Information Technology Reference
In-Depth Information
2
E
=
L
N
α
.
(10)
S,
mark
S
S
The parameters
E
S,mark
, BER
S
, and
L
S
can be used to represent imperceptibility, robust-
ness, and embedding capacity, respectively. It is obvious from Equations (9) and (10)
that there are conflicts between these basic specifications. With the same values of
I
and
N
, any improvement in one of the three specifications can only be made at some
cost of the other two.
It is clear that simply extending a single-bit scheme by superposition of mutually
independent sequences to achieve multi-bit embedding is not satisfactory because of
the direct conflicts between the three basic specifications. Achieving a higher capacity
by using a one-bit-per-sequence scheme implies increasing the total watermark en-
ergy therefore inevitably sacrificing the robustness and imperceptibility. The problem
is that every PN sequence is only mapped to a single bit in the watermark, and the
information carrying capacity is not fully exploited. In order to resolve this problem, a
novel scheme is introduced in the next section.
3 Multi-bit Watermarking with Addition
of Orthogonal Sequences
3.1
Embedding Procedure
The key to the proposed approach is a mapping between a set of orthogonal sequences
and groups of bits in the embedded data so that each sequence can carry more than
one bit. The embedding procedure is as follows.
i) Assume that there are
N
coefficients in the host signal available to modification
for watermark hiding. Thus, a total of
N
orthogonal sequences, Hadamard codes for
example, with a length of
N
bits and element values of either +1 or
1 can be found.
ii) Divide the
N
binary sequences into
R
=
N
/
M
subsets denoted
S
0
,
S
1
,
−
…
,
S
R
−
1
,
where
M
= 2
m
. Each subset contains
M
sequences: {
S
0,0
,
S
0,1
,
…
,
S
0,
M
−
1
}, {
S
1,0
,
S
1,1
,
…
,
S
1,
M
−
1
},
,
S
R
−
1,
M
−
1
}.
iii) Convert a meaningful watermark into binary, and expand the binary sequence
by padding zeros to yield an array of length
L
M
= 2
mR
. Truncate the binary sequence
if the length is greater than
L
M
.
iv) Segment the
L
M
bit binary sequence into 2
R
sections of length
m
. The
m
-bit bi-
nary numbers in these sections may be referenced to in decimal, denoted
W
= {
W
(0),
W
(1),
…
, {
S
R
−
1,0
,
S
R
−
1,1
,
…
1)}.
v) Divide
W
into two halves:
W
1
= {
W
(0),
W
(1),
…
,
W
(2
R
−
…
,
W
(
R
−
1)}, and
W
2
= {
W
(
R
),
W
(
R
+1),
1)}, and map the
M
possible values in each pair,
W
(
i
) and
W
(
i
+
R
)
from the two halves respectively, to the
M
sequences in the subset of the same index
i
.
vi) Add the sequences in
S
i
corresponding to
W
(
i
),
i
= 0, 1,
…
,
W
(2
R
−
1, to the host
data, and subtract the sequences in
S
i
corresponding to
W
(
i
+
R
),
i
= 0, 1,
…
,
R
−
…
,
R
−
1,
from the host data, respectively.
The arrangements of the watermark-carrying sequences and the watermark bits,
and the mapping between them are illustrated in Figure 1. In this way, each sequence
