Roman Tzschoppe

Scalar Costa scheme for information embedding

Research on information embedding, particularly information hiding techniques, has received considerable attention within the last years due to its potential application in multimedia security. Digital watermarking, which is an information hiding technique where the embedded information is robust against malicious or accidental attacks, might offer new possibilities to enforce the copyrights of multimedia data. In this paper, the specific case of information embedding into independent identically distributed (IID) data and attacks by additive white Gaussian noise (AWGN) is considered. The original data is not available to the decoder. For Gaussian data, in 1983, Costa proposed a scheme that theoretically achieves the capacity of this communication scenario. However, Costas scheme is not practical. Thus, several research groups have proposed suboptimal practical communication schemes based on Costas idea. The goal of this paper is to give a complete performance analysis of the scalar Costa scheme (SCS), which is a suboptimal technique using scalar embedding and reception functions. Information theoretic bounds and simulation results with state-of-the-art coding techniques are compared. Further, reception after amplitude scaling attacks and the invertibility of SCS embedding are investigated.

Lattice Costa schemes using subspace projection for digital watermarking

A general watermarking scheme employing lattice quantization is proposed and analyzed. This scheme is based on the equivalence of embedding in digital watermarking and transmission over so-called modulo-A channels. Main intention is to increase the maximum data rate which can be transmitted reliably (Shannon capacity of the scheme), tolerating a certain embedding and attack distortion. For this, a general concept of embedding in a subspace rather than the signal space itself is discussed, by which the capacity can be increased particularly for very low watermark-to-noise ratios. Numerical results show that the eight-dimensional Gosset lattice seems to be a promising compromise between achievable capacity and complexity in blind digital watermarking.

Noncoherent continuous-phase modulation for DS-CDMA

The combination of continuous phase modulation (CPM) with direct-sequence code-division multiple access (DS-CDMA) for multiuser transmission over the additive white Gaussian noise channel is discussed. Concentrating on the important special case of generalized minimum-shift keying, particularly simple receiver structures are obtained. To emphasize on low complexity, noncoherent reception is proposed and appropriate transmitter and receiver designs are provided. The application of reduced-state noncoherent sequence detection and noncoherent filter adaptation ensures high power efficiency and robustness against channel phase variations. Simulation results confirm that the chosen approach of CPM for DS-CDMA achieves high performance with very moderate complexity.

Channel model for watermarks subject to desynchronization attacks

One of the most important practical problems of blind Digital Watermarking is the resistance against desynchronization attacks, one of which is the Stirmark random bending attack in the case of image watermarking. Recently, new blind digital watermarking schemes have been proposed which do not suffer from host-signal interference. One of these quantization based watermarking scheme is the Scalar Costa Scheme (SCS). We present an attack channel for SCS which tries to model typical artefacts of local desynchronization. Within the given channel model, the maximum achievable watermark rate for imperfectly synchronized watermark detection is computed. We show that imperfect synchronization leads to inter-sample-interference by other signal samples, independent from the considered watermark technology. We observe that the characteristics of the host signal play a major role in the performance of imperfectly synchronized watermark detection. Applying these results, we propose a resynchronization method based on a securely embedded pilot signal. The watermark receiver exploits the embedded pilot watermark signal to estimate the transformation of the sampling grid. This estimate is used to invert the desynchronization attack before applying standard SCS watermark detection. Experimental results for the achieved bit error rate of SCS watermark detection confirm the usefulness of the proposed resynchronization algorithm.

Signal shaping for peak-power and dynamics reduction in transmission schemes employing precoding

Precoding, i.e., nonlinear pre-equalization, at the transmitter side has been proved to be a very efficient strategy for channel equalization in single-carrier digital transmission schemes. It enables the application of coded modulation in a seamless fashion. A drawback of precoding is that the signal at the input of the decision device exhibits a huge dynamic range. Based on dynamics shaping, a combined precoding/shaping technique introduced in the paper by Fischer et al. (1995), a new shaping strategy is developed in this paper. This technique enables a flexible tradeoff among: (1) reduction of the average transmit power; (2) avoidance of peaks in the transmit signal in order to facilitate line driver implementation; and (3) restriction of the maximum amplitude at the receiver side to a prescribed value. Over a wide range, all three demands can be met simultaneously. As the scheme is fully compatible with Tomlinson-Harashima (1971, 1972) precoding, it can replace the precoder even in existing and standardized schemes. Simulation results for a typical digital subscriber line scenario show the achievable gains.

