Institut für Systemdynamik - ISD
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Flatness-based feed-forward control of solenoid actuators is considered. For precise motion planning and accurate steering of conventional solenoids, eddy currents cannot be neglected. The system of ordinary differential equations including eddy currents, that describes the nonlinear dynamics of such actuators, is not differentially flat. Thus, a distributed parameter approach based on a diffusion equation is considered, that enables the parametrization of the eddy current by the armature position and its time derivatives. In order to design the feedforward control, the distributed parameter model of the eddy current subsystem is combined with a typical nonlinear lumped parameter model for the electrical and mechanical subsystems of the solenoid. The control design and its application are illustrated by numerical and practical results for an industrial solenoid actuator.
Four-Dimensional Hurwitz Signal Constellations, Set Partitioning, Detection, and Multilevel Coding
(2021)
The Hurwitz lattice provides the densest four-dimensional packing. This fact has motivated research on four-dimensional Hurwitz signal constellations for optical and wireless communications. This work presents a new algebraic construction of finite sets of Hurwitz integers that is inherently accompanied by a respective modulo operation. These signal constellations are investigated for transmission over the additive white Gaussian noise (AWGN) channel. It is shown that these signal constellations have a better constellation figure of merit and hence a better asymptotic performance over an AWGN channel when compared with conventional signal constellations with algebraic structure, e.g., two-dimensional Gaussian-integer constellations or four-dimensional Lipschitz-integer constellations. We introduce two concepts for set partitioning of the Hurwitz integers. The first method is useful to reduce the computational complexity of the symbol detection. This suboptimum detection approach achieves near-maximum-likelihood performance. In the second case, the partitioning exploits the algebraic structure of the Hurwitz signal constellations. We partition the Hurwitz integers into additive subgroups in a manner that the minimum Euclidean distance of each subgroup is larger than in the original set. This enables multilevel code constructions for the new signal constellations.
In this article, we give the construction of new four-dimensional signal constellations in the Euclidean space, which represent a certain combination of binary frequency-shift keying (BFSK) and M-ary amplitude-phase-shift keying (MAPSK). Description of such signals and the formulas for calculating the minimum squared Euclidean distance are presented. We have developed an analytic building method for even and odd values of M. Hence, no computer search and no heuristic methods are required. The new optimized BFSK-MAPSK (M = 5,6,···,16) signal constructions are built for the values of modulation indexes h =0.1,0.15,···,0.5 and their parameters are given. The results of computer simulations are also provided. Based on the obtained results we can conclude, that BFSK-MAPSK systems outperform similar four-dimensional systems both in terms of minimum squared Euclidean distance and simulated symbol error rate.
Generalized Concatenated Codes over Gaussian and Eisenstein Integers for Code-Based Cryptography
(2021)
The code-based McEliece and Niederreiter cryptosystems are promising candidates for post-quantum public-key encryption. Recently, q-ary concatenated codes over Gaussian integers were proposed for the McEliece cryptosystem together with the one-Mannheim error channel, where the error values are limited to Mannheim weight one. Due to the limited error values, the codes over Gaussian integers achieve a higher error correction capability than maximum distance separable (MDS) codes with bounded minimum distance decoding. This higher error correction capability improves the work factor regarding decoding attacks based on information-set decoding. The codes also enable a low complexity decoding algorithm for decoding beyond the guaranteed error correction capability. In this work, we extend this coding scheme to codes over Eisenstein integers. These codes have advantages for the Niederreiter system. Additionally, we propose an improved code construction based on generalized concatenated codes. These codes extent the rate region where the work factor is beneficial compared to MDS codes. Moreover, generalized concatenated codes are more robust against structural attacks than ordinary concatenated codes.
