# Angebotene Arbeiten

Bei Interesse an einer Bachelor oder Master Arbeit, einer Ingenieurs- oder Forschungspraxis oder einer Werkstudententätigkeit, können Sie sich auch direkt an unsere Doktoranden wenden. Es sind oftmals Themen in Vorbereitung, die hier noch nicht aufgelistet sind und es besteht die Möglichkeit ein Thema entsprechend Ihrer Interessenlage zu finden.

Bitte legen Sie jeder Bewerbung einen **Lebenslauf **sowie eine **Liste der besuchten Lehrveranstaltungen** bei.

Wenn Ihre Ingenieurspraxis vom Studiendekanat an einen unserer Professoren zugeteilt wurde, wenden Sie sich damit bitte an Frau Dorn (Raum N2401).

The Weight Enumerators of Product Codes

## The Weight Enumerators of Product Codes

**Stichworte: **

weight enumerator, input-output weight enumerator, input-redundancy weight enumerator, distance spectrum

#### Beschreibung

For product codes (PCs), it is very easy to find the minimum distance and its multiplicity once those of the component codes are known. However, the characterization of its complete distance spectrum is a largely open problem even if those of the component codes are given. In [1], they provide a feasible method to compute the weight enumerators (WEs) of PCs where at least one component code is a single parity check (SPC) code. In addition, an extension to compute the exact input-output weight enumerator (IO-WE) for 2-dimensional PCs with SPC component codes and a lower bound for those with more dimensions are available in [2].

The student will understand the ideas presented there and develop a software to compute them efficiently.

References:

[1] http://ieeexplore.ieee.org/document/512606/

[2] ttps://dspace.library.uvic.ca/bitstream/handle/1828/5487/Rankin_DavidM_EURASIPJAdvSignalProcess_2005.pdf?sequence=1&isAllowed=y

#### Voraussetzungen

**Necessary:**

- Basics of channel coding
- C++ (The applicant can suggest an alternative with a good reason)

**Related Courses:**

- Channel Coding
- Channel Codes for Iterative Decoding
- Coding Theory for Storage and Networks

#### Kontakt

mustafa.coskun@tum.de

#### Betreuer:

Synchronization error correcting codes

## Synchronization error correcting codes

#### Beschreibung

Synchronization errors occur when the transmitter and receiver of a communication system are not perfectly synchronized and result in insertions or deletions of symbols from the transmited word. These errors are fundamentally different from the well-researched substitution errors and conventional error correcting codes cannot be applied on these kinds of errors. Although synchronization errors can significantly impact the performance of conventional codes, still little is known about these errors and basic questions like the capacity of the binary deletion channel remain unknown. Current research, and the topic of this thesis, is directed towards finding the minimum redundancy of such codes and developing constructions that can correct insertion and deletion errors.

#### Voraussetzungen

You should have good knowledge in linear Algebra and interest in coding theory.

#### Betreuer:

Analysis of Deep Neural Networks using Information Theory

## Analysis of Deep Neural Networks using Information Theory

#### Beschreibung

The aim of this thesis is to take the recently introduced methods for explaining individual predictions of DNNs and adapt them to build statistical methods using information theoretic quantities that can help in understanding the internal functionality of the DNN. This can later be used to improve the performance of the DNN or to reduce the inference complexity by pruning the parts which do not play a significant role in the operation of DNN.

The work will consist of both theory and experimentation.

#### Voraussetzungen

- Basic knowledge information theory

- Basic knowledge of DNNs and their operation.

#### Betreuer:

Two-way MIMO Communications

## Two-way MIMO Communications

**Stichworte: **

MIMO, interactive communications, channel estimation

#### Beschreibung

Massive MIMO, or equipping a huge number of co-located antennas to a base station, has been considered as a key enabling technique for 5G to fulfill the high performance requirements in terms of spectral efficiency, energy efficiency, coverage, and reliability [Larsson2014 ]. We study massive MIMO on the frequency division duplexing (FDD) mode. MIMO FDD is one of the most challenging problems in the MIMO FDD, because the resource overhead is overwhelming with a conventional closed-loop channel estimation and feedback [Caire2010]. The project aims to take a fresh look at this difficult open problem.

Let us consider two-way point-to-point MIMO FDD channels and assume that both nodes have M antennas each. W_1 to node 2 over the M * M channel H while node 2 wishes to convey a message W_2 over the M * M channel G. This model with FDD MIMO if into a special case of a two-way communication where both nodes share the same resource [Chapter 17.5, El2011]. Note that the two-way channel is used either to feedback the observations or to convey fresh information symbols. The amount of time needed for feedback depends on the size of the MIMO channels.

Possible directions are:

- Study achievable transmission strategies for the case of perfect channel.
- Characterize the capacity region.

