Abdellatif Zaidi

Audio watermarking under desynchronization and additive noise attacks

Digital watermarking is often modeled as the transmission of a message over a noisy channel denoted as watermark channel. Distortions introduced by the watermark channel result mainly from attacks and may include interference from the original signal. One of the main differences with classical transmission situations stems from the fact that perceived distortions have to be taken into account. However, measuring the perceived impact an attack has on a watermarked signal is currently an unsolved problem. Possible means of circumventing this problem would be 1) to define the distortion in a so-called perceived domain and define an ad hoc equivalence between objective and perceived distortion or 2) to define an equivalent distortion by removing from the attack noise the part that is correlated to the host signal. This paper concentrates on the second approach and first shows that the resulting equivalent attack is a particular case of a thoroughly studied channel: filtering plus additive noise. However, the approach in this paper emphasizes the fact that the additive noise in the model has to be decorrelated with the signal. Then, the formalism is applied to (desynchronization plus noise) attacks on audio signals. In this context, this paper provides the corresponding capacities, as well as optimal attack and defense strategies in a game theory context.

Modulo lattice additive noise channel for QIM watermarking

Information embedding has recently been recognized as power-limited communication over a super-channel with state information non-causally known at the encoder. Based on this equivalence many encoding schemes have been proposed. Quantization index modulation (QIM) family has emerged as an asymptotically information-theoretically optimal embedding function. Optimum transmission rates are achieved when both the watermark-to-noise ratio (WNR) and quantizers dimensionality become sufficiently large. At low WNR however, a trade-off between transmission rate and robustness should be found. This paper is concerned with deriving lattice encoding performances over the resulting modulo lattice additive noise channel (MLAN) for both high and low WNR regimes. To this end, some lattices with good packing and quantizing properties are used and corresponding capacity and bit-error rate (BER) curves are provided for both regular QIM, and distortion-compensated QIM.

Scalar scheme for multiple user information embedding

Multiple watermarking is concerned with embedding several messages into the same host signal, with different robustness and transparency requirements. This paper proposes two implementable scalar schemes for multiple user dirty paper coding. The first - straightforward - approach consists of an independent superposition of two scalar dirty paper coding schemes. The second consists in the joint design of a scalar dirty paper coding. This joint approach is based on the ideal dirty paper coding scheme for broadcast channels with noncausal side information known to the transmitter. For this purpose, the scalar Costa scheme that has been originally conceived for one user is extended to two users. Performance evaluations, including bit error rates and capacity region curves are provided for both methods, illustrating the improvements brought by a joint design.

On Channel Sensitivity to Partially Known Two-sided State Information

In some situations of channel coding with state information (CCSI), the encoder and/or the decoder may not have perfect knowledge of the state information. In these situations, the state information may be viewed as the sum of a dominant (nominal) state information and a relatively weak perturbation. We consider the general case of channel with arbitrary pair of independent and identically distributed (i.i.d), possibly correlated, state information (S1, S2) available at the transmitter and at the receiver, respectively. We first analyze the decrease in capacity, or channel sensitivity to this perturbing noise. Both lower and upper bounds on this channel sensitivity are provided, using Fisher Information. The lower bound turns to be relatively tight, at low Signal-to-Noise-Ratio (SNR), in the Gaussian case, for which we provide a closed form expression of channel capacity degradation. Next, we show that these results can be used so as to increase system immunity to noise, by adapting the encoder to the channel uncertainty. Also, we straightforwardly extend these results to the more practical case where the state information is known only causally at the transmitter. Finally, for illustration purposes, two possible applications in the non-causal and the causal case, respectively, are discussed.

