# Open Theses

You may also contact one of our doctoral candidates directly, if you are interested in a Bachelor or Master thesis, a student job, an "Ingenieurspraxis" or a "Forschungspraxis". It often happens, that topics are being prepared which are not adverdised yet. It may also be possible to find a topic matching your specific interests.

Please include a **curriculum vitae** together with a **list of attended courses** when applying for a thesis.

If your "Ingenieurspraxis" is selected to be supervised by one of our professors, please hand in the documents to Doris Dorn (Room N2401).

## Bachelor or Master Theses

Error Correcting Codes for Insertion/Deletion Errors | ||

The discussion of synchronization errors, like insertions and deletions of symbols into codewords goes back to the early 1960's. Still, little is known about these kinds of errors and basic questions, like the capacity of the binary deletion channel remain unsolved. This stems from the fact that errors in the insertion/deletion metric are fundamentally different from the well-researched substitution errors and conventional error correcting codes cannot be applied on these kinds of errors. Current research, and the topic of this Bachelor or Master thesis, is directed towards finding the minimum redundancy of such codes and constructing codes that can correct insertion and deletion errors. Prerequisites:
You should have good knowledge in linear Algebra and interest in channel coding. |
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Supervisor: Andreas Lenz |

## Master Theses

A Deterministic Approach to the Gaussian Multiple-Input Multiple-Output (MIMO) Broadcast Channel | ||

Multi-user communication systems (such as wireless systems) are different than point to point channels in two key aspects; namely, the broadcast nature of transmissions (e.g., wireless transmissions can be picked up by any receiver in the vicinity of the transmitter) and the superposition (e.g., a wireless receiver picks up a linear combination of transmissions from all transmitters in its vicinity). Recently a deterministic approach to multi-user information theory has proved promising by achieving progress in some of the long-standing open problems by finding approximate solutions. The idea behind a deterministic approach, on a high level, is to focus on the interaction of signals rather than the background noise, through a simpler appropriate model; find exact solutions for the simpler model; and then translate the intuitions and techniques to new techniques and/or approximate solutions on noisy models. The goal of thesis is to undertake a deterministic approach to Gaussian MIMO broadcast channels. Prerequisite: Linear Algebra, Information Theory |
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Supervisor: Shirin Saeedi |

Role of Feedback in Broadcasting | ||

This project intends to investigate the role of feedback in broadcast channels. More information available upon request.
Pre-requisite (at least one of the following): Basic knowledge of Network Coding (see [2]) Basic knowledge of Algorithms Basic knowledge of Information Theory |
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Supervisor: Shirin Saeedi |

Code and Algorithm Design for Physical-layer Security | ||

We are looking for motivated students to work on algorithm and code design for privacy and security applications. For realistic channel models, we want to implement a set of codes and algorithms to analyse their complexity, reliability, privacy, and secrecy performance. The thesis basically consists of Pre-requisites: Information theory, Channel Coding |
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Supervisor: Onur Günlü |

Designing codes for secret key generation and extracting the secret bits in left over hash lemma | ||

The source model of secret key generation deals with the idea of Alice and Bob generating a key in a distributed manner from correlated observations. This key must be kept secret from an evesdropper. In this internship/thesis the student will start by looking at a simpler model which corresponds to the left over hash lemma. The student will build on some preliminary work done by me to design codes for the extraction of left over hash in a simple setting. After this the student will extend the work to design codes for distributed secret key generation for the source model. | ||

Supervisor: Rana Ali Amjad |

MIMO Multiport Communications | ||

The topic of the thesis is to develop a simulator for MIMO communications including the transmit and receive RF frontends of a single user link. The simulator should be able to support different types of antenna elements and array configurations as well as matching circuits and amplifier models. In addition it should be able to estimate rates of communication over deterministic and stochastic channels. | ||

Supervisor: Andrei Nedelcu |

Rate-Distortion Theory for Sparse Sources | ||

Rate-Distortion Theory for Sparse Sources
This project investigates information theory limits for the lossy compression of sparse sources.
Motivated by the recent mathematical theory Compressed Sensing that deals with the efficient acquisition and reconstruction of sparse signals, we try to determine the fundamental limits of digitally storing data created by such sources.
A sparse source emits a string of symbols of which - loosely speaking - only a few contain information. There are different ways to model these sources. An example is the Gaussian spike source which emits a Gaussian symbol with probability p and a zero with probability 1-p.Possible directions of a project are: - Investigating different source models - (Numerically) determining the rate distortion function of a sparse source - Computing finite length performance bounds for sparse sources Prerequisites: - Information Theory (must) - Pleasure with mathematics (must) - Multiuser information theory (beneficial) |
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Supervisor: Lars Palzer |