Code-based cryptography is a promising candidate for post-quantum public-key encryption. The classic McEliece system uses binary Goppa codes, which are known for their good error correction capability. However, the key generation and decoding procedures of the classic McEliece system have a high computation complexity. Recently, q-ary concatenated codes over Gaussian integers were proposed for the McEliece cryptosystem together with the one-Mannheim error channel, where the error values are limited to Mannheim weight one. For this channel, concatenated codes over Gaussian integers achieve a higher error correction capability than maximum distance separable (MDS) codes with bounded minimum distance decoding. This improves the work factor regarding decoding attacks based on information-set decoding. This work proposes an improved construction for codes over Gaussian integers. These generalized concatenated codes extent the rate region where the work factor is beneficial compared to MDS codes. They allow for shorter public keys for the same level of security as the classic Goppa codes. Such codes are beneficial for lightweight code-based cryptosystems.
In this letter, we present an approach to building a new generalized multistream spatial modulation system (GMSM), where the information is conveyed by the two active antennas with signal indices and using all possible active antenna combinations. The signal constellations associated with these antennas may have different sizes. In addition, four-dimensional hybrid frequency-phase modulated signals are utilized in GMSM. Examples of GMSM systems are given and computer simulation results are presented for transmission over Rayleigh and deep Nakagami- m flat-fading channels when maximum-likelihood detection is used. The presented results indicate a significant improvement of characteristics compared to the best-known similar systems.
This paper proposes a novel transmission scheme for generalized multistream spatial modulation. This new approach uses one Mannheim error correcting codes over Gaussian or Eisenstein integers as multidimensional signal constellations. These codes enable a suboptimal decoding strategy with near maximum likelihood performance for transmission over the additive white Gaussian noise channel. In this contribution, this decoding algorithm is generalized to the detection for generalized multistream spatial modulation. The proposed method can outperform conventional generalized multistream spatial modulation with respect to decoding performance, detection complexity, and spectral efficiency.
With the high resolution of modern sensors such as multilayer LiDARs, estimating the 3D shape in an extended object tracking procedure is possible. In recent years, 3D shapes have been estimated in spherical coordinates using Gaussian processes, spherical double Fourier series or spherical harmonics. However, observations have shown that in many scenarios only a few measurements are obtained from top or bottom surfaces, leading to error-prone estimates in spherical coordinates. Therefore, in this paper we propose to estimate the shape in cylindrical coordinates instead, applying harmonic functions. Specifically, we derive an expansion for 3D shapes in cylindrical coordinates by solving a boundary value problem for the Laplace equation. This shape representation is then integrated in a plain greedy association model and compared to shape estimation procedures in spherical coordinates. Since the shape representation is only integrated in a basic estimator, the results are preliminary and a detailed discussion for future work is presented at the end of the paper.
Extracting suitable features from acquired data to accurately depict the current health state of a system is crucial in data driven condition monitoring and prediction. Usually, analogue sensor data is sampled at rates far exceeding the Nyquist-rate containing substantial amounts of redundancies and noise, imposing high computational loads due to the subsequent and necessary feature processing chain (generation, dimensionality reduction, rating and selection). To overcome these problems, Compressed Sensing can be used to sample directly to a compressed space, provided the signal at hand and the employed compression/measurement system meet certain criteria. Theory states, that during this compression step enough information is conserved, such that a reconstruction of the original signal is possible with high probability. The proposed approach however does not rely on reconstructed data for condition monitoring purposes, but uses directly the compressed signal representation as feature vector. It is hence assumed that enough information is conveyed by the compression for condition monitoring purposes. To fuse the compressed coefficients into one health index that can be used as input for remaining useful life prediction algorithms and is limited to a reasonable range between 1 and 0, a logistic regression approach is used. Run-to-failure data of three translational electromagnetic actuators is used to demonstrate the health index generation procedure. A comparison to the time domain ground truth signals obtained from Nyquist sampled coil current measurements shows reasonable agreement. I.e. underlying wear-out phenomena can be reproduced by the proposed approach enabling further investigation of the application of prognostic methods.
