Efficient coherent phase quantization for audio watermarking

Abstract

The weighted overlap add (WOLA) technique is routinely used in audio processing to avoid introducing audible clicks. This process introduces inter-dependencies between WOLA coefficients and it is thus necessary to revisit watermarking algorithms to accommodate for such dependencies and prevent introducing self-inflicted interferences. In this paper, we focus on an existing phase quantization based audio watermarking system. Instead of the original computationally expensive ad-hoc process for dealing with the inter dependencies between WOLA coefficients, we introduce an alternative strategy. Experimental results show a notable reduction of the complexity while maintaining robustness performances.

Full text

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EFFICIENT COHERENT PHASE QUANTIZATION FOR AUDIO WATERMARKING
Xiao-Ming Chen, Gwena¨ el Do¨ err, Michael Arnold, and Peter G. Baum
Technicolor – Security & Content Protection Labs
ABSTRACT
The weighted overlap add (WOLA) technique is routinely used in
audio processing to avoid introducing audible clicks. This process
introduces inter-dependencies between WOLA coefficients and it
is thus necessary to revisit watermarking algorithms to accommo-
date for such dependencies and prevent introducing self-inflicted
interferences. In this paper, we focus on an existing phase quan-
tization based audio watermarking system. Instead of the original
computationally expensive ad-hoc process for dealing with the inter-
dependencies between WOLA coefficients, we introduce an alterna-
tive strategy. Experimental results show a notable reduction of the
complexity while maintaining robustness performances.
Index Terms— Signal coherent watermarking, phase quantiza-
tion, WOLA transform.
1. INTRODUCTION
Most watermarking systems can be reduced to a three steps process:
(i) apply some transform (e.g. DCT, DWT, etc) to an original content
and pseudo randomly select a set of transform coefficients, (ii) apply
a watermark embedding technique to the selected transform coeffi-
cients, and (iii) incorporate the modified coefficients and apply the
inverse transform to obtain the final watermarked content. It is com-
monly accepted that state-of-the art watermarking techniques, such
as spread-spectrum watermarking [1] or binning schemes [2], are
readily applicable when the transform produces independent trans-
form coefficients. Though manageable, dealing with correlated coef-
ficients is much more complex.
In practice, however, it may is needed to use transforms that
introduce inter-dependencies. In audio processing for instance, the
weighted overlap add (WOLA) mechanism inherently produces
correlated transform coefficients.
the appearance of audible clicks after processing an audio signal.
Using such transforms requires revisiting baseline watermarking
techniques so as to guarantee that the modifications introduced
by the watermarking process are coherent with the natural inter-
dependencies induced by the transform. This is a vital element
to avoid introducing undesired self-inflicted interferences between
watermark samples.
In this paper, we focus on a previously published audio water-
marking algorithm [3]. Section 2 details the characteristics of this
algorithm based on quantizing the phase of WOLA coefficients. It
also emphasizes an ad-hoc reference angles generation strategy nec-
essary to reduce the impact of the WOLA transform on the embed-
ding effectiveness of the watermarking algorithm. Section 3 then
analytically surveys the impact of the WOLA transform and derives
a simplified strategy to generate reference angles. Experimental re-
sults reported in Section 4 clearly demonstrates that the proposed
strategy reduces the computational complexity notably while main-
taining robustness performances. Finally, Section 5 reviews the find-
ings of the article and suggests further routes for investigations.
It is routinely used to prevent
2. PREVIOUS WORK
Over the last few years, a number of audio watermarking techniques
exploiting the analysis-synthesis framework have been proposed [4,
5]. In the remainder of this paper, we will focus on a previously
published audio watermarking system relying on phase quantization
in the WOLA domain [3].
2.1. The WOLA Domain
In audio processing, it is common practice to combine (i) filtering
along a temporally sliding window and (ii) a reconstruction mecha-
nism in an attempt to keep control over the psychoacoustic impact
of audio processing primitives. This is commonly referred to as the
analysis-synthesis framework, which the WOLA mechanism [6] is
simply an example of.
During the analysis phase of the WOLA process, the input audio
signal x is segmented in B-samples long blocks x(m)using a sliding
window with a hop-size of R samples. The discrete Fourier trans-
form (DFT) is then applied to each block. To avoid potential cross-
talk in the estimated spectrum, each block x(m)is multiplied by an
analysis window wAto obtain a windowed block ˜ x(m)before apply-
ing the DFT transform. The resulting collection of DFT-transformed
windowed blocks˜X(m)can subsequently be input to an audio pro-
cessing algorithm, e.g. watermarking.
