Cryptography Reference
In-Depth Information
i
1
= l
1
(i
B
)andi
2
= l
2
(i
B
). They map the quantizer output index i
B
to the
two descriptions i
1
and i
2
.
After completing the embedding of W
1,k
and W
2,k
in X
k
, i
1
and i
2
are
transmitted over two memoryless and mutually independent channels with
erasure probabilities p
1
for Channel 1, and p
2
for Channel 2, respectively.
This procedure finishes when all the blocks X
k
, k∈[0,M
W
N
W
−1], are
processed and the relating indices are transmitted.
12.5.2 The Multiple Watermarks Extraction Algorithm
Corresponding to the watermark embedding algorithm, we describe the
schemes used for extracting the two embedded watermarks. It is an inverse
procedure to the multiple-watermark embedding process. We first extract the
second embedded watermark, then the first embedded one.
Extracting the Second Watermark and Obtaining the
Watermarked Reconstruction Containing W
1
At the decoder side in Fig. 12.6, the first step is to determine the outcome
i
′
B
from the received indices i
′
1
and i
′
2
with the MDSQ decoder by doing the
inverse of the index assignment process, l
−1
. Then, i
′
B
is shifted to the right
by one bit to smooth away the effects of watermark embedding,
′
S
=(i
′
B
>> 1) .
i
(12.8)
′
S
It next does a table look-up process on i
to obtain the codeword c
i
,0≤i≤
′
k
that contains the watermark bit W
1,k
.By
L−1. Then we find the block X
′
k
,0≤k≤M
W
N
W
−1, we obtain the watermarked
gathering all the blocks X
′
reconstruction X
, which contains the watermark W
1
.
When extracting W
2
, we do the estimation using the received indices to
determine the value of the watermark bits by using
′
′
W
2,k
= i
B
mod 2,
k∈[0,M
W
N
W
−1] ,
(12.9)
where mod denotes the modulus operation. Fig. 12.7 is a demonstration
of how W
′
2,k
is extracted. From Fig. 12.7, and by calculating the conditional
probabilities with two descriptions in MDC, one of the following conditions
will be satisfied.
(1) If both descriptions for one block X
k
are received, then the resulting index
decoded by using MDSQ can be then determined uniquely as shown in
Fig. 12.7. By visualizing the intersection between the row of the received
i
1
, and the column of the received i
2
. The estimated watermark bit W
′
2,k
is extracted by taking out the last bit from i
′
B
using Eq. (12.9).