Causal discrete-time system approximation of non-bandlimited continuous-time systems by means of discrete prolate spheroidal wave functions

SUMMARY In general, linear time-invariant (LTI) continuous-time (CT) systems can be implemented by means of LTI discrete-time (DT) systems, at least for a certain frequency band. If a causal CT system is not bandlimited, the equivalent DT system may has be to non-causal for perfectly implementing the CT system within a certain frequency band. This paper studies the question to which degree a causal DT system can approximate the CT system. By reducing the approximation frequency band, the approximation accuracy can be increased—at the expense of a higher energy of the impulse response of the DT system. It turns out, that there exists a strict trade-off between approximation accuracy, measured in the squared integral error, and energy of the impulse response of the DT system. The theoretically optimal trade-off can be achieved by approximations based on a weighted linear combination of the discrete prolate spheroidal wave functions (DPSWFs). The results are not limited to the case of approximating a CT system by means of a causal DT system, but they generally hold for the approximation of an arbitrary spectrum by means of a spectrum of an indexlimited time sequence. Copyright

Additive Non-Gaussian Noise Attacks on the Scalar Costa Scheme (SCS)

The additive attack public mutual information game is explicitly solved for one of the simplest quantization based watermarking schemes, the scalar Costa scheme (SCS). It is a zero-sum game played between the embedder and the attacker, and the payoff function is the mutual information. The solution of the game, a subgame perfect nash equilibrium, is found by backward induction. Therefore, the Blahut-Arimoto algorithm is employed for numerically optimizing the mutual information over noise distributions. Although the worst case distribution is in general strongly non-Gaussian, the capacity degradation compared to a suboptimal Gaussian noise attack is quite small. The loss, if the embedder optimizes SCS for a Gaussian attack but the worst case attack is employed, is negligible.

Optimality of SCS watermarking

Blind spread-spectrum watermarking schemes with correlation based detection algorithms suffer significantly from host signal interference. Improvements are possible when considering the host signal as side-information to the watermark encoder. Costa showed that, in a specific case, host signal interference can be avoided completely. The scalar Costa scheme, which operates on structured codebooks based on scalar quantizers, performs relatively close to the ideal Costa scheme in terms of maximum rate of reliable communication (capacity) over a channel with AWGN attack. The concept of amplitude limited channels in conjunction with repetition of the signal constellation is also known in the communications community by the name modulo channel, which has been studied into great detail. Starting from the modulo channel, which implies a constraint on the amplitude in the receiver, we model the watermarking scenario based on scalar quantizers. The capacity of this model is presented and compared to the theoretical results for SCS watermarking in the case of AWGN attacks. A final analysis of SCS in terms of optimality, based on the results with the modulo channel, shows that even binary SCS is near optimum for one-dimensional (symbol-by-symbol) embedding in terms of capacity for an i.i.d. Gaussian host signal and an appropriate AWGN attack.

Signal shaping for reduction of peak-power and dynamic range in precoding schemes

Precoding at the transmitter side has been proved to be a very efficient strategy for channel equalization in single-carrier digital transmission schemes. It enables the application of coded modulation in a seamless fashion. A drawback of precoding is that the signal at the input of the decision device exhibits a huge dynamic range. Based on dynamics shaping, a combined precoding/shaping technique introduced previously (see Fischer, R. et al., IEEE JSAC, p.1622-33, 1995), a new shaping strategy is developed. This technique enables a flexible trade-off between (i) reduction of the average transmit power, (ii) avoidance of peaks in the transmit signal in order to facilitate a line driver implementation, and (iii) restriction of the maximum amplitude at the receiver side to a prescribed value. Over a wide range, all three demands can be met simultaneously. As the scheme is fully compatible with Tomlinson-Harashima precoding, it can replace the precoder even in existing and standardized schemes. Simulation results for a typical DSL scenario show the achievable gains.