During the synthesis phase of the WOLA process, the modified
blocks˜Y(m)output by the audio algorithm are used to reconstruct the
audio signal. First, the inverse discrete Fourier transform (IDFT) is
applied to the blocks in order to get back in the time domain. In
general, audio applications may involve non-linear spectral process-
ing and it is thus recommended to apply a synthesis window wSto
the blocks ˜ y(m)after the IDFT, so as to suppress audible artifacts by
fading out spectral modifications at block boundaries. Finally, the
resulting blocks y(m)are aligned according to the hop-size R before
being added together to obtain the output audio signal y.
In the remainder of this paper, we will abusively refer to em-
bedding the watermark in between the analysis and synthesis phases
as watermarking in the WOLA domain. Moreover, we will use a
half-window hop size (R = B/2) and the same sine windows w for
analysis and synthesis:
w[n] = wA[n] = wS[n] = sin
?πn
B
?
, 0 ≤ n < B.
(1)
This setup guarantees perfect reconstruction if the signal is not mod-
ified between the analysis and synthesis phases.
2.2. Watermarking in the WOLA Domain
The baseline audio watermarking system detailed in [3] basically re-
duces to embedding a watermark by quantizing the phase of WOLA
coefficients while maintaining psychoacoustic fidelity. Moreover, a
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correlation-based detector in the time domain is employed at the re-
ceiver side to retrieve the embedded watermark.
2.2.1. Phase Quantization-based Embedding
The embedding process consists in (i) extracting the phase1of
WOLA coefficients from incoming transformed blocks ˜X(m)and
arranging them sequentially in a 1-D signal ϕ, (ii) applying a
quantization based embedding algorithm to obtain the watermarked
phases ψ, and (iii) segmenting the resulting signal in B-samples
long blocks to reconstruct the watermarked transformed blocks˜Y(m)
which is inverse transformed back to the time domain.
Assuming that the system embeds symbols taken from an A-ary
alphabet A, the embedding process can be written:
ψ[i] = θa,K[i],
a ∈ A,
where θa,Kis a sequence of reference angles in [−π,π) associated to
the symbol a, pseudo-randomly generated from a secret key K. The
parameter S indicates that each symbol may be spread across several
WOLA blocks to guarantee robustness. This is a pure replacement
watermarking strategy: the output angles ψ are independent of the
input angles ϕ derived from the host signal x.
i ∈ S.B.N + [0 : S.B[,
(2)
Psycho-acoustic adaptation. Unfortunately, this straightforward
embedding strategy produces very audible artifacts and it is neces-
sary to slightly adjust the embedding protocol in practice, so as to
accommodate for the sensitivity of human auditory system. First,
the embedding process is limited to a specified frequency band F =
[fl, fh]. Angles below frequency tap flare discarded due to their high
audibility whereas angles above frequency tap fhare ignored be-
cause of their high variability. In addition, within F, the embedding
process is modified so that the angle difference δ[i] = |ψ[i] − ϕ[i]|
remains below psycho-acoustic slacks υ[i] ∈ [0,π] obtained after
spectra analysis [3, 7]. This can be formally written:
ψ[i]
=
ϕ[i] +
˚δ[i]
|˚δ[i]|
˚δ[i] = θa,K[i] − ϕ[i].
min
?
|˚δ[i]|,υ[i]
?
,
i ∈ B.N + [fl: fh]
with(3)
Controlling distortion this way guarantees that the introduced
changes are strictly inaudible.
Reference angles generation strategies. To generate the reference
angles θa,K, one could be tempted to generate for each symbol a a
sequence of angles in [−π,π) using a pseudo-random number gener-
ator seeded with the secret key K. Although intuitive and straightfor-
ward, this strategy results in very poor performances: the angles set
after embedding are severely distorted by the WOLA reconstruction
process i.e. without any subsequent attack.
