) E5Q^
26 E25Q^
6
E5Q^
6 Q
E5Q^
6 3
`
`
G(Y) # fY (y) dy
Q^
G(Y)
which we will rewrite as follows, after redefining the integration limits:
(8.10)
where we have introduced the error detector h0(v), and it is defined as
(8.11)
We notice the error probability can then be represented in the following notation:
(8.12)
This can be estimated by the sample mean, given N is the number of bits observed.
(8.13)
The estimator ?†P
0(v) is sometimes called an error counter. Assume n bits have been observed to be in
error, out of the total N bits observed; then the error counter can be written as
(8.
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