## Forschungspraxis (12 ECTS)

Error-Correction for Partially Stuck Memory Cells | ||

Supervisor: Antonia Wachter-Zeh |

## Forschungspraxis or MSCE Internships

Code design for Physical Layer Security | ||

Wiretap channel represents the basic setup for physical layer security. It has been extensively studied in the last four decades and the fundamental limits of communication for this channel are known in a wide variety of scenarios. Nevertheless the only explicit code construction that can achieve wiretap secrecy capacity uses Polar codes. Designing codes for secrecy involve the combined design of codes for reliability and channel resolvability. In 2015 a new coding scheme for channel resolvability was introduced by Amjad and Kramer. The aim of this internship is to combine this channel resolvability code with existing channel codes in order to design wiretap code. | ||

Supervisor: Rana Ali Amjad |

Code Design for Secret Key Generation/ Left over Hash Lemma | ||

The source model of secret key generation deals with the idea of Alice and Bob generating a key in a distributed manner from correlated observations. This key must be kept secret from an evesdropper. In this internship/thesis the student will start by looking at a simpler model which corresponds to the left over hash lemma. The student will build on some preliminary work done by me to design codes for the extraction of left over hash in a simple setting. After this the student will (if time permits) extend the work to design codes for simple cases of distributed secret key generation for the source model. | ||

Supervisor: Rana Ali Amjad |

# Theses in Progress

## Bachelor Theses

Mohamed Ben Chikha: Lossy Source Coding Performance of Low-Complexity Compressive Sensing | ||

The subject of this Bachelor’s thesis is the performance analysis of recent one-bit com- pressive sensing (CS) algorithms in a lossy source coding framework.
Based on the seminal works of Donoho as well as Cand ́es and Tao that deal with the efficient linear encoding of a sparse real-valued vector into a real-valued vector of smaller dimension, Boufounos and Baraniuk [1] proposed a one-bit CS algorithm where each linear measurement is quantized to +1 or -1. From these binary measurements, the original signal can then be approximated using various optimization techniques. A major drawback of simple sign measurements is that the quantization error decreases only inversely proportional to the number of bits, as opposed to an exponential decay with optimal vector quantization. To overcome this limitation, Boufounos proposed the usage of discontiguous scalar quantization regions while still keeping a single bit per measurement. In [2], it is shown that the quantization error can indeed decrease exponentially in the number of mea- surements. A possible decoding structure for this method is Generalized Approximate Message Passing, which is used in [3] and indicates that good performance is achievable in practice. In lossy compression, the performance of a quantization code is usually measured with respect to its average distortion (the average quantization error) or excess distortion, that is, the probability of exceeding a given quantization error. Recently, there has been significant progress in finding the fundamental limits for the excess-distortion performance of fixed length vector quantizers, see [4, 5] and the references. These results can be seen as benchmarks for the performance of practical algorithms. The aim of this thesis is thus to implement one-bit CS algorithms based on discontiguous scalar quantization and investigate their lossy source coding performance. [1] P. T. Boufounos and R. G. Baraniuk, “1-bit compressive sensing,” in 42nd Annual Conference on Information Sciences and Systems (CISS), pp. 16–21, March 2008. [2] P. T. Boufounos, “Universal rate-efficient scalar quantization,” IEEE Trans. Inf. Theory, vol. 58, pp. 1861 – 1872, Mar 2012. [3] U. S. Kamilov, V. K. Goyal, and S. Rangan, “Message-passing de-quantization with applications to compressed sensing,” IEEE Trans. Sig. Proc., vol. 60, pp. 6270 – 6281, Dec 2012. [4] V. Kostina and S. Verdu ́, “Fixed-length lossy compression in the finite blocklength regime,” IEEE Trans. Inf. Theory, vol. 58, pp. 3309 – 3338, June 2012. [5] L. Palzer, R. Timo, and G. Kramer, “Compression for letter-based fidelity measures,” preprint, Jan 2016. [6] http://dsp.rice.edu/1bitCS/. |
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Supervisor: Lars Palzer |

Alberto Diago Gallardo : Atmospheric Influence on Free Space Optical Communications | ||

