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and '5', corresponding to
W
(
i
)=99 and
W
(
i
+
R
)=53, respectively. Additive white
Gaussian noise has been added to the data with SNR = 30 dB. There is considerable
undulation in the correlation output because of the effects of the host data as well as
the noise. In this example the noise interference has not destroyed the watermark
detection, meaning that the method has certain noise resisting capability.
10
8
6
4
2
0
-2
-4
-6
-8
-10
0
20
40
60
80
100
120
140
Fig. 2.
Cross-correlation between a set of 128 sequences and received data. The data are con-
taminated by noise with SNR=30dB. The positive and negative peaks show that the two em-
bedded characters are 'c' and '5'
4
Performance Analysis
Suppose that
ρ
0
,W
(0)
is the cross-correlation between the detected data and
S
0,
W
(0)
. Ac-
cording to the central limit theorem,
2
2
σ
+
σ
1
N
−
1
[
]
∑
I
N
ρ
=
I
'
j
)
S
(
j
)
~
N
α
,
,
(13)
0
,
W
(
0
)
0
,
w
(
0
)
M
N
N
j
=
0
while the cross-correlations between the detected data and other sequences in
S
0
are
2
2
σ
N
σ
I
N
.
ρ
~
N
0
(14)
0
,
other
Thus, the probability density function of (
ρ
0
,W
(0)
−
ρ
0
,
other
) is
2
2
2
σ
+
σ
)
(
)
I
N
.
ρ
−
ρ
~
N
α
,
(15)
0
,
W
(
0
)
0
,
other
M
N
Therefore, the probability of
ρ
0
,W
(0)
being greater than one
ρ
0
,
other
can be obtained:
