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... W; � � d(y,v)fY,V(y,v) ≤ σ 2 Z, (1) x∈X N y∈YN y∈YN v∈VN where d(x,y) = 1 �N N i=1 d(xi,yi). Costa considered the Gel’fand-Pinsker problem for the i.i.d. Gaussian case and mean square error distance =-=[5]-=-. The embedder ϕ produces Y = W + X, X ∼ N(0,σ 2 XIN) and the channel output is obtained as: V = X+W+Z, where Z ∼ N(0,σ 2 ZIN). The estimate of the message ˆm is obtained at the decoder as in the Gel’...

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...not indeed be the WCAA because of its infinite support. Vila-Forcén et al. [19] and Goteti and Moulin [9] solved independently the min-max problem for distortion-compensated dither modulation (DC-DM) =-=[3]-=- in terms of probability of error for the fixed decoder, binary signaling, the subclass of additive attacks in data-hiding and detection-formulation, respectively. The additional difference between th...

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...ed attention in the watermarking community. They are a practical implementation of a binning technique for channels whose state is non-causally available at the encoder considered by Gel’fand-Pinsker =-=[8]-=-. Recently it has been also demonstrated [13] that quantization-based data-hiding performance coincides with the spread-spectrum (SS) data-hiding at the low-WNR by taking into account the host statist...

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...ion codes. In general, the digital data-hiding can be considered as a game between the data-hider and the attacker. This three-party two-players game was already investigated by Moulin and O’Sullivan =-=[12]-=- where two set-ups are analyzed. In the first one, the host is assumed to be available at both encoder and decoder prior to the transmission, the so-called private game. In the second one, the host is...

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...fixes the encoder structure for the quantization-based methods. Although the optimal α ′ can easily be determined when the power of the noise is available at 3s4 the encoder prior to the transmission =-=[6]-=-, this is not always feasible for various practical scenarios. Nevertheless, the availability of the attacking power and of the attacking pdf is a very common assumption in most data-hiding schemes. W...

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...n noise (AWGN) is not the WCAA for discrete input alphabets such as pulse amplitude modulation in digital communications [10]. Similar conclusion for data-hiding was obtained by Pérez-González et al. =-=[14]-=-, who demonstrated that the uniform noise attack performs worse than the AWGN attack for some watermark-to-noise ratios (WNRs). In [15], PérezGonzález demonstrated that the AWGN cannot indeed be the W...

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...he group of WCAA conforms to the signal processing attacks and directly exploits the knowledge of the watermark statistics caused by the structured codebook design. We refer the interested readers to =-=[23, 24]-=- for more information about attacks classification. More recent studies [4, 17, 22] address the impact of security leakages in the scope of information-theoretic analysis for geometrically structured ...

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.... Somekh-Baruch and Merhav considered the data-hiding problem in terms of maximum achievable rates and error exponents. They assumed that the host data is available either at both encoder and decoder =-=[1]-=- or only at the encoder [16] and supposed that neither encoder nor decoder is aware of the attacker strategy. In their consideration, the class of potentially applied attacks is significantly broader ...

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...k for some watermark-to-noise ratios (WNRs). In [15], PérezGonzález demonstrated that the AWGN cannot indeed be the WCAA because of its infinite support. Vila-Forcén et al. [19] and Goteti and Moulin =-=[9]-=- solved independently the min-max problem for distortion-compensated dither modulation (DC-DM) [3] in terms of probability of error for the fixed decoder, binary signaling, the subclass of additive at...

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...considered the data-hiding problem in terms of maximum achievable rates and error exponents. They assumed that the host data is available either at both encoder and decoder [1] or only at the encoder =-=[16]-=- and supposed that neither encoder nor decoder is aware of the attacker strategy. In their consideration, the class of potentially applied attacks is significantly broader than in the previous study c...

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...imum likelihood (ML) decoding is applied. A similar game-theoretic analysis of the |M|-ary information detection problem, the so-called zero-rate spread spectrum watermarking problem, is performed in =-=[11]-=-. As in the previous case, it is assumed that the detector has the possibility to learn the statistics of the attacking channel. In both cases [11, 12], the results were obtained under the assumption ...

