arXiv subjects

Christian Schindelhauer

Publications and source records attributed to Christian Schindelhauer.

At least 19 recordsLinked to original sources

arXiv2026

The 2D Ray Tracing Problem using ABCD Lenses and Mirrors is Turing Complete

We establish that the two-dimensional ray tracing problem with thin lenses and plane mirrors is Turing-complete, thereby resolving an open question posed by Reif et al. in 1994 as to whether three-dimensional space is necessary for computational universality in optical systems. To this end, we consider the standard approximation of reflection and refraction, namely the ABCD model for paraxial optics, which describes ray propagation through lenses (refraction) via a 2 x 2 matrix, combined with the geometric reflection model for plane mirrors. In the absence of mirrors, two-dimensional ray tracing using any combination of lenses in this ABCD matrix model can be described by a single 2 x 2 matrix-vector product, where the matrix has real entries and determinant 1. Conversely, we show that any such matrix with determinant 1 can be represented as a composition of exactly three appropriately spaced thin lenses. When mirrors are combined with lenses, the ray tracing problem can be described by a flowchart using only two variables, which establishes Turing computability for rational-valued inputs, spaces and matrix entries. Building on this observation, we present a construction of ray tracing that simulates a reversible Turing machine. We begin with a restricted version of the reversible flowchart problem, in which only two variables and certain linear functions are permitted. We prove that this restricted variant is Turing-complete. We then show that such a flowchart admits a geometric realization using lenses and mirrors in our model, thereby establishing the main result: Turing-completeness of the two-dimensional ray tracing problem with ABCD-model lenses and mirrors.

cs.CC↗

arXiv2025

How Pinball Wizards Simulate a Turing Machine

We introduce and investigate the computational complexity of a novel physical problem known as the Pinball Wizard problem. It involves an idealized pinball moving through a maze composed of one-way gates (outswing doors), plane walls, parabolic walls, moving plane walls, and bumpers that cause acceleration or deceleration. Given the initial position and velocity of the pinball, the task is to decide whether it will hit a specified target point. By simulating a two-stack pushdown automaton, we show that the problem is Turing-complete -- even in two-dimensional space. In our construction, each step of the automaton corresponds to a constant number of reflections. Thus, deciding the Pinball Wizard problem is at least as hard as the Halting problem. Furthermore, our construction allows bumpers to be replaced with moving walls. In this case, even a ball moving at constant speed -- a so-called ray particle -- can be used, demonstrating that the Ray Particle Tracing problem is also Turing-complete.

cs.CC↗

arXiv2024

Critical Near-Field Impedance Matrices

We investigate the theoretical impedance equations for several near-field antenna positions. In the standard model one computes the currents at the antennas for given voltages using the impedance matrix of the antennas, which is only possible if the determinant of the impedance matrix is non-zero. We consider Hertzian group antennas, its relative corresponding impedance and two approximations (mid and far) of it. For the approximations we show that for many situations the determinant is zero. We find three antenna configurations for three antennas, i.e., on a line, on a right triangle, and an isosceles triangle, which result in a zero determinant of the impedance for the far-field approximation. This means that with existing methods, one cannot determine the behavior of this antenna system. For the better mid approximation, we find a configuration of 15 triangular-positioned antennas resulting in a singular impedance matrix. Furthermore, we investigate $n\times n$ grid placed antennas in the more accurate Hertzian impedance model and find that for $d \approx 0.65$ wavelengths of grid distance for n = 2, ..., 8 the absolute value of the determinant of the corresponding impedance matrix decreases by an order of magnitude with each increased grid size.

eess.SP↗

arXiv2024

Robust time-of-arrival localization via ADMM

This article considers the problem of source localization (SL) using possibly unreliable time-of-arrival (TOA) based range measurements. Adopting the strategy of statistical robustification, we formulate TOA SL as minimization of a versatile loss that possesses resistance against the occurrence of outliers. We then present an alternating direction method of multipliers (ADMM) to tackle the nonconvex optimization problem in a computationally attractive iterative manner. Moreover, we prove that the solution obtained by the proposed ADMM will correspond to a Karush-Kuhn-Tucker point of the formulation when the algorithm converges, and discuss reasonable assumptions about the robust loss function under which the approach can be theoretically guaranteed to be convergent. Numerical investigations demonstrate the superiority of our method over many existing TOA SL schemes in terms of positioning accuracy and computational simplicity. In particular, the proposed ADMM achieves estimation results with mean square error performance closer to the Cramér-Rao lower bound than its competitors in our simulations of impulsive noise environments.

