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This work introduces new signal constellations based on Eisenstein integers, i.e., the hexagonal lattice. These sets of Eisenstein integers have a cardinality which is an integer power of three. They are proposed as signal constellations for representation in the equivalent complex baseband model, especially for applications like physical-layer network coding or MIMO transmission where the constellation is required to be a subset of a lattice. It is shown that these constellations form additive groups where the addition over the complex plane corresponds to the addition with carry over ternary Galois fields. A ternary set partitioning is derived that enables multilevel coding based on ternary error-correcting codes. In the subsets, this partitioning achieves a gain of 4.77 dB, which results from an increased minimum squared Euclidean distance of the signal points. Furthermore, the constellation-constrained capacities over the AWGN channel and the related level capacities in case of ternary multilevel coding are investigated. Simulation results for multilevel coding based on ternary LDPC codes are presented which show that a performance close to the constellation-constrained capacities can be achieved.
Recently published nonlinear model-based control
approaches achieve impressive performances in complex real-
world applications. However, due to model-plant mismatches
and unforeseen disturbances, the model-based controller’s per-
formance is limited in full-scale applications. In most applica-
tions, low-level control loops mitigate the model-plant mismatch
and the sensitivity to disturbances. But what is the influence
of these low-level control loops? In this paper, we present
the model predictive path integral (MPPI) control of a self-
balancing vehicle and investigate the influence of subordinate
control loops on closed-loop performance. Therefore, simulation
and full-scale experiments are performed and analyzed. Subor-
dinate control loops empower the MPPI controller because they
dampen the influence of disturbances, and thus improve the
model’s accuracy. This is the basis for the successful application
of model-based control approaches in real-world systems. All
in all, a model is used to design a low-level controller, then
its closed-loop behavior is determined, and this model is used
within the superimposed MPPI control loop – modeling for
control and vice versa.
Modular arithmetic over integers is required for many cryptography systems. Montgomeryreduction is an efficient algorithm for the modulo reduction after a multiplication. Typically, Mont-gomery reduction is used for rings of ordinary integers. In contrast, we investigate the modularreduction over rings of Gaussian integers. Gaussian integers are complex numbers where the real andimaginary parts are integers. Rings over Gaussian integers are isomorphic to ordinary integer rings.In this work, we show that Montgomery reduction can be applied to Gaussian integer rings. Twoalgorithms for the precision reduction are presented. We demonstrate that the proposed Montgomeryreduction enables an efficient Gaussian integer arithmetic that is suitable for elliptic curve cryptogra-phy. In particular, we consider the elliptic curve point multiplication according to the randomizedinitial point method which is protected against side-channel attacks. The implementation of thisprotected point multiplication is significantly faster than comparable algorithms over ordinary primefields.
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.
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.
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 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.
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.
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.
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.