References

[Larsson2014] EG Larsson, O. Edfors, F. Tufvesson, and TL Marzetta, `` Massive MIMO for next generation wireless systems '', IEEE Communicaions Magazine, vol. 52, no. 2, pp. 186-195, 2014

[Caire2010] G. Caire, N. Jindal, M. Kobayashi, and N. Ravindran, `` Multiuser MIMO achievable rates with downlink training and channel state feedback '', IEEE Transactions on Information Theory, vol. 56, no. 6, pp. 2845-2866, 2010

[El2011] A. El Gamal and YH Kim, `` Network Information Theory '', Cambridge University Press, 2011

#### Voraussetzungen

- Basic knowledge of network information theory, signal processing, linear algebra.
- Matlab programming skills.

#### Kontakt

Prof. Mari Kobayashi

Room: N406

mari.kobayashi@tum.de

#### Betreuer:

Unmanned Aerial Vehicle (UAV)-aided Cellular Networks

## Unmanned Aerial Vehicle (UAV)-aided Cellular Networks

**Stichworte: **

UAV, multi-cell broadcast channel, relay channel, feedback

#### Beschreibung

Recently, UAVs (ie, known as drones) have recently been viewed as highly selective (see eg [Zeng2016]).

Considering the network scenario depicted in Figure 1. One macro BS communicating with groups of users through relaying UAVs due to non-line of sight (NLoS) between the macro BS and each group of users. By assuming that the macro BS is equipped by radar, we consider a UAVs UAVs while estimating the channel state of each UAV. The channel estimation is performed by generalized feedback, ie a round-trip channel output available at the BS. The channel at hand to multi-cell broadcast channels with radar-aided backhaul links, or hierarchical downlink channels. Note that multi-cell broadcast channels have been extensively studied in literature (see [Gesbert2010] and references therein). In our setting, the BS-UAV backhaul link evolves in time due to mobility of UAVs.

Possible directions are:

- For the case of a single and static relaying UAV, study relay strategies to maximize the network throughput.
- Study the tradeoff between the quality of channel estimation and the resulting network throughput.
- Generalize to the case of multiple static relaying UAVs or / and moving UAVs.

This thesis can be done in collaboration with Prof. David Gesbert at EURECOM, Sophia-Antipolis, France.

References

[Zeng2016] Y. Zeng, R. Zhang, TJ Lim, `` Wireless communications with unmanned aerial vehicles: opportunities and challenges '', IEEE Communications Magazine, vol. 54, no. 5, pp. 36-42, 2016

[Gesbert2010] D. Gesbert, S. Hanly, H. Huang, S. Shamai, O. Simeone, and W. Yu, `` Multi-cell MIMO Cooperative Networks: A New Look at Interference '', IEEE Journal on Selected Areas in Communications, vol. 28. no. 9, pp. 1380-1408, 2010.

#### Voraussetzungen

- Basic knowledge of network information theory, signal processing.
- Matlab programming skills.

#### Kontakt

Prof. Mari Kobayashi

Room: N406

mari.kobayashi@tum.de

#### Betreuer:

Waveform Design for Joint Radar and V2X Communication

## Waveform Design for Joint Radar and V2X Communication

**Stichworte: **

waveform, radar, mutual information, state estimation

#### Beschreibung

The key-enabler of mobility-driven networks as well as vehicle-to-everything (V2X) communications is the ability to continuously track and react to the dynamically changing environment (hereafter called the network `` state ') while exchanging information with each other The same millimeter wave frequency bands are used as a radar and data communication system. One of the important tools for waveform design is to use the information theory to maximize the mutual information [Bell1993, Blum2007, Nehorai2007]. While these works focus on extracting the information on the state parameters (eg velocity or range) as much as possible, or equivalently decreasing the uncertainty, it is possible to convey a message to the receiver simultaneously.

The objective is summarized below.

- Understand the seminal paper on the waveform design [Bell1993].
- Adapt the waveform design to a joint sensing and communication system.
- If time allows, extend the study to the multi-user case [Nehorai2007]

References

[Bell1993] MR Bell, `` Information Theory and radar waveform design '', IEEE Transactions on Information Theory, vol. 39, no. 5, pp. 1578--1597, 1993

[Blum2007] Y. Yang and RS Blum, `` MIMO radar waveform design based on mutual information and minimum mean-square error estimation '', IEEE Transactions on Aerospace and Electronic Systems, vol. 43, no. 1, 2007

[Nehorai2007] A. Leshem, O. Naparstek, and A. Nehorai, "Information theoretic adaptive radar waveform design for multiple extended targets", IEEE Journal of Selected Topics in Signal Processing, vol. 1, no. 1, pp. 42-55, 2007

#### Voraussetzungen

- Basic knowledge of information theory, signal processing, convex optimization.
- Matlab programming skills.