eess.SP↗

arXiv2023

Simulation of a first prototypical 3D solution for Indoor Localization based on Directed and Reflected Signals

We introduce a solution for a specific case of Indoor Localization which involves a directed signal, a reflected signal from the wall and the time difference between them. This solution includes robust localization with a given wall, finding the right wall from a group of walls, obtaining the reflecting wall from measurements, using averaging techniques for improving measurements with errors and successfully grouping measurements regarding reflecting walls. It also includes performing self-calibration by computation of wall distance and direction introducing algorithms such as All pairs, Disjoint pairs and Overlapping pairs and clustering walls based on Inversion and Gnomonic Projection. Several of these algorithms are then compared in order to ameliorate the effects of measurement errors.

cs.RO↗

arXiv2023

Globally Optimized TDOA High Frequency Source Localization Based on Quasi-Parabolic Ionosphere Modeling and Collaborative Gradient Projection

We investigate the problem of high frequency (HF) source localization using the time-difference-of-arrival (TDOA) observations of ionosphere-refracted radio rays based on quasi-parabolic (QP) modeling. An unresolved but pertinent issue in such a field is that the existing gradient-type scheme can easily get trapped in local optima for practical use. This will lead to the difficulty in initializing the algorithm and finally degraded positioning performance if the starting point is inappropriately selected. In this paper, we develop a collaborative gradient projection (GP) algorithm in order to globally solve the highly nonconvex QP-based TDOA HF localization problem. The metaheuristic of particle swarm optimization (PSO) is exploited for information sharing among multiple GP models, each of which is guaranteed to work out a critical point solution to the simplified maximum likelihood formulation. Random mutations are incorporated to avoid the early convergence of PSO. Rather than treating the geolocation of HF transmitter as a pure optimization problem, we further provide workarounds for addressing the possible impairments and challenges when the proposed technique is applied in practice. Numerical results demonstrate the effectiveness of our PSO-assisted re-initialization strategy in achieving the global optimality, and the superiority of our method over its competitor in terms of positioning accuracy.

eess.SP↗

arXiv2021

Neurodynamic TDOA localization with NLOS mitigation via maximum correntropy criterion

In this paper, we exploit the maximum correntropy criterion (MCC) to robustify the traditional time-difference-of-arrival (TDOA) location estimator in the presence of non-line-of-sight (NLOS) propagation conditions. For the sake of statistical efficiency, the correntropy-based robust loss is imposed on the underlying time-of-arrival composition via joint estimation of the source position and onset time, instead of the TDOA counterpart generated in the postprocessing of sensor-collected timestamps. We then employ a neurodynamic optimization approach to tackle the highly nonconvex MCC formulation. Furthermore, we examine the local stability of equilibrium for the corresponding projection-type neural network model. Simulation investigations in representative NLOS propagation scenarios demonstrate that our neurodynamic robust TDOA localization solution is capable of outperforming several existing schemes in terms of positioning accuracy.

eess.SP↗

arXiv2021

QUDOS: Quorum-Based Cloud-Edge Distributed DNNs for Security Enhanced Industry 4.0

Distributed machine learning algorithms that employ Deep Neural Networks (DNNs) are widely used in Industry 4.0 applications, such as smart manufacturing. The layers of a DNN can be mapped onto different nodes located in the cloud, edge and shop floor for preserving privacy. The quality of the data that is fed into and processed through the DNN is of utmost importance for critical tasks, such as inspection and quality control. Distributed Data Validation Networks (DDVNs) are used to validate the quality of the data. However, they are prone to single points of failure when an attack occurs. This paper proposes QUDOS, an approach that enhances the security of a distributed DNN that is supported by DDVNs using quorums. The proposed approach allows individual nodes that are corrupted due to an attack to be detected or excluded when the DNN produces an output. Metrics such as corruption factor and success probability of an attack are considered for evaluating the security aspects of DNNs. A simulation study demonstrates that if the number of corrupted nodes is less than a given threshold for decision-making in a quorum, the QUDOS approach always prevents attacks. Furthermore, the study shows that increasing the size of the quorum has a better impact on security than increasing the number of layers. One merit of QUDOS is that it enhances the security of DNNs without requiring any modifications to the algorithm and can therefore be applied to other classes of problems.

cs.CR↗

arXiv2021

Maximum correntropy criterion for robust TOA-based localization in NLOS environments