Digitale Signaturen zum Überprüfen der Integrität von Daten, beispielsweise von Software-Updates, gewinnen zunehmend an Bedeutung. Im Bereich der eingebetteten Systeme kommen derzeit wegen der geringen Komplexität noch überwiegend symmetri-sche Verschlüsselungsverfahren zur Berechnung eines Authentifizierungscodes zum Einsatz. Asym-metrische Kryptosysteme sind rechenaufwendiger, bieten aber mehr Sicherheit, weil der Schlüssel zur Authentifizierung nicht geheim gehalten werden muss. Asymmetrische Signaturverfahren werden typischerweise zweistufig berechnet. Der Schlüssel wird nicht direkt auf die Daten angewendet, sondern auf deren Hash-Wert, der mit Hilfe einer Hash-funktion zuvor berechnet wurde. Zum Einsatz dieser Verfahren in eingebetteten Systemen ist es erforder-lich, dass die Hashfunktion einen hinreichend gro-ßen Datendurchsatz ermöglicht. In diesem Beitrag wird eine effiziente Hardware-Implementierung der SHA-256 Hashfunktion vorgestellt.
In multi-extended object tracking, parameters (e.g., extent) and trajectory are often determined independently. In this paper, we propose a joint parameter and trajectory (JPT) state and its integration into the Bayesian framework. This allows processing measurements that contain information about parameters and states. Examples of such measurements are bounding boxes given from an image processing algorithm. It is shown that this approach can consider correlations between states and parameters. In this paper, we present the JPT Bernoulli filter. Since parameters and state elements are considered in the weighting of the measurement data assignment hypotheses, the performance is higher than with the conventional Bernoulli filter. The JPT approach can be also used for other Bayes filters.
Lernfabrik
(2016)
Die Einführung von cyberphysischen Systemen in der Fertigung wird die Arbeitsbedingungen und Prozesse genauso wie Geschäftsmodelle stark verändern. In der Praxis kann eine wachsende Diskrepanz zwischen Großunternehmen und KMU beobachtet werden. Genau diese Diskrepanz soll die im Folgenden präsentierte Lernfabrik überbrücken, die Unternehmen eine Plattform zum Probieren bietet, die Möglichkeit zur Ausbildung von Studenten und Mitarbeitern schafft und Beratungsangebote bereithält. Zur Umsetzung wird ein integriertes, offenes und standardisiertes Automatisierungskonzept vorgestellt, das einzelne Geräte, ganze Produktionslinien bis hin zu höheren Automatisierungssystemen umfasst und auch eine Community bereitstellt sowie zur Umsetzung neuer Geschäftsmodelle dient.
List decoding for concatenated codes based on the Plotkin construction with BCH component codes
(2021)
Reed-Muller codes are a popular code family based on the Plotkin construction. Recently, these codes have regained some interest due to their close relation to polar codes and their low-complexity decoding. We consider a similar code family, i.e., the Plotkin concatenation with binary BCH component codes. This construction is more flexible regarding the attainable code parameters. In this work, we consider a list-based decoding algorithm for the Plotkin concatenation with BCH component codes. The proposed list decoding leads to a significant coding gain with only a small increase in computational complexity. Simulation results demonstrate that the Plotkin concatenation with the proposed decoding achieves near maximum likelihood decoding performance. This coding scheme can outperform polar codes for moderate code lengths.
This work proposes a suboptimal detection algorithm for generalized multistream spatial modulation. Many suboptimal detection algorithms for spatial modulation use two-stage detection schemes where the set of active antennas is detected in the first stage and the transmitted symbols in the second stage. For multistream spatial modulation with large signal constellations the second detection step typically dominates the detection complexity. With the proposed detection scheme, the modified Gaussian approximation method is used for detecting the antenna pattern. In order to reduce the complexity for detecting the signal points, we propose a combined equalization and list decoding approach. Simulation results demonstrate that the new algorithm achieves near-maximum-likelihood performance with small list sizes. It significantly reduces the complexity when compared with conventional two-stage detection schemes.
