Information Technology Reference
In-Depth Information
carries
m
watermark bits, and all together
L
M
bits carried by 2
R
orthogonal sequences
are embedded. Note that
W
(
i
) and
W
(
i
+
R
) are independently embedded if they are
different. Otherwise, instead of subtracting
S
i
,
W
(
i
+
R
)
,
S
i
,
W
(
i
+
R
)+1
is added to the host data
where operation +1 in the subscripts are modulo-
R
. The watermark to be embedded is
now given in the following expression:
S
−
S
W
(
i
)
≠
W
(
i
+
R
)
ˆ
i
,
W
(
i
)
i
,
W
(
i
+
R
)
.
S
=
(11)
i
S
+
S
W
(
i
)
=
W
(
i
+
R
)
i
,
W
(
i
)
i
,
W
(
i
)
+
1
S
0
S
1
S
R
−
1
Mark-carrying sequences:
N
sequences in
R
subsets.
Each subset contains
M
sequences of
N
bits.
W
1
:
Watermark:
L
M
bits in
2
R
sections. Each sec-
tion contains
m
bits.
W
(0)
W
(1)
W
(R
−
1)
W
2
:
W
(
R
)
W
(1+
R
)
W
(2
R
−
1)
Fig. 1.
Embedding scheme: Organization of watermark-carrying sequences and watermark bits,
and the mapping
Finally, the watermarked data are obtained:
R
−
1
ˆ
∑
I
'
=
I
+
α
S
,
(12)
M
i
i
=
0
where
α
M
is the watermarking strength, which is different from
α
S
.
3.2
Watermark Extraction
Cross-correlations between the received data and the known sequences
S
i,
0
,
S
i
,1
,
,
and
S
i
,
M
−
1
, respectively, are calculated. If positive and negative peaks occur when cor-
related respectively with, say,
S
i
,
A
and
S
i
,
B
, and the magnitude of correlation with
S
i
,
B
is
no less than that both with
S
i
,
A+
1
and with
S
i
,
A
−
1
, a decision can be made that
W
(
i
) is
A
,
and
W
(
i
+
R
) is
B
. Otherwise,
W
(
i
+
R
) =
A
if the magnitude of correlation with
S
i
,
A+
1
is
greater than that with
S
i
,
A
−
1
, and
W
(
i
+
R
) =
A
…
1 if the reverse is true.
In this way, the entire watermark can be extracted from the received data. Figure 2
shows the correlation outputs between a subset of 128 orthogonal sequences and a
simulated received data. Two distinct peaks, one positive and the other negative, are
present. These 7 bit binary codes can represent any characters drawn from the 128
alphanumeric-character set. In this example, the extracted ASCII characters are 'c'
−
