arXiv subjects

Robert F. H. Fischer

Publications and source records attributed to Robert F. H. Fischer.

At least 19 recordsLinked to original sources

arXiv2026

Preprocessing for Physical-Layer Security in Wireless THz-Communication

In this paper, the usage of preprocessing to achieve physical-layer security in a wireless THz-MIMO scenario is investigated. The goal is a reliable and secure communication. Optimization of the preprocessing is done either based on the error performance or the transmission rate. For both criteria, we present a variant that is based only on the legitimate receiver or also includes the eavesdropper. For each variant, linear and lattice-reduction-aided approaches are considered. Numerical simulations are used to assess the resulting secrecy rates and error ratios. A comparison between all variants is compiled and the possible trade-offs are discussed.

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arXiv2024

Helper Data Schemes for Coded Modulation and Shaping in Physical Unclonable Functions

In this paper, we consider the generation and utilization of helper data for physical unclonable functions (PUFs) that provide real-valued readout symbols. Compared to classical binary PUFs, more entropy can be extracted from each basic building block (PUF node), resulting in longer keys/fingerprints and/or a higher reliability. To this end, a coded modulation and signal shaping scheme that matches the (approximately) Gaussian distribution of the readout has to be employed. A new helper data scheme is proposed that works with any type of coded modulation/shaping scheme. Compared to the permutation scheme from the literature, less amount of helper data has to be generated and a higher reliability is achieved. Moreover, the recently proposed idea of a two-metric helper data scheme is generalized to coded modulation and a general S-metric scheme. It is shown how extra helper data can be generated to improve decodability. The proposed schemes are assessed by numerical simulations and by evaluation of measurement data. We compare multi-level codes using a new rate design strategy with bit-interleaved coded modulation and trellis shaping with a distribution matcher. By selecting a suitable design, the rate per PUF node that can be reliably extracted can be as high as 2~bit/node.

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arXiv2022

Algorithms and Bounds for Complex and Quaternionic Lattices With Application to MIMO Transmission

Lattices are a popular field of study in mathematical research, but also in more practical areas like cryptology or multiple-input/multiple-output (MIMO) transmission. In mathematical theory, most often lattices over real numbers are considered. However, in communications, complex-valued processing is usually of interest. Besides, by the use of dual-polarized transmission as well as by the combination of two time slots or frequencies, four-dimensional (quaternion-valued) approaches become more and more important. Hence, to account for this fact, well-known lattice algorithms and related concepts are generalized in this work. To this end, a brief review of complex arithmetic, including the sets of Gaussian and Eisenstein integers, and an introduction to quaternion-valued numbers, including the sets of Lipschitz and Hurwitz integers, are given. On that basis, generalized variants of two important algorithms are derived: first, of the polynomial-time LLL algorithm, resulting in a reduced basis of a lattice by performing a special variant of the Euclidean algorithm defined for matrices, and second, of an algorithm to calculate the successive minima - the norms of the shortest independent vectors of a lattice - and its related lattice points. Generalized bounds for the quality of the particular results are established and the asymptotic complexities of the algorithms are assessed. These findings are extensively compared to conventional real-valued processing. It is shown that the generalized approaches outperform their real-valued counterparts in complexity and/or quality aspects. Moreover, the application of the generalized algorithms to MIMO communications is studied, particularly in the field of lattice-reduction-aided and integer-forcing equalization.

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arXiv2021

Stabilization Techniques for Iterative Algorithms in Compressed Sensing

Algorithms for signal recovery in compressed sensing (CS) are often improved by stabilization techniques, such as damping, or the less widely known so-called fractional approach, which is based on the expectation propagation (EP) framework. These procedures are used to increase the steady-state performance, i.e., the performance after convergence, or assure convergence, when this is otherwise not possible. In this paper, we give a thorough introduction and interpretation of several stabilization approaches. The effects of the stabilization procedures are examined and compared via numerical simulations and we show that a combination of several procedures can be beneficial for the performance of the algorithm.

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arXiv2021

Semantic Security for Indoor THz-Wireless Communication

Physical-layer security (PLS) for industrial indoor terahertz (THz) wireless communication applications is considered. We use a similar model as being employed for additive white Gaussian noise (AWGN) wireless communication channels. A cell communication and a directed communication scenario are analyzed to illustrate the achievable semantic security guarantees for a wiretap channel with finite-blocklength THz-wireless communication links. We show that weakly directed transmitter (Alice) antennas, which allow cell-type communication with multiple legitimate receivers (Bobs) without adaptation of the alignment, result in large insecure regions. In the directed communication scenario, the resulting insecure regions are shown to cover a large volume of the indoor environment only if the distance between Alice and Bob is large. Thus, our results for the two selected scenarios reveal that there is a stringent trade-off between the targeted semantic security level and the number of reliably and securely accessible legitimate receivers. Furthermore, the effects of secrecy code parameters and antenna properties on the achievable semantic security levels are illustrated to show directions for possible improvements to guarantee practically-acceptable security levels with PLS methods for industrial indoor THz-wireless communication applications.