The work is based on Free Space Optical (FSO) communications and will include the following parts: • Case Study: Ground-to-Ground laser Links: o Link budget calculations; (Done) o Tracking Power budget calculations; o Scintillation analysis (optional: atmospheric simulations and fade statistics); (Ongoing) o Atmospheric Attenuation: Link availability calculations. (Ongoing) • Support the design, integration of testing of the “Frame-Steering Concept” as a demonstrator terminal for static links. (Ongoing) • Outdoor link demonstration and measurement campaign. • Analysis and evaluation of the measurement data. | ||

Supervisor: Norbert Hanik, Luis Martin Navajas |

Anas Azouni: Error Detection Outer Codes for Polar Codes | ||

Polar codes are capacity achieving codes that have rather bad performance for short and medium length codes. Its performance can be improved using list decoding and outer error detection codes, like CRC codes. The goal of this Bachelor's thesis is to investigate different outer codes that work for error detection. | ||

Supervisor: Tobias Prinz |

Alexander Matthies: Inbetriebnahme und Test eines DSP-Boards | ||

Supervisor: Gerhard Kramer, Fa. Rohde & Schwarz GmbH & Co. KG, 81671 München |

Alyssa Akremi: Reduced complex precoding for CoMP massive MIMO sparse Channels | ||

In this thesis, we investigate the low complex algorithms applicable to Zero-Forcing process of Coordinated Multi Point (CoMP) sparse channel matrices | ||

Supervisor: Amir Ahmadian |

Houssem Amami: Inter-channel interference in optical narrow-band multi-channel systems with distributed filters | ||

The nonlinear nature of the fiber optic channel produces frequency mixing and the appearance of spurious frequencies. Careful design of the fiber can mitigate this effect by removing the spurious components, but there is still residual interference between channels in multi-channel systems. In this thesis, narrow-band channels are considered, and the nature of the residual interference is explored. | ||

Supervisor: Francisco Javier Garcia Gomez |

Rouven Fischer: Investigation into control concepts of modern industrial automation | ||

Supervisor: Norbert Hanik |

## Master Theses

Clemens Bloechl: Aggregation of (Hidden) Markov Models - Theory and Applications | ||

The topic of the thesis is to develop and analyze information-theoretic aggregation methods to reduce the state space and/or the observation space of hidden Markov models. Using the Kullback-Leibler divergence rate as cost function, we expect connections with the information bottleneck method, lumpability, and spectral aggregation techniques. In the second part of the thesis, the developed methods shall be applied to practical examples, such as speech recognition systems. As a further example, the techniques shall be used to collapse output states of a discrete memoryless channel, without affecting the error probability of a Viterbi algorithm decoding a convolutional code. |
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Supervisor: Bernhard Geiger, Rana Ali Amjad |

Mustafa Cemil Coskun: Successive Cancellation Decoding of Product Codes | ||

Product codes were introduced by Peter Elias in 1954. He showed that the bit error probability can be made arbitrarily small by constructing a multidimensional product code with a positive code rate although it was far below the capacity limit. After almost half a decade, Erdal Arıkan has come with a channel code, which is provably capacity-achieving under successive cancellation decoding as block length tends to infinity. The construction of both codes shows many similarities, which can be exploited. The thesis will investigate these similarities between two classes of codes and, in particular, it will borrow some tools from polar code setting and apply to product codes, e.g. successive cancellation decoder. After finding some theoretical results, the work will be concluded by implementing a simulator for product codes to show whether the findings are accurate or not. |
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Supervisor: Dr. Gianluigi Liva (DLR) |

Dhanush Krishna: Development of a variable data rate transceiver for real-time operation in Free-Space Optical communications systems | ||