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...stance (MD) decoder is implemented as a low-complexity equivalent of the ML decoder under the assumption of a channel pdf created by the symmetric extension of a monotonically non-increasing function =-=[2]-=-. It is a common practice in the data-hiding community to measure the performance in terms of the error rate for a given decoding rule as well as the maximum achievable rate of reliable communications...

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...tion-based methods the mutual information is measured between the communicated message M and the channel output V [15] and the above problem is given by: maxφ min fV |Y (·|·) I φ,fV |Y (·|·)(M;V ′ ). =-=(13)-=- where V ′ = Q∆(V ) − V , since it was shown in [15] that modulo operation does not reduce the mutual information between V and M if the host is assumed to be flat within the quantization bins. Rewrit...

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...s worse than the AWGN attack for some watermark-to-noise ratios (WNRs). In [15], PérezGonzález demonstrated that the AWGN cannot indeed be the WCAA because of its infinite support. Vila-Forcén et al. =-=[19]-=- and Goteti and Moulin [9] solved independently the min-max problem for distortion-compensated dither modulation (DC-DM) [3] in terms of probability of error for the fixed decoder, binary signaling, t...

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...wer-limited attacks. McKellips and Verdu showed that the additive white Gaussian noise (AWGN) is not the WCAA for discrete input alphabets such as pulse amplitude modulation in digital communications =-=[10]-=-. Similar conclusion for data-hiding was obtained by Pérez-González et al. [14], who demonstrated that the uniform noise attack performs worse than the AWGN attack for some watermark-to-noise ratios (...

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... the knowledge of the watermark statistics caused by the structured codebook design. We refer the interested readers to [23, 24] for more information about attacks classification. More recent studies =-=[4, 17, 22]-=- address the impact of security leakages in the scope of information-theoretic analysis for geometrically structured and quantizationbased codebooks and general reversibility of watermark embedding. T...

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...he group of WCAA conforms to the signal processing attacks and directly exploits the knowledge of the watermark statistics caused by the structured codebook design. We refer the interested readers to =-=[23, 24]-=- for more information about attacks classification. More recent studies [4, 17, 22] address the impact of security leakages in the scope of information-theoretic analysis for geometrically structured ...

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... the knowledge of the watermark statistics caused by the structured codebook design. We refer the interested readers to [23, 24] for more information about attacks classification. More recent studies =-=[4, 17, 22]-=- address the impact of security leakages in the scope of information-theoretic analysis for geometrically structured and quantizationbased codebooks and general reversibility of watermark embedding. T...

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...gies, in the latter one the Bhatacharyya bound is exploited in order to reduce the complexity of the considered game optimization problem. Simultaneously, Vila-Forcén et al. [20] and Tzschoppe et al. =-=[18]-=- derived the WCAA for DC-DM using the mutual information as objective function for additive attacks and binary signaling. The goal of this paper is to provide an overview of the WCAA against quantizat...

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...stortion constraints. Their resistance against different attacks determine the possible application scenarios. An extensive review of various application of digital data-hiding techniques is given in =-=[21]-=-. The knowledge of the WCA allows to create a fair benchmark for data-hiding techniques and makes it possible to provide reliable communications with the use of appropriate error correction codes. In ...

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... of random ones. The most famous discrete approximations of Costa problem are known as DC-DM [3] and scalar Costa scheme (SCS) [6]. The structured codebooks are designed using quantizers (or lattices =-=[7]-=-) in order to achieve host interference cancellation. In the case of DC-DM, the stego data is obtained as follows: φDC-DM(m,x,α ′ ) = y = x + α ′ (Qm(x) − x), (2) where Qm(·) denotes a vector or scala...

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...conclusion for data-hiding was obtained by Pérez-González et al. [14], who demonstrated that the uniform noise attack performs worse than the AWGN attack for some watermark-to-noise ratios (WNRs). In =-=[15]-=-, PérezGonzález demonstrated that the AWGN cannot indeed be the WCAA because of its infinite support. Vila-Forcén et al. [19] and Goteti and Moulin [9] solved independently the min-max problem for dis...

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... the knowledge of the watermark statistics caused by the structured codebook design. We refer the interested readers to [23, 24] for more information about attacks classification. More recent studies =-=[4, 17, 22]-=- address the impact of security leakages in the scope of information-theoretic analysis for geometrically structured and quantizationbased codebooks and general reversibility of watermark embedding. T...