Cryptography Reference
In-Depth Information
MD Encoder with
Watermark Embedding
MD Decoder with
Watermark Extraction
index
assignment
p
1
C
i
1
i
X
′
W
′
1
i
1
codeword
selection
Channel
1
MD
Decoder
l
1
(•)
VQ
−1
i
Embed
1
i
S
Embed
2
W
2
i
B
X
VQ
i
2
i
2
or
W
1
Channel
2
p
2
Gather
last bits
W
′
2
l
2
(•)
C
′
C
′′
Fig. 12.6.
The structure for embedding two watermarks with two descriptions for
transmission in MDC. The two independent channels have mutually independent
breakdown probabilities.
′
′′
′
′′
C
, and will
search for the tradeoff between watermark imperceptibility and watermark
robustness, in Sec. 12.7. For one index in C
C
=∅. We employ tabu search to split C into C
and C
′
, there is a one-to-one corre-
sponding counterpart, with the same subscript, in C
′′
′
t
. For example, let c
0,
2
denote the index for the current block X
k
, t∈
. When embedding
the first watermark, the output index i
S
, which denotes the index containing
Single
watermark for representing X
k
, is generated according to the value of
the watermark bit W
1,k
:
−1
c
′
t
, if W
1,k
=0;
0,
L
2
i
S
=
t∈
−1
,k∈[0,M
W
N
W
−1] . (12.6)
c
′′
t
, if W
1,k
=1;
Then, i
S
is fed into the MD encoder in Fig. 12.6 to embed the second water-
mark.
Embedding the Second Watermark
We employ the watermarking algorithm in Sec. 12.4 for embedding the second
watermark. It contains two parts. The first is to shift the watermarked index
i
S
to the left by one bit, and the second is to tag watermark bit W
2,k
to the
end of the shifted index. That is,
i
B
=(i
S
<< 1) + W
2,k
,
k∈[0,M
W
N
W
−1] ,
(12.7)
where i
B
denotes the index containing
Both
watermarks. This step is the
same as that in Eq. (12.5). Next, we make use of the MDSQ algorithms in
Fig. 12.3(b) for index assignment. The index assignments in Fig. 12.6, are