On Coding With a Partial Knowledge of the State Information

In some situations of channel coding with state information (CCSI) available at the transmitter, the encoder may not have perfect knowledge of the state information. In these situations, the state information may be viewed as the sum of a dominant (nominal) state information and a relatively weak perturbation. We analyze the decrease in capacity, or sensitivity of channel capacity to this perturbing noise. We first address the decrease in Gelfand-Pinsker capacity due to the situation and use Fisher information to give both lower and upper bounds on channel sensitivity. These bounds translate to upper and lower bounds on channel capacity, respectively. We also provide closed form expression of channel sensitivity in the Gaussian case and discuss the practical usefulness of the above bounds. For instance, we show that under certain conditions, the encoder should adapt to the available knowledge of the channel by changing its encoding strategy. Next, we show that these results can be straightforwardly extended to the general vector channel case and to the case when the state information is known only causally. Finally, for illustration purposes we give two possible applications in the non-causal and the causal case, respectively

Mac Aware Coding Strategy for Multiple User Information Embedding

Multiple user information embedding is concerned with embedding several messages into the same host signal. While emphasizing the tight relationship with conventional multiple user information theory, this paper presents several implementable dirty paper coding (DPC) based schemes for multiple user information embedding. These are obtained by exploring strong connections with the well-known Gaussian multiple access channel (MAC) with state information at the encoders. Two practical schemes are compared. The first -rather intuitive- consists in a straightforward superimposition of DPC schemes. The second consists in a joint design of these dirty paper coding schemes, based on the ideal DPC-based coding for the equivalent MAC channel. These results extend to the multiple user case the practical implementations (QIM and SCS) that have been originally conceived for one user. Then, we extend the results to a more general coding based on lattice (vector) codebooks, showing that the gap to full performances can be bridged up by using finite dimensional lattice codebooks, at the cost of an increased computational complexity. The improvements brought by a joint design are illustrated by bit error rates curves and achievable rates region

A scaled signal plus noise model for digital watermarking, application to time jitter

Digital watermarking is often modelled as the transmission of a message over a noisy channel denoted as watermark channel. Distortions introduced by the watermark channel result mainly from attacks but, depending on the attack, may include interference from the original signal. One of the main-differences with classical transmission situations comes from the fact that only perceptual distortions have to be taken into account. However, measuring the perceptual impact an attack has on a watermarked signal is currently an unsolved problem. Possible means of circumventing this problem would be (i) to define the distortion in a so-called perceptual domain and defining an ad hoc equivalence between objective and perceptual distortion, or (ii) to define an equivalent distortion, by removing from the attack noise the part that is correlated to the host signal. We concentrate on the second approach, and first show that the resulting equivalent attacks is a particular case of a thoroughly studied channel: attacks by filtering plus additive noise. However, our approach emphasizes the fact that the additive noise has to be decorrelated with the signal. Finally, the method is applied to desynchronization attacks on audio signals, provides the corresponding capacities, and outlines further work.

An Efficient Low Bit-Rate Information Embedding Costa Based Scheme using a Perceptual Model

In this paper, we propose an audio watermarking scheme based on the scalar Costa scheme specifically calibrated with a perceptual model allowing to increase the embedding power. For our study, this scheme is designed to be efficient for low bit-rate embedding with sufficient robustness to channel degradations. We present here the main characteristics of our scheme and the way for introducing perceptual models in such a Costa based watermarking scheme without introducing any noticeable artifacts. An evaluation of the robustness of the embedding system is also theoretically discussed by the way of the main channel attack : additive noise from low to high level. We illustrate its relevance in practice using Monte Carlo simulations.

Time jitter versus additive noise in a game theory context

Imperfectly synchronized watermark communication is almost the most hostile watermark channel. A desynchronization attack can yield a very high probability of bit error rate by simply moving the watermark from elements it has been embedded in, inhibiting hence its reliable retrieval from the original. In this paper, we adress attacks that can be modelled by an Additive White Gaussian Noise and Jitter (AWGN&J) channel in a game theory context. The AWGN&J channel was initially introduced to model local time fluctuations in the context of magnetic recording media. This channel is first briefly presented and characterized in terms of induced objective and perceptual distorsions. Also, performance loss of the one-bit watermarking Spread-Spectrum based scheme over an AWGN&J channel is derived. Then, results are applied in a game theoretic context to answer some questions such as: (i) for a given distortion budget, and from the attacker point of view, what part should be allocated to the desynchronization, and what part should be allocated to the additive noise?, (ii) from the defender point of view, what is the worst distortion? and (iii) is there means to countermeasure the attacker (limit the amount of objective distorsion)?