Ullrich J. Mönich

Physical layer security is an approach to implement security directly at the physical layer of a communication system. In the Advanced Communication Systems and Embedded Security Lab (ACES Lab) we experimentally study a modular scheme for semantic security. This form of security is information theoretically provable, and, in contrast to classical key-based encryption, does not rely on the (unproven) assumption that certain mathematical problems are hard to solve. As a consequence, they are inherently secure against quantum computer attacks.

Turing computability deals with the question of what is theoretically computable on a digital computer. Interestingly, there are non-computable numbers and functions. Since nowadays most signal processing operations are performed on digital computers, the question of computability arises. For example, we analyzed the computability of the Fourier transform and the discrete-time Fourier transform, and showed that there exist well-behaved signals for which the transforms exist mathematically, but cannot be computed on any digital hardware (including CPUs, FPGAs, or DSPs), because the Fourier transforms are not Turing computable. This result also implies that there is no duality between time and frequency domain with respect to computability.

Orthogonal transmission schemes, e.g., orthogonal frequency division multiplexing (OFDM), are widely used in modern communication systems, because of many desirable properties. However, one drawback is the large peak to average power ratio (PAPR) of such systems. In order to reduce the PAPR, different ideas were developed, among them the popular tone reservation method. In this method, the set of available carriers is partitioned into two sets, the first of which is used to carry the information, and the second of which to reduce the PAPR.

Central questions are: What is the best possible reduction of the PAPR? What is the optimal information set that achieves this reduction, and how can it be found? What is the general structure of the optimal information set? So far, no theoretical results have been available. In a series of publications we study the above questions.

Recently a lot of effort has been put in studying fully continuous interpretation approaches for DNA mixtures, where not only the location of a peak is used but also the actual peak heights. Since the peak heights contains additional information, these methods are superior to previous methods, where thresholds have been applied.

An important step toward the development of these methods is a complete understanding of the statistical properties of the peak heights and the derivation of a signal model. Based on such a model, algorithms for finding the number of contributors in a DNA mixture and for determining the probability that a given suspect contributed to a DNA sample can be developed.

Deep convolutional neural networks have proven their power in numerous applications, e.g., in image and speech processing. However, the theoretical understanding of those networks is difficult and lags behind.

Deformation stability, i.e., the robustness of the network's output to small deformations of the input, is an important property. Recently, for scattering networks, a deformation error stability bound has been established, however, it remained unclear for which signal classes the bound is actually finite.

For pointwise sampling it is known that there exist stable LTI systems and functions in the the Paley-Wiener space \(\mathcal{PW}_{\pi}^{1}\) such that the approximation process diverges, regardless of the oversampling factor. Recently, it was shown that the divergence can be overcome by using more general measurement functionals that are based on a complete orthonormal system. However, this approach requires the approximation process to have an increased bandwidth.

However, there exists a two channel system approximation process that is uniformly convergent for all stable LTI systems and all functions in \(\mathcal{PW}_{\pi}^{1}\). An advantage of the two channel approach compared to the one channel approach is the reduction of the approximation bandwidth, which can be exactly the same as the input function bandwidth.

Today's information society is based on the power of digital signal processing, and the theoretical foundation for the digital processing of analog signals is the Shannon sampling theorem. Without any further information about the signal, except its bandlimitedness, Nyquist rate sampling is optimal. However, if the signal to exhibits some additional structure, it is possible to reduce the sampling rate below the Nyquist rate. Compressed sensing provides a framework for sampling and recovering of sparse signals, however, sparsity is only one of many possible structures a signal can have.

Since signal processing is concerned with the processing of signals, a fundamental question is: which analog systems can be stably approximated by digital systems? The answer depends on many parameters, like the signal space under consideration, the sampling rate, the kind of sampling, etc. Recently, it has been shown that by using suitable generalized measurement functionals, it is possible to have a uniformly convergent approximation of stable linear time-invariant systems for the space \(\mathcal{PW}_\pi^1\) if oversampling is applied.

Quantization and thresholding are two important operations in practical systems. Although quantization is a purely deterministically process, it is usually analyzed stochastically to simplify the mathematical treatment. Quantization and thresholding of signal samples can lead to divergent reconstruction processes. A deterministic treatment of quantization reveals surprising facts. For example, for certain signals the reconstruction error increases unboundedly as the quantization step size is reduced to zero.

Robust face detection algorithms are important, especially in the computer-human interaction and in surveillance applications. In this work a component-based face detection algorithm is developed, which is more robust in particular in the presence of occlusions. The four face components (eyes, nose, mouth) are detected, using a cascade of boosted classifiers, where the classifiers work with Haar-like features. An online demonstrator is available at http://facedetection.nue.tu-berlin.de/.