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arXiv2020

On Discrete-Time/Frequency-Periodic End-to-End Fiber-Optical Channel Models

A discrete-time end-to-end fiber-optical channel model is derived based on the first-order perturbation approach. The model relates the discrete-time input symbol sequences of co-propagating wavelength channels to the received symbol sequence after matched filtering and T-spaced sampling. To this end, the interference from both self- and cross-channel nonlinear interactions of the continuous-time optical signal is represented by a single discrete-time perturbative term. Two equivalent discrete-time models can be formulated---one in the time-domain, the other in the 1/T-periodic continuous-frequency domain. The time-domain formulation coincides with the well-known pulse-collision picture. The novel frequency-domain picture incorporates the sampling operation via an aliased and periodic kernel description. This gives rise to an alternative perspective on the end-to-end input/output relation between the spectrum of the discrete-time transmit symbol sequence and the spectrum of the receive symbol sequence. Both views can be extended from a regular, i.e., solely additive model, to a combined regular-logarithmic model to take the multiplicative nature of certain distortions into consideration. An alternative formulation of the Gaussian Noise model is provided to take the aliasing of frequency components correctly into account. A novel algorithmic implementation of the discrete and periodic frequency-domain model is presented. The derived end-to-end model requires only a single computational step and shows good agreement in the mean-squared error sense compared to the oversampled and inherently sequential split-step Fourier method.

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arXiv2018

Bias Compensation in Iterative Soft-Feedback Algorithms with Application to (Discrete) Compressed Sensing

In all applications in digital communications, it is crucial for an estimator to be unbiased. Although so-called soft feedback is widely employed in many different fields of engineering, typically the biased estimate is used. In this paper, we contrast the fundamental unbiasing principles, which can be directly applied whenever soft feedback is required. To this end, the problem is treated from a signal-based perspective, as well as from the approach of estimating the signal based on an estimate of the noise. Numerical results show that when employed in iterative reconstruction algorithms for Compressed Sensing, a gain of 1.2 dB due to proper unbiasing is possible.

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arXiv2017

Space-Time Codes Based on Rank-Metric Codes and Their Decoding

We propose a new class of space-time block codes based on finite-field rank-metric codes in combination with a rank-metric-preserving mapping to the set of Eisenstein integers. It is shown that these codes achieve maximum diversity order and improve upon certain existing constructions. Moreover, we present a new decoding algorithm for these codes which utilizes the algebraic structure of the underlying finite-field rank-metric codes and employs lattice-reduction-aided equalization. This decoder does not achieve the same performance as the classical maximum-likelihood decoding methods, but has polynomial complexity in the matrix dimension, making it usable for large field sizes and numbers of antennas.

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arXiv2017

Low-Complexity Iterative Algorithms for (Discrete) Compressed Sensing

We consider iterative (`turbo') algorithms for compressed sensing. First, a unified exposition of the different approaches available in the literature is given, thereby enlightening the general principles and main differences. In particular we discuss i) the estimation step (matched filter vs. optimum MMSE estimator), ii) the unbiasing operation (implicitly or explicitly done and equivalent to the calculation of extrinsic information), and iii) thresholding vs. the calculation of soft values. Based on these insights we propose a low-complexity but well-performing variant utilizing a Krylov space approximation of the optimum linear MMSE estimator. The derivations are valid for any probability density of the signal vector. However, numerical results are shown for the discrete case. The novel algorithms shows very good performance and even slightly faster convergence compared to approximative message passing.

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arXiv2017

Unveiling Bias Compensation in Turbo-Based Algorithms for (Discrete) Compressed Sensing

In Compressed Sensing, a real-valued sparse vector has to be recovered from an underdetermined system of linear equations. In many applications, however, the elements of the sparse vector are drawn from a finite set. Adapted algorithms incorporating this additional knowledge are required for the discrete-valued setup. In this paper, turbo-based algorithms for both cases are elucidated and analyzed from a communications engineering perspective, leading to a deeper understanding of the algorithm. In particular, we gain the intriguing insight that the calculation of extrinsic values is equal to the unbiasing of a biased estimate and present an improved algorithm.

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arXiv2016

Algorithms for the Iterative Estimation of Discrete-Valued Sparse Vectors

In Compressed Sensing, a real-valued sparse vector has to be estimated from an underdetermined system of linear equations. In many applications, however, the elements of the sparse vector are drawn from a finite set. For the estimation of these discrete-valued vectors, matched algorithms are required which take the additional knowledge of the discrete nature into account. In this paper, the estimation problem is treated from a communications engineering point of view. A powerful new algorithm incorporating techniques known from digital communications and information theory is derived. For comparison, Turbo Compressed Sensing is adapted to the discrete setup and a simplified and generalized notation is presented. The performance of the algorithms is covered by numerical simulations.