To circumvent this issue, the original paper [3] used the follow-
ing ad-hoc generation strategy for each symbol a:
1. GenerateS+1
2
B-samples long white Gaussian noise patterns
directly in the frequency domain by combining a unit magni-
tude over the full spectrum and pseudo-randomly generated
angles ϑ(n)
respecting the symmetry property of the DFT of real signals;
2. Apply the IDFT to all the patterns and concatenate the result-
ing time-domain signals r(n)
long reference signal ra,Kin the time domain;
a,K, 0 ≤ n <
S+1
2, uniformly distributed over [−π,π)
a,Kto obtain a L =
S+1
2B-samples
1In this paper, all angles or angle differences lie in the interval [−π,π)
after appropriate modulo-2π operations, if not otherwise stated.
3. Apply the forward WOLA transform and retrieve the phase of
the resulting WOLA coefficients to obtain the S.B reference
angles θa,Kto be used for watermarking.
In other words, the reference angles θa,Khave already experienced
the WOLA transform and are thus less impacted by the subsequent
WOLA reconstruction process.
2.2.2. Correlation-based Detection in the Time Domain
At the receiver side, an audio signal z is presented to the detector
that may, or may not contain a watermark. Since the embedder re-
lies on quantization, a natural detection strategy would be to use
some nearest codeword identification technique. Still, this approach
is extremely sensitive to desynchronization and is computationnally
expensive if it needs to performed over some sliding window. In
their original paper [3], the authors suggested using a practical time
domain detector using cross-correlation.
For each potential symbol a, the following array of correlation
scores is computed:
ρz,a[l] =1
L
L−1
?
n=0
˘ z[n]˘ ra,K[n + l],
−L + 1 ≤ l ≤ L − 1(4)
where ˘ z its the whitened version of the tested audio signal z, ˘ ra,K
is the whitened version of time-domain reference signal ra,K, and
l is the correlation lag. Since the watermark is embedded in the
WOLA phase domain, spectral amplitudes are irrelevant for water-
mark detection. This is the reason why the tested/reference signals
are whitened prior to detection in order to eliminate potential in-
terferences from the host signal. The whitening process reduces to
(i) applying the forward WOLA transform to the tested/reference
signal, (ii) normalizing the magnitude of all WOLA coefficients
to 1, and (iii) applying the inverse WOLA transform to obtain the
whitened signal.
Eventually, the detector isolates the symbol ˆ a exhibiting the
highest correlation in absolute value:
ˆ a = argmax
a∈Aρz,a,
with
ρz,a= max
l
|ρz,a[l]|.
(5)
If the correlation score ρz,ˆ aexceeds a specified threshold τ, then the
tested signal z is considered to be watermarked and to carry the sym-
bol ˆ a. Otherwise, the tested signal is considered not to convey any
watermarking information.
3. EFFICIENT REFERENCE ANGLE GENERATION
The reference angles generation strategy described in Subsec-
tion 2.2.1 involves a number of (I)DFT transforms, which induce
a significant computational load. More precisely, computing the
S.B-samples long sequence θa,KrequiresS+1
S.B multiplications for windowing and S times length-B DFTs.
Assuming that B = 2pis a power of 2, performing a length-B
(I)DFT involves 2.B.p real multiplications and 2.B.p additions with
the Cooley-Tukey algorithm [8].
coefficients roughly needs 6.p real additions and 6.p + 2 real multi-
plications to be computed.
This section carefully analyzes the impact of the WOLA recon-
struction process to highlight an alternative means to generate the
reference angles θa,Kefficiently so as to facilitate the incorporation
of this watermarking algorithm onto embedded systems. For clarity,
2times length-B IDFTs,
In other words, each WOLA
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Fig. 1. Illustration of the reference angles generation in the original
audio watermarking system [3].
Figure 1 illustrates the previously described phase generation pro-
cess. It is straightforward to realize that the reference angles are de-
rived either from a single reference signal segment r(n)
or from two segments (WOL case).
a,K(WIN case)
3.1. WIN Case
In this setup, the WOLA transform reduce to the DFT of the multi-
plication of some pseudo-random reference signal r(n)
window w. Using an elementary property of the DFT, this is equiv-
alent to computing the circular convolution between the DFT of the
reference signal and the DFT of the sine window:
a,Kand the sine
˜R(m)
a,K[u] =1
B
B−1
?
v=0
ejϑ(n)
a,K[v]W[< u − v >],
(6)
where the notation < n >= n − ?n
which maps any integer to the interval [0, B). The DFT of the sine
window defined in Equation (1) is real valued and equal to:
B?B indicates the modulo operation
W[u] =
−sin(π
B) − cos(2π
B)
cos(π
Bu),
0 ≤ u < B.