RF-based technologies are extensively used for wireless communication systems because of its multiple advantages such as the absence of wiring infrastructure and there inherent flexibility to integrate Ad-hoc networks. However, the free radio-electric spectrum for communications is decreasing due to the constant increase of bandwidth demand and services. In order to solve this problem aerospace industry is assessing the possibility of using Free-Space Optical (FSO) communications as an alternative solution. The main advantages of such systems are potential higher data rates (several Gigabits per second), small communication devices, tap-proofness and license free spectrum bands. Unfortunately, FSO systems are sensible to atmospheric perturbations, i.e. fog, clouds, rain, that attenuate the signal and thus lead to fades at the receiver. Additionally, mobile applications suffer from fades caused by atmosphere and imperfect pointing and tracking systems. For all the above mentioned reasons, Deutsches Zentrum für Luft- und Raumfahrt (DLR) Institute of Communications and Navigation is designing and developing a FSO communication transceiver for aeronautical applications using commercial FPGAs. This transceiver, Laser Ethernet transceiver (LET), acts as a media converter between Ethernet frames and proprietary LET frames for FSO. It features novel fading-robust communication protocols combined with error correction schemes to allow error free transmission through the atmosphere. High rate codes and long interleavers can be used to cope against such fades and thus the system has to be designed for bad channel condition. However, it is waste of resources when the channel is good. Therefore, an intelligent way to optimize resources is to vary the data rate of the system according to the channel condition. As part of this initiative, the main objectives of this Master’s Thesis are first to study and analyze the different methodologies to perform variations in the line data rate. Second, to develop, test and verify the necessary RTL structures in VHDL for implementing a reliable, automatic system capable of switching between different data rates up to 10Gbps. This RTL structures will be integrated into an existing LET system thus it will have to communicate with existing parts of the design which constitutes the starting point of this Master’s Thesis. As secondary objectives, a minimization of third party development resources is desirable and will be carried out in close collaboration with hardware designers. In addition, all the work development shall be oriented to fulfil the requirements for the qualification process. This implies that both internal and external documentation of the project shall be provided. Block Diagram and how VarDR relates Channel Estimation: The earlier topic which was the real-time channel estimator, we needed to evaluate the different channel conditions taking into consideration system loss, geometric loss, misalignment loss, atmospheric loss, atmospheric turbulence induced fading, and ambient noise. By taking into account each of the losses that are present in a real-time channel, we needed to evaluate what kind off loss reduction mechanism could be employed. Since we need to even take care that the design components shouldn’t be redundant as there could be cases wherein all the loss prevention mechanisms won’t be applied at the same time. Whereas the main objective of the former topic was to analyze and to estimate the current conditions of an optical link, this new thesis focuses into the understanding and development of techniques which allow the system to adapt itself to the changing channel situation. As seen from the diagram, we see that the Variable Data-Rate transceiver Block is included. We also observe that Channel Estimation Block runs in parallel with the Variable Data-Rate Transceiver. Now the question would be the use of this variable data transceiver. It is not always feasible to transmit the data at the same rate for all the atmospheric conditions. For Ex: In case of Foggy climate it is feasible to transmit the data at lower rate whereas in case of the clear sky, higher rates can be used. Taking into account the output from the Channel Estimator, different data rates can be used to transmit the data and this variable data rate is adapted across all the components in the design. In general, the real time channel state information (CSI) is considered and the data rate across the transceivers are modified. After analyzing, the implementation is carried out on the FPGA providing the control signals for different channel conditions which then determines the data rate. | ||

Supervisor: Norbert Hanik, Jorge Pacheco (DLR, Oberpfaffenhofen) |

Keykavoos Afghahi: Methods for Adaptive Channel Allocation in a Multi-cell System | ||

Supervisor: Markus Staudacher, Neda Petreska (Frauenhofer ESK) |

Julian Leyh: Evaluation of Transmission Parameters of a Digitally Modulated TV Signal | ||

During modulation and transmission of OFDM signals there are various disturbance effects taking place, which can influence the quality of the signal at the receiver and therefore also the system performance. The commonly used metric 'Modulation Error Rate', which represents the magnitude of all transmitter impairments, is not sufficient to adequately track errors in the development and operation of modern digital broadcasting systems.
This thesis aims at developing, assessing, simulating, and implementing new algorithms that can provide continuous estimation of a number of transmission parameters for a real world digital television broadcasting standard for which existing methods do not give satisfactory results, which is due to the used frame structure. |
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Supervisor: Onur Günlü, Dipl.-Ing. Medientechnologie (TU) Hardi Klenner (Rohde&Schwarz) |

Daniel Sander: Development of a measurement device for characterization of the signal quality in optical satellite-to-ground communications | ||

The Institute of Communications and Navigation develops new systems and algorithms for optical communications with satellites and aircraft. The atmosphere significantly degrades signal quality, which can be seen in phase and intensity distortions as well as signal blockage by clouds. The institute operates an optical ground station to characterize these distortions and conducts measurement campaigns with satellites and aircraft. The new measurement device shall be designed to be directly attached aside the main receiver reflector of a ground station. The measurement device shall be independent from the receiver reflector e.g. the optical telescope but shall use the same tracking mount. The prime application will be the characterization of channel impairments at existing ground station sites worldwide, either of optical or RF type. This drives the requirement that the measurement device must be weatherproof taking into account typical climate conditions at ground station sites and it shall be of a small form factor (2” system). To ensure simple and continuous operations it must be able to be operated autonomously. In this work, this measurement device for signal quality shall be designed, assembled and tested. The design shall consider boundary conditions given by possible installations on an optical or RF receive antenna system as well as availability of possible signals sources in space. This includes analysis of characteristics of different antenna types (optical/RF), recommendations given by standardization activities regarding the space-to-ground link and expected dynamics and signal levels from potential test sources. | ||