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arXiv2016

Layering of Communication Networks and a Forward-Backward Duality

In layered communication networks there are only connections between intermediate nodes in adjacent layers. Applying network coding to such networks provides a number of benefits in theory as well as in practice. We propose a "layering procedure" to transform an arbitrary network into a layered structure. Furthermore, we derive a "forward-backward duality" for linear network codes, which can be seen as an analogon to the "uplink-downlink duality" in MIMO communication systems.

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arXiv2015

Error Correction for Differential Linear Network Coding in Slowly-Varying Networks

Differential linear network coding (DLNC) is a precoding scheme for information transmission over random linear networks. By using differential encoding and decoding, the conventional approach of lifting, required for inherent channel sounding, can be omitted and in turn higher transmission rates are supported. However, the scheme is sensitive to variations in the network topology. In this paper, we derive an extended DLNC channel model which includes slow network changes. Based on this, we propose and analyze a suitable channel coding scheme matched to the situation at hand using rank-metric convolutional codes.

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arXiv2013

Discrete Sparse Signals: Compressed Sensing by Combining OMP and the Sphere Decoder

We study the reconstruction of discrete-valued sparse signals from underdetermined systems of linear equations. On the one hand, classical compressed sensing (CS) is designed to deal with real-valued sparse signals. On the other hand, algorithms known from MIMO communications, especially the sphere decoder (SD), are capable to reconstruct discrete-valued non-sparse signals from well- or overdefined system of linear equations. Hence, a combination of both approaches is required. We discuss strategies to include the knowledge of the discrete nature of the signal in the reconstruction process. For brevity, the exposition is done for combining the orthogonal matching pursuit (OMP) with the SD; design guidelines are derived. It is shown that by suitably combining OMP and SD an efficient low-complexity scheme for the detection of discrete sparse signals is obtained.

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arXiv2012

The PAPR Problem in OFDM Transmission: New Directions for a Long-Lasting Problem

Peak power control for multicarrier communications has been a long-lasting problem in signal processing and communications. However, industry and academia are confronted with new challenges regarding energy efficient system design. Particularly, the envisioned boost in network energy efficiency (e.g. at least by a factor of 1000 in the Green Touch consortium) will tighten the requirements on component level so that the efficiency gap with respect to single-carrier transmission must considerably diminish. This paper reflects these challenges together with a unified framework and new directions in this field. The combination of large deviation theory, de-randomization and selected elements of Banach space geometry will offer a novel approach and will provide ideas and concepts for researchers with a background in industry as well as those from academia.

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arXiv2011

Capacity of BICM Using (Bi-)Orthogonal Signal Constellations in Impulse-Radio Ultra-Wideband Systems

Bit-interleaved coded modulation (BICM) using (bi-)orthogonal signals is especially well suited for the application in impulse-radio ultra-wideband transmission systems, which typically operate in the power-limited regime and require a very low-complexity transmitter and receiver design. In this paper we analyze the capacity of BICM using (bi-)orthogonal signals with coherent and noncoherent detection and put particular focus on the power-limited or wideband regime. We give analytical expressions for the ratio energy per bit vs. noise power spectral density in the limit of infinite bandwidth and the respective wideband slope, and thus, are able to quantify the loss incurred by the restriction to BICM in contrast to coded modulation. The gained theoretical insights allow to derive design rules for impulse-radio ultra-wideband transmission systems.

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arXiv2011

Decision-Feedback Differential Detection in Impulse-Radio Ultra-Wideband Systems

In this paper we present decision-feedback differential detection (DF-DD) schemes for autocorrelation-based detection in impulse-radio ultra-wideband (IR-UWB) systems, a signaling scheme regarded as a promising candidate in particular for low-complexity wireless sensor networks. To this end, we first discuss ideal noncoherent sequence estimation and approximations thereof based on block-wise multiple-symbol differential detection (MSDD) and the Viterbi algorithm (VA) from the perspective of tree-search/trellis decoding. Exploiting relations well-known from tree-search decoding, we are able to derive the novel decision-feedback differential detection (DF-DD) schemes. A comprehensive comparison with respect to performance and complexity of the presented schemes in a typical IR-UWB scenario reveals---along with novel insights in techniques for complexity reduction of the sphere decoder applied for MSDD---that sorted DF-DD achieves close-to-optimum performance at very low, and in particular constant receiver complexity.

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arXiv2010

Notes on Lattice-Reduction-Aided MMSE Equalization

Over the last years, novel low-complexity approaches to the equalization of MIMO channels have gained much attention. Thereby, methods based on lattice basis reduction are of special interest, as they achieve the optimum diversity order. In this paper, a tutorial overview on LRA equalization optimized according to the MMSE criterion is given. It is proven that applying the zero-forcing BLAST algorithm to a suitably augmented channel matrix (the inverse of the square root of the correlation matrix of the data symbols times the noise variance forms its lower part) results in the optimum solution. This fact is already widely used but lacks a formal proof. It turns out that it is more important to take the correlations of the data correctly into account than what type of lattice reduction actually is used.

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