Information Technology Reference
In-Depth Information
IDFT of the vector
Y
is now a real vector of length
N
2
. To avoid redundant computa-
tion, two real vectors of length
N
2
may be used as real and imaginary parts respec-
tively to form a complex vector of the same length. Nonetheless, the negative fre-
quency components are omitted for simplicity in the following discussion.
Among the
N
spectral lines (subcarriers) of the candidate frame, only
N
/4 are
modified, using a combination of QAM and dither modulation as illustrated in Fig.1,
by the embedded data while the other components are unchanged. The original
n
-th
spectral component
C
n
is first quantized to
Q
[
C
n
] in the complex plane. The intro-
duced distortion is determined by the quantization step
. The
n
-th watermark vector
W
n
is then added to
Q
[
C
n
] to produce a dithered spectral component
C'
n
:
[]
∆
C
'
=
Q
C
+
W
(4)
n
n
n
where
W
n
is obtained using QAM, representing
D
=2 bits of the stego-data. Schemes
other than QAM can also be used with different embedding capacity and robustness.
Let the magnitude of
W
n
be
so that all coded data are located at centers of the
grid quadrants as indicated by the circles in Fig.1. In the extreme case where
∆
2
2
=
max[|
C
n
|] thus
Q
[
C
n
]=0, the host spectral components in the selected band is com-
pletely replaced by
W
n
.
∆
j
⋅
2
∆
00
01
00
01
00
01
C
n
C'
n
10
11
11
10
W
n
j
⋅∆
Q
[C
n
]
01
00
01
00
10
11
10
11
10
11
0
∆
2
∆
3
∆
Fig. 1.
Dither modulation in the complex frequency plane
2.3
Synchronization Pilot
Synchronization is essential to correctly recover the embedded data. A search process
is used in the watermark detector to locate the encoded frame. For this purpose, a pilot
signal is attached to the data as a part of the embedded sequence. The pilot must not
take too large a portion of the watermark band and be easy to track. In the present
system, it is composed of a number of symbols (1
j
) corresponding to an
m
-sequence of length
L
and occupies the lower part of the watermark band. The pilot
is inserted into the signal spectrum in the same way as the mark symbols.
+
j
) and
−
(1
+