Supervisor: Norbert Hanik, Dirk Giggenbach / Florian Moll / Hennes Henniger |

Kairen Liu: Information Theoretic Analysis of Neural Networks | ||

Various types of neural networks have gained a lot of attention in recent years and have found numerous practical applications with impressive results. Albeit their success, their behaviour is not very well understood mathematically. The aim of this thesis is to approach the topic from an information theoretic perspective and see if one can use insight from information and coding theory to analyze/design neural networks for specific applications. | ||

Supervisor: Rana Ali Amjad, Bernhard Geiger |

Zafzouf Ghassen: Investigation into signal wave-forms for 5G & information theoretic analysis of MIMO OFDM systems | ||

5G communication systems aim to put a large range of devices onto a network, ranging from high bandwidth systems which can transfer video and large files to small devices which only sporadically send data. Similarly the devices may be battery powered or not. The problem that can exist is that many modern communication systems are based on OFDM modulation which when used by multiple users simultaneously can have problems with synchronization, bit resolution, and the need to achieve good channel estimation. Our goal will be to characterize the fundamental information theoretic limits of such communication systems,as well as to design practical communication schemes that can approach these limits. This project will look into MIMO OFDM systems with a view to improve them towards being suitable for 5G communication systems. | ||

Supervisor: Markus Staudacher |

Jianwei Zhang: Probabilistic Signal Shaping for Short-Reach Optical Fiber Systems | ||

Optical fiber systems form the backbone of the internet. Despite their large usable bandwidth, they are going to running out of capacity due to an increasing demand for services such as high-definition video streaming. In order to obtain the largest possible transmission rates for a fixed link, a shaped input should replace the common uniform input. In particular, non-iid inputs lead to less fiber nonlinearities, which improves the system performance. This Master thesis investigates such temporally correlated fiber inputs. | ||

Supervisor: Tobias Fehenberger |

## Ingenieurspraxis

Mahmoud Marcam Helmy: Erstellung einer App für Smartphones der BITS mobile ERP Linie auf Basis von IOS Plattformen | ||

Supervisor: Gerhard Kramer, BITS better it solutions GmbH, Wallenmahd 47, A-6850 Dornbirn |

Lukas Püttner: Evaluierung verschiedener Tools zur Extraktion und Auswertung von Metadaten aus IP-Verkehrsdaten | ||

Supervisor: Norbert Hanik, ESG Elektroniksystem- und Logistik GmbH, 82256 Fürstenfeldbruck |

Francesco Montanari: Dynamic Dead Pixel Correction | ||

Supervisor: Norbert Hanik, Fa. ARRI, Arnold & Richter Cine Technik GmbH & Co KG, München, Fr. E. Kögel |

Barbara Lenz: Durchführung/Auswertung von RCS-Messungen | ||

Supervisor: Gerhard Kramer, MBDA Deutschland GmbH, Schrobenhausen |

## Forschungspraxis (12 ECTS)

Liu Xiaotong: Simulator in Matlab for MIMO Multiport Communications | ||

The purpose is to build a Matlab simulator that can incorporate both circuit and channel models for MIMO communications in order to evaluate the achievable rates with different RF front-end designs in various propagation scenarios. | ||

Supervisor: Andrei Nedelcu |

Afghahi Keikavoos: Development of adaptive radio systems for industrial applications | ||

Wireless real-time communication plays an increasingly pivotal role in industrial automation. Next generation high performance wireless technologies have to meet highest demands regarding latency, efficiency and reliability. Further, they have to be smart and adapt to an ever changing radio environment. In this internship you will participate in the research and development of adaptive wireless communication systems for application in the novel field of Industry 4.0. Using a Software Defined Radio (SDR) system you will develop a spectrum sensing procedure, which enables higher efficiency and reliability of wireless communication technologies for industrial applications. This internship will consist of the following tasks: · Getting familiar with the SDR development using USRP (Universal Software Radio Peripheral) and GNU Radio · Development of a spectrum sensing algorithm using the USRP hardware platform · Software development for interferer detection and smart adaptive channel allocation · Creation of a wireless network prototype, which dynamically adapts to a changing radio environment in an industrial scenario | ||