Multi-dimensional spatial modulation is a multipleinput/ multiple-output wireless transmission technique, that uses only a few active antennas simultaneously. The computational complexity of the optimal maximum-likelihood (ML) detector at the receiver increases rapidly as more transmit antennas or larger modulation orders are employed. ML detection may be infeasible for higher bit rates. Many suboptimal detection algorithms for spatial modulation use two-stage detection schemes where the set of active antennas is detected in the first stage and the transmitted symbols in the second stage. Typically, these detection schemes use the ML strategy for the symbol detection. In this work, we consider a suboptimal detection algorithm for the second detection stage. This approach combines equalization and list decoding. We propose an algorithm for multi-dimensional signal constellations with a reduced search space in the second detection stage through set partitioning. In particular, we derive a set partitioning from the properties of Hurwitz integers. Simulation results demonstrate that the new algorithm achieves near-ML performance. It significantly reduces the complexity when compared with conventional two-stage detection schemes. Multi-dimensional constellations in combination with suboptimal detection can even outperform conventional signal constellations in combination with ML detection.
The computational complexity of the optimal maximum likelihood (ML) detector for spatial modulation increases rapidly as more transmit antennas or larger modulation orders are employed. Hence, ML detection may be infeasible for higher bit rates. This work proposes an improved suboptimal detection algorithm based on the Gaussian approximation method. It is demonstrated that the new method is closely related to the previously published signal vector based detection and the modified maximum ratio combiner, but can improve the detection performance compared to these methods. Furthermore, the performance of different signal constellations with suboptimal detection is investigated. Simulation results indicate that the performance loss compared to ML detection depends heavily on the signal constellation, where the recently proposed Eisenstein integer constellations are beneficial compared to classical QAM or PSK constellations.
This work proposes a construction for low-density parity-check (LDPC) codes over finite Gaussian integer fields. Furthermore, a new channel model for codes over Gaussian integers is introduced and its channel capacity is derived. This channel can be considered as a first order approximation of the additive white Gaussian noise channel with hard decision detection where only errors to nearest neighbors in the signal constellation are considered. For this channel, the proposed LDPC codes can be decoded with a simple non-probabilistic iterative decoding algorithm similar to Gallager's decoding algorithm A.
Embodiments are generally related to the field of channel and source coding of data to be sent over a channel, such as a communication link or a data memory. Some specific embodiments are related to a method of encoding data for transmission over a channel, a corresponding decoding method, a coding device for performing one or both of these methods and a computer program comprising instructions to cause said coding device to perform one or both of said methods.
This paper describes the development of a control system for an industrial heating application. In this process a moving substrate is passing through a heating zone with variable speed. Heat is applied by hot air to the substrate with the air flow rate being the manipulated variable. The aim is to control the substrate’s temperature at a specific location after passing the heating zone. First, a model is derived for a point attached to the moving substrate. This is modified to reflect the temperature of the moving substrate at the specified location. In order to regulate the temperature a nonlinear model predictive control approach is applied using an implicit Euler scheme to integrate the model and an augmented gradient based optimization approach. The performance of the controller has been validated both by simulations and experiments on the physical plant. The respective results are presented in this paper.
The Montgomery multiplication is an efficient method for modular arithmetic. Typically, it is used for modular arithmetic over integer rings to prevent the expensive inversion for the modulo reduction. In this work, we consider modular arithmetic over rings of Gaussian integers. Gaussian integers are subset of the complex numbers such that the real and imaginary parts are integers. In many cases Gaussian integer rings are isomorphic to ordinary integer rings. We demonstrate that the concept of the Montgomery multiplication can be extended to Gaussian integers. Due to independent calculation of the real and imaginary parts, the computation complexity of the multiplication is reduced compared with ordinary integer modular arithmetic. This concept is suitable for coding applications as well as for asymmetric key cryptographic systems, such as elliptic curve cryptography or the Rivest-Shamir-Adleman system.