We investigate the problem of time-of-arrival (TOA) based localization under possible non-line-of-sight (NLOS) propagation conditions. To robustify the squared-range-based location estimator, we follow the maximum correntropy criterion, essentially the Welsch $M$-estimator with a redescending influence function which behaves like $\ell_0$-minimization towards the grossly biased measurements, to derive the formulation. The half-quadratic technique is then applied to settle the resulting optimization problem in an alternating maximization (AM) manner. By construction, the major computational challenge at each AM iteration boils down to handling an easily solvable generalized trust region subproblem. It is worth noting that the implementation of our localization method requires nothing but merely the TOA-based range measurements and sensor positions as prior information. Simulation and experimental results demonstrate the competence of the presented scheme in outperforming several state-of-the-art approaches in terms of positioning accuracy, especially in scenarios where the percentage of NLOS paths is not large enough.

eess.SP↗

arXiv2021

Two Efficient and Easy-to-Use NLOS Mitigation Solutions to Indoor 3-D AOA-Based Localization

This paper proposes two efficient and easy-to-use error mitigation solutions to the problem of three-dimensional (3-D) angle-of-arrival (AOA) source localization in the mixed line-of-sight (LOS) and non-line-of-sight (NLOS) indoor environments. A weighted linear least squares estimator is derived first for the LOS AOA components in terms of the direction vectors of arrival, albeit in a sub-optimal manner. Next, data selection exploiting the sum of squared residuals is carried out to discard the error-prone NLOS connections. In so doing, the first approach is constituted and more accurate closed-form location estimates can be obtained. The second method applies a simulated annealing stochastic framework to realize the robust $\ell_1$-minimization criterion, which therefore falls into the methodology of statistical robustification. Computer simulations and ultrasonic onsite experiments are conducted to evaluate the performance of the two proposed methods, demonstrating their outstanding positioning results in the respective scenarios.

eess.SP↗

arXiv2020

Crucial and Redundant Shares and Compartments in Secret Sharing

Secret sharing is the well-known problem of splitting a secret into multiple shares, which are distributed to shareholders. When enough or the correct combination of shareholders work together the secret can be restored. We introduce two new types of shares to the secret sharing scheme of Shamir. Crucial shares are always needed for the reconstruction of the secret, whereas mutual redundant shares only help once in reconstructing the secret. Further, we extend the idea of crucial and redundant shares to a compartmented secret sharing scheme. The scheme, which is based on Shamir's, allows distributing the secret to different compartments, that hold shareholders themselves. In each compartment, another secret sharing scheme can be applied. Using the modifications the overall complexity of general access structures realized through compartmented secret sharing schemes can be reduced. This improves the computational complexity. Also, the number of shares can be reduced and some complex access structures can be realized with ideal amount and size of shares.

cs.CR↗

arXiv2020

Partitioned Private User Storages in End-to-End Encrypted Online Social Networks

In secure Online Social Networks (OSN), often end-to-end encryption approaches are used. This ensures the privacy of communication between the participants. To manage, store, or transfer the cryptographic keys from one device to another one, encrypted private storages can be used. To gain access to such storages, login credentials, only known to the user, are needed. Losing these credentials results in a permanent loss of cryptographic keys and messages because the storage is encrypted. We present a scheme to split encrypted user storages into multiple storages. Each one can be reconstructed with the help of other participants of the OSN. The more of the storages can be reconstructed, the higher the chance of successfully reconstructing the complete private storage is. Therefore, regaining possession of the cryptographic keys used for communication is increased. We achieve high rates of successful reconstructions, even if a large fraction of the distributed shares are not accessible anymore because the shareholders are inactive or malicious.

cs.CR↗

arXiv2020

A Proxy-Based Encrypted Online Social Network With Fine-Grained Access

When using Online Social Networks, users often share information with different social groups. When considering the backgrounds of the groups there is often no or little intersection within the members. This means that a user who shares information often has to share it with all members of all groups. It can be problematic that the user cannot decide which group sees which information. Our approach therefore, allows users to decide for every bit of information who can access it. Further, protected circles can be created, where users can share information within. Shared information and circles are encrypted and the keys can be distributed by proxies.

cs.CR↗

arXiv2020

Concealed Communication in Online Social Networks

Online social networks are used frequently by many people: Staying in contact with friends and sharing experiences with them is very important. However, users are increasingly concerned that their data will end up in the hands of strangers or that personal data may even be misused. Secure OSNs can help. These often use different types of encryption to keep the communication between the participants incomprehensible to outsiders. However, participants in such social networks cannot be sure that their data is secure. Various approaches show that even harmless-looking metadata, such as the number of contacts of users, can be evaluated to draw conclusions about the users and their communication. These attack methods are analyzed, and existing secure OSNs are examined, whether these attack methods can be utilized to violate the user's privacy. To prevent these privacy attacks, protocols for a secure centralized OSN are developed. Metadata is obscured in the presented OSM and end-to-end encryption is used for secure communication between clients. Additionally, communication channels are concealed using mix networks such that adversaries cannot determine which user is accessing which data or which user is communicating with whom even with access to the server.