(7)
This spectrum is characterized by the fact that most its energy is
concentrated around u = 0, leading to the following approximation:
˜R(m)
a,K[u] ≈1
B
Lw
?
v=−Lw
ejϑ(n)
a,K[<u−v>]W[< v >],
(8)
when only the 2.Lw+1 dominant terms of W are kept. Moreover, W
being symmetric, the previous equation can be further reduced to:
˜R(m)
a,K[u]≈W[0]
B
ejϑ(n)
a,K[u]+
Lw
?
v=1
W[v]
B
?
ejϑ(n)
a,K[<u−v>]+ ejϑ(n)
a,K[<u+v>]?
. (9)
The Lw+ 1 coefficients W[< v >] do not depend of the secret key
K, and can thus be precomputed and stored in a lookup table for
later use. In the WIN setup, each WOLA coefficients can then be
computed with 2.Lw+1 real multiplications and 4.Lwreal additions.
3.2. WOL Case
In this setup, the block r(m−1)
structed by concatenating segments of the sequences derived from
a,K
input to the WOLA process is con-
the angles ϑ(n−1)
WOLA transform can be written:
a,K
and ϑ(n)
a,K. The spectrum of this block prior to
R(m−1)
a,K[u] =(−1)u
2
B−1
?
?
F[v](−1)u−v?
ejϑ(n−1)
a,K
[u]+ ejϑ(n)
a,K[u]?
ejϑ(n−1)
+1
B
v=0
a,K
[<u−v>]+ ejϑ(n)
a,K[<u−v>]?
,(10)
where the spectrum F is defined as follows:
F[v] =
⎧⎪⎪⎨⎪⎪⎩
1−(−1)v
1−ej2πv
0
B
if v ? 0,
if v = 0.
(11)
As in the WIN case, the WOLA process then reduces to a circular
convolution with W and the WOLA coefficients can be rewritten:
R(m−1)
a,K[u] =1
B
B−1
?
B−1
?
v=0
W[v](−1)u−v
2
?
ejϑ(n−1)
ejϑ(n−1)
a,K
[<u−v>]+ ejϑ(n)
a,K[<u−v>]?
a,K[<u−v>]?
+1
B
v=0
G[v](−1)u−v?
a,K
[<u−v>]+ ejϑ(n)
,(12)
where G is the circular convolution of W and F. For the sine win-
dow defined in Equation (1), the expression of G can be analytically
derived and is given by:
G[v] =(−1)v
2
⎛⎜⎜⎜⎜⎜⎜⎝−1 + j
sin
?π
?2πv
− cos
B
?
cos
B
??2πv
B
?
⎞⎟⎟⎟⎟⎟⎟⎠
(13)
Again, most of the energy of G is concentrated around v = 0 and
derivations can be simplified by keeping only the 2.Lg+ 1 most sig-
nificant terms. Moreover, the spectrum G in this narrow band is
heavily dominated by the imaginary component, which allows to ig-
nore the real component in the previous equation. Putting everything
altogether, WOLA coefficients can be expressed as follows:
R(m−1)
a,K[u] ≈1
B
Lw
?
Lg
?
v=−Lw
W[< v >](−1)u−v
2
?
ejϑ(n−1)
a,K
[<u−v>]+ ejϑ(n)
a,K[<u−v>]?
a,K[<u−v>]?
+1
B
v=−Lg
G[< v >](−1)u−v?
ejϑ(n−1)
a,K
[<u−v>]+ ejϑ(n)
. (14)
By storing appropriate pre-computed coefficients in lookup tables
and exploiting the (a)symmetric properties of the spectra W and G,
it is then possible to compute each WOLA coefficient in the WIN
setup with 2.Lw+ 2.Lg+ 2 real multiplications and 8.Lw+ 8.Lg+ 2
real additions.
4. EXPERIMENTAL RESULTS
For experiments, the block length B has been set to 1,024 samples
(i.e. p = 10) and each embedded symbol a is spread over S = 31
blocks. In other words, each watermarked symbol requires 16 k sam-
ples for embedding. Additionally, the frequency range for embed-
ding has been limited to 300–10,000 Hz, For PCM audio sampled at
48 kHz, it implies that 418 WOLA coefficients are modified by the
embedding process instead of 1,024. The next subsections clearly
demonstrate that the proposed phase generation technique succeeds
in decreasing the computational load while maintaining similar ro-
bustness performances.