Supervisor: Ginni Khanna, Neda Petreska |

Niklas Jünger: Energy-Efficiency of Massive MIMO and Network MIMO in a Local Area Acenario | ||

Multiple-input multiple-output (MIMO) methods increase spectral efficiency. These methods can also be used to decrease energy consumption. Using many more antennas at the base station then served users is called massive MIMO. With each added antenna at the base station spectral efficiency is increased. It is however not obvious if the energy efficiency is decreased with every added antenna. The student should review how much energy is consumed and review existing precoding and power allocation strategies for energy efficient transmission. The most well suited strategies should be adopted to the local area scenario deployments. Simulations should be run in the 3GPP two stripe building. |
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Supervisor: Stefan Dierks |

Muhammad Firas Hammosh: Is Online PCA Information-Preserving? | ||

In this research internship, and overview over existing online (i.e., iterative, recursive, etc.) algorithms for Prinicipal Components Analysis (PCA) should be given. We try to find our which (if any) of these algorithms is invertible in the sense that one can reconstruct the original data from only looking at the rotated data. For those algorithms for which this is not possible, the (relative) information loss should be computed. This work thus builds the bridge between PCA given knowledge of the covariance matrix (given-statistics) and PCA given only the sample covariance matrix (given-data). While no information is lost in the former, the information loss in the latter was shown to be substantial. We believe that the information loss of online PCA lies somewhere in between. |
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Supervisor: Bernhard Geiger |

Ralf Peteranderl: Gaussian Noise Models for Optical Fiber Systems | ||

The propagation of a signal through an optical fiber is typically modelled by a nonlinear partial differential equation known as the Nonlinear Schrödinger Equation (NLSE). Unfortunately, there exists no analytical solution to this equation and numerical approximations are computationally expensive. Approximate closed-form equations have been introduced that model the impact of fiber nonlinearities as additive white Gaussian noise. Recently, these Gaussian noise (GN) Models have been extended to take into account the dependence of fiber nonlinearities on the modulation format. The student’s task is to give an overview of the classical GN models and their recent extensions. A focus shall be made on the key steps of the derivation and the underlying approximations. | ||

Supervisor: Tobias Fehenberger |

Thomas Wiegart: Evaluation of Non-Binary LDPC codes for Coded Modulation | ||

In this Forschungspraxis, the student reviews the principles of non-binary LDPC codes and will apply it to a coded modulation scenario. In particular, the internship will deal with the efficient implementation of a non-binary LDPC decoder and the evaluation of different codes presented in literature for higher-order modulation. As the Forschungspraxis progresses, it should also focus on the combination with probabilistic amplitude shaping. | ||

Supervisor: Fabian Steiner |

Maximilian Schädler: Monte Carlo Integration for Optical Communication Systems | ||

Modern optical communication sytems suffer from nonlinear fiber effects that are the main limiting factor to increased spectral efficiencies. The split-step Fourier method, which is used to simulate the propagation of an optical signal through fiber, is computationally highly complex, which makes a detailed analysis of the impact of various system parameters on the fiber nonlinearities practically impossible. In this project, Monte Carlo methods are studied in general and applied to optical communication systems. The aim is to find approximate solutions for non-closed-form expressions that describe the impact of the fiber nonlinearities on the signal. | ||

Supervisor: Tobias Fehenberger |

Emna Ben Yacoub: M-Type Approximation of Hidden Markov Models | ||

In this research project, we replace transition and observation probability matrices of hidden Markov models (HMMs) by matrices where each entry is an integer multiple of integer M (i.e., is "M-type"). The problem is an immediate extension of approximating finite-length probability vectors by M-type vectors. The Viterbi algorithm can be used to infer the state sequence from the observation sequence, given that the algorithm has knowledge of the transition and observation matrices. If, instead of the true matrices, the algorithm has knowledge only of their M-type approximations, this will lead to an increase in error probability. We try to find a connection between a probabilistic divergence measure between the true and the M-type model (e.g., Kullback-Leibler divergence rate, matrix norms, etc.) and this increase in error probability. |
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Supervisor: Bernhard Geiger, Rana Ali Amjad |

## Forschungspraxis (6 ECTS)

Joachim Neu: Evaluation of Spatially Coupled LDPC Codes | ||

The student will review the basics of LDPC convolutional codes and implement a window decoder. Using regular LDPC code ensembles, the student will investigate their performance on the biAWGN channel. If time permits, the work will also consider coded modulation setups involving higher order modulations with probabilistic shaping. | ||

Supervisor: Fabian Steiner |