cs.CR↗

arXiv2020

TDOA-based localization with NLOS mitigation via robust model transformation and neurodynamic optimization

This paper revisits the problem of locating a signal-emitting source from time-difference-of-arrival (TDOA) measurements under non-line-of-sight (NLOS) propagation. Many currently fashionable methods for NLOS mitigation in TDOA-based localization tend to solve their optimization problems by means of convex relaxation and, thus, are computationally inefficient. Besides, previous studies show that manipulating directly on the TDOA metric usually gives rise to intricate estimators. Aiming at bypassing these challenges, we turn to retrieve the underlying time-of-arrival framework by treating the unknown source onset time as an optimization variable and imposing certain inequality constraints on it, mitigate the NLOS errors through the $\ell_1$-norm robustification, and finally apply a hardware realizable neurodynamic model based on the redefined augmented Lagrangian and projection theorem to solve the resultant nonconvex optimization problem with inequality constraints. It is validated through extensive simulations that the proposed scheme can strike a nice balance between localization accuracy, computational complexity, and prior knowledge requirement.

eess.SP↗

arXiv2019

Collaborative Broadcast in O(log log n) Rounds

We consider the multihop broadcasting problem for $n$ nodes placed uniformly at random in a disk and investigate the number of hops required to transmit a signal from the central node to all other nodes under three communication models: Unit-Disk-Graph (UDG), Signal-to-Noise-Ratio (SNR), and the wave superposition model of multiple input/multiple output (MIMO). In the MIMO model, informed nodes cooperate to produce a stronger superposed signal. We do not consider the problem of transmitting a full message nor do we consider interference. In each round, the informed senders try to deliver to other nodes the required signal strength such that the received signal can be distinguished from the noise. We assume sufficiently high node density $ρ= Ω(\log n)$. In the unit-disk graph model, broadcasting needs $O(\sqrt{n/ρ})$ rounds. In the other models, we use an Expanding Disk Broadcasting Algorithm, where in a round only triggered nodes within a certain distance from the initiator node contribute to the broadcasting operation. This algorithm achieves a broadcast in only $O(\frac{\log n}{\log ρ})$ rounds in the SNR-model. Adapted to the MIMO model, it broadcasts within $O(\log \log n - \log \log ρ)$ rounds. All bounds are asymptotically tight and hold with high probability, i.e. $1- n^{-O(1)}$.

cs.IT↗

arXiv2017

T-ROME: A Simple and Energy Efficient Tree Routing Protocol for Low-Power Wake-up Receivers

Wireless sensor networks are deployed in many monitoring applications but still suffer from short lifetimes originating from limited energy sources and storages. Due to their low-power consumption and their on-demand communication ability, wake-up receivers represent an energy efficient and simple enhancement to wireless sensor nodes and wireless sensor network protocols. In this context, wake-up receivers have the ability to increase the network lifetime. In this article, we present T-ROME, a simple and energy efficient cross-layer routing protocol for wireless sensor nodes containing wake-up receivers. The protocol makes use of the different transmission ranges of wake-up and main radios in order to save energy by skipping nodes during data transfer. With respect to energy consumption and latency, T-ROME outperforms existing protocols in many scenarios. Here, we describe and analyze the cross layer multi-hop protocol by means of a Markov chain model that we verify using a laboratory test setup.

cs.NI↗

arXiv2016

Cyclone Codes

We introduce Cyclone codes which are rateless erasure resilient codes. They combine Pair codes with Luby Transform (LT) codes by computing a code symbol from a random set of data symbols using bitwise XOR and cyclic shift operations. The number of data symbols is chosen according to the Robust Soliton distribution. XOR and cyclic shift operations establish a unitary commutative ring if data symbols have a length of $p-1$ bits, for some prime number $p$. We consider the graph given by code symbols combining two data symbols. If $n/2$ such random pairs are given for $n$ data symbols, then a giant component appears, which can be resolved in linear time. We can extend Cyclone codes to data symbols of arbitrary even length, provided the Goldbach conjecture holds. Applying results for this giant component, it follows that Cyclone codes have the same encoding and decoding time complexity as LT codes, while the overhead is upper-bounded by those of LT codes. Simulations indicate that Cyclone codes significantly decreases the overhead of extra coding symbols.

cs.IT↗