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Table 1. Benchmarking results. Detection rate (%) for the original
scheme are given in brackets. No false positive was observed during
benchmarking.
Lossy compression
mp3mp3Pro
79 (80) 94 (94)
86 (86)61 (65)
27 (28) 27 (27)
Bit rate
64 kb/s
48 kb/s
32 kb/s
AAC
85 (85)
49 (50)
22 (23)
ACC+
95 (95)
58 (58)
9 (8)
Additive white Gaussian noise (AWGN)
SNR 20 dB
65 (65)
10 dB
33 (32)
3 dB
12 (12)
4.1. Detection SNR Preservation
To evaluate the impact of the WOLA reconstruction process on the
generated reference sequences, the detection signal-to-noise ratio
(SNRdet) is introduced:
SNRdet?
var{ra,K[n]}
var{ra,K[n] − ˘ z[n]}.
(15)
For calibration, the psycho-acoustic adaptation module has been
disabled and a zero-mean Gaussian signals have been used as host
signals. While using purely random reference angles leads to a de-
tection SNR of 3.3 dB, the original phase generation process actually
raises this performances metric up to 12.2 dB. It clearly highlights
that the WOLA process naturally introduces inter-dependencies
between coefficients and that if, the watermarking process do not
mimic them in some way, the WOLA reconstruction process will
self-damage the embedded watermark signal even in the absence of
any attack. Using the newly proposed reference angles generation
mechanism with parameters Lw= 2 and Lg= 3 has been found to
yield a similar detection SNR i.e. around 12 dB.
4.2. Computational Complexity Reduction
Using the original scheme, computing a WOLA coefficient requires
60 real additions and 62 real multiplications. In contrast, the pro-
posed strategy only requires in average around 24 real additions and
8 real multiplications per coefficient with the parameters setup ob-
tained after calibration (Lw= 2 and Lg= 3). This is a computational
gain of roughly a factor 4. However, in practice in our implementa-
tions on embedded systems, we observed a reduction from 34 kCy-
cles to 13 kCycles corresponding to a computational gain of a factor
of approximately 2.6. The difference is due to the fact that our im-
plementation is not optimized assembler but C code. Furthermore
we observed that the not optimal random memory access in the em-
bedded device has a significant influence on the computational load.
Nevertheless the achieved computational gain enables the real-time
generation of the references, which would otherwise not be possible
in the set-up used.
4.3. Benchmarking
As a sanity check, both variants of the audio watermarking scheme
were submitted to an intensive benchmarking campaign including a
wide scope of signal processing primitives (AWGN, filtering, lossy
compression, denoising, desynchronization, etc) and involving 100
different audio files with a total play length of more than 7 hours.
Due to the lack of space, we only report in Table 1 the detection
rates under lossy compression using a variety of audio codecs with
bit rates up to 64 kb/s and under additive white Gaussian noise. The
findings are similar in all cases: the proposed algorithm for reference
angles generation does not incur any notable performances loss.
5. CONCLUSION
To facilitate integration onto embedded systems, this paper revisited
a previously published audio watermarking system relying on some
reference angles in the WOLA domain for embedding [3]. The
WOLA reconstruction process introduces some inter-dependencies
between transform coefficients which need to be properly taken
into account during watermarking to avoid introducing self-inflicted
interferences. This phenomenon was originally addressed with a
computationally expensive procedure and the paper proposed an
alternate strategy by reducing the original procedure to a couple of
frequency-domain short-length convolutions. Experimental results
clearly demonstrate that this new strategy reduces computational
complexity while maintaining robustness.
This paper focuses on making the embedded watermark coher-
ent with the inter-dependencies imposed by a transform and nicely
complements other works aiming at making the embedded water-
mark coherent with the natural redundancy of the host signal itself,
either for higher security issues [9] or for guaranteed embedding ef-
fectiveness [10]. Futureworkwillbededicatedtoanalyzingindepth
the effects of the WOLA process in an attempt to further decrease the
amount of self-inflicted interferences. For instance, the magnitude of
the host signal spectrum is likely to play a role at embedding time
which is not yet fully understood.
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