## Institut für Systemdynamik - ISD

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A nonlinear mathematical model for the dynamics of permanent magnet synchronous machines with interior magnets is discussed. The model of the current dynamics captures saturation and dependency on the rotor angle. Based on the model, a flatness-based field-oriented closed-loop controller and a feed-forward compensation of torque ripples are derived. Effectiveness and robustness of the proposed algorithms are demonstrated by simulation results.

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.

Soft-input decoding of concatenated codes based on the Plotkin construction and BCH component codes
(2020)

Low latency communication requires soft-input decoding of binary block codes with small to medium block lengths.
In this work, we consider generalized multiple concatenated (GMC) codes based on the Plotkin construction. These codes are similar to Reed-Muller (RM) codes. In contrast to RM codes, BCH codes are employed as component codes. This leads to improved code parameters. Moreover, a decoding algorithm is proposed that exploits the recursive structure of the concatenation. This algorithm enables efficient soft-input decoding of binary block codes with small to medium lengths. The proposed codes and their decoding achieve significant performance gains compared with RM codes and recursive GMC decoding.

The reliability of flash memories suffers from various error causes. Program/erase cycles, read disturb, and cell to cell interference impact the threshold voltages and cause bit errors during the read process. Hence, error correction is required to ensure reliable data storage. In this work, we investigate the bit-labeling of triple level cell (TLC) memories. This labeling determines the page capacities and the latency of the read process. The page capacity defines the redundancy that is required for error correction coding. Typically, Gray codes are used to encode the cell state such that the codes of adjacent states differ in a single digit. These Gray codes minimize the latency for random access reads but cannot balance the page capacities. Based on measured voltage distributions, we investigate the page capacities and propose a labeling that provides a better rate balancing than Gray labeling.

Side Channel Attack Resistance of the Elliptic Curve Point Multiplication using Eisenstein Integers
(2020)

Asymmetric cryptography empowers secure key exchange and digital signatures for message authentication. Nevertheless, consumer electronics and embedded systems often rely on symmetric cryptosystems because asymmetric cryptosystems are computationally intensive. Besides, implementations of cryptosystems are prone to side-channel attacks (SCA). Consequently, the secure and efficient implementation of asymmetric cryptography on resource-constrained systems is demanding. In this work, elliptic curve cryptography is considered. A new concept for an SCA resistant calculation of the elliptic curve point multiplication over Eisenstein integers is presented and an efficient arithmetic over Eisenstein integers is proposed. Representing the key by Eisenstein integer expansions is beneficial to reduce the computational complexity and the memory requirements of an SCA protected implementation.

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.

This work presents a new concept to implement the elliptic curve point multiplication (PM). This computation is based on a new modular arithmetic over Gaussian integer fields. Gaussian integers are a subset of the complex numbers such that the real and imaginary parts are integers. Since Gaussian integer fields are isomorphic to prime fields, this arithmetic is suitable for many elliptic curves. Representing the key by a Gaussian integer expansion is beneficial to reduce the computational complexity and the memory requirements of secure hardware implementations, which are robust against attacks. Furthermore, an area-efficient coprocessor design is proposed with an arithmetic unit that enables Montgomery modular arithmetic over Gaussian integers. The proposed architecture and the new arithmetic provide high flexibility, i.e., binary and non-binary key expansions as well as protected and unprotected PM calculations are supported. The proposed coprocessor is a competitive solution for a compact ECC processor suitable for applications in small embedded systems.

Modeling a suitable birth density is a challenge when using Bernoulli filters such as the Labeled Multi-Bernoulli (LMB) filter. The birth density of newborn targets is unknown in most applications, but must be given as a prior to the filter. Usually the birth density stays unchanged or is designed based on the measurements from previous time steps.
In this paper, we assume that the true initial state of new objects is normally distributed. The expected value and covariance of the underlying density are unknown parameters. Using the estimated multi-object state of the LMB and the Rauch-Tung-Striebel (RTS) recursion, these parameters are recursively estimated and adapted after a target is detected.
The main contribution of this paper is an algorithm to estimate the parameters of the birth density and its integration into the LMB framework. Monte Carlo simulations are used to evaluate the detection driven adaptive birth density in two scenarios. The approach can also be applied to filters that are able to estimate trajectories.

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.

In this work, we investigate a hybrid decoding approach that combines algebraic hard-input decoding of binary block codes with soft-input decoding. In particular, an acceptance criterion is proposed which determines the reliability of a candidate codeword. For many received codewords the stopping criterion indicates that the hard-decoding result is sufficiently reliable, and the costly soft-input decoding can be omitted. The proposed acceptance criterion significantly reduces the decoding complexity. For simulations we combine the algebraic hard-input decoding with ordered statistics decoding, which enables near maximum likelihood soft-input decoding for codes of small to medium block lengths.