#### Kontakt

Prof. Mari Kobayashi

Room: N406

mari.kobayashi@tum.de

#### Betreuer:

Polar Coding with Non-Binary Kernels

## Polar Coding with Non-Binary Kernels

#### Beschreibung

This thesis will focus on polar codes with non-binary kernels on GF(q). Some of the following tasks might be covered:

- Kernel selection
- Decoder implementation
- Efficient construction
- Comparison of binary and non-binary polar codes

#### Voraussetzungen

- Channel Coding
- Information Theory
- Matlab/C++

#### Betreuer:

Data Storage in DNA

## Data Storage in DNA

#### Beschreibung

Encoding information into synthetic DNA is a novel approach for data storage. Due to its natural robustness and size in molecular dimensions, it can be used for long-term and very high-density archiving of data. Since the DNA molecules can be corrupted by thermal process and the writing/reading process of DNA molecules can be faulty, it is necessary to encode the data using error-correcting codes.

In this thesis, the student analyzes errors that occur in such a storage system and designs coding schemes that can be used for error correction.

#### Betreuer:

Adaptive List Decoding for Polar Codes

## Adaptive List Decoding for Polar Codes

#### Beschreibung

The finite-length performance of polar codes can be improved by using successive cancellation list decoding. In this thesis, decoder design/implementation and performance prediction are investigated.

#### Voraussetzungen

- Information Theory
- Channel Coding
- Channel Codes for Iterative Decoding
- Matlab/C++

#### Betreuer:

Information Theoretic Security for Secret Key Generation Based Authentication

## Information Theoretic Security for Secret Key Generation Based Authentication

#### Beschreibung

The student should get familiar with the basics of information theory tools used for key generation problems. Specific instances of private authentication constructions will be used to obtain low-complexity system designs and we will later compare their performance with the optimal rate regions.

#### Voraussetzungen

Information Theory

#### Betreuer:

Protected Code-based Post-Quantum Security

## Protected Code-based Post-Quantum Security

#### Beschreibung

The foreseeable breakthrough of quantum computers represents a risk for communication which uses public-key cryptography. In order to prepare for such an event, embedded devices must integrate post-quantum cryptography, a set of algorithms based on mathematical problems that remains secure even in the presence of the quantum computers. Code-based is one of the most promising post-quantum cryptography. However, the implementation of code-based cryptography has two main challenges: i) satisfy performance and power constraints; and ii) resist side-channel attacks, which uses leakages derived from the implementation (timing, power or electromagnetic characteristics) to retrieve the secret information. The goal of this thesis is to implement a protected version (resistant to side-channel attack) of the newest version of the Gabidulin-Paramonov-Tretjakov code-based post-quantum cryptosystem. This Master thesis will be supervised by Dr. Johanna Sepúlveda (Chair of Security in Information Technology) and Prof. Dr.-Ing. Antonia Wachter-Zeh (Professorship for Coding for Communications and Data Storage).

Some of the following tasks might be covered:

- Getting familiar with Code-based Post-quantum security
- Getting familiar with Gabidulin codes
- Getting familiar with secure implementation
- Secure C/VHDL implementations
- Performance evaluation
- Security evaluation

The thesis can be done in German or English language.

**Literature:**

- Daniel J. Bernstein, Johannes Buchmann, and Erik Dahmen, editors. Post-quantum cryptography. Mathematics and Statistics Springer-11649; ZDB-2-SMA. Springer Berlin Heidelberg, 2009.

- M. Taha, T. Einsenbarth. Implementation Attacks on Post-Quantum Cryptographic Schemes. IACR, 2015.

- P. Loidreau. An evolution of GPT cryptosystem. In Proceedings of ACCT 2016, Fifteenth International Workshop on Algebraic and Combinatorial Coding Theory, Albena, 2016.

Mail: johanna.sepulveda@tum.de, tel.: +49 89 289 28256, room N1009.</br>

Prof. Dr.-Ing. Antonia Wachter-Zeh</br>

Mail: antonia.wachter-zeh@tum.de, tel.: +49 89 289 23495, room N4402.</br>

#### Voraussetzungen

- VHDL/Verilog or C/C++ programming skills
- Basic knowledge in security concepts
- Basic knowledge in channel coding or information theory

#### Kontakt

Dr. Johanna Sepúlveda (Doutora em Ciencias, Microeletrônica, University of São Paulo).

Mail: johanna.sepulveda@tum.de, tel.: +49 89 289 28256, room N1009.

Prof. Dr.-Ing. Antonia Wachter-Zeh

Mail: antonia.wachter-zeh@tum.de, tel.: +49 89 289 23495, room N4402.

#### Betreuer:

Generalized Concatenated Codes with BCH and Polar Codes

## Generalized Concatenated Codes with BCH and Polar Codes

#### Beschreibung

Polar Codes [1] are a class of channel codes that are proven to achieve the capacity of binary input discrete memoryless channels, asymptotically in the block length. Nevertheless, the performance for finite block lengths is not competitive with state-of-the-art channel codes like Turbo or LDPC codes.

In [2], outer cyclic redundancy check (CRC) codes and list decoding are used to improve the distance properties and the performance of polar codes. The main idea of generalized concatenated codes (GCC) [3] is to concatenate several inner and outer codes to improve the distance properties of the resulting overall code.

The goal of the thesis is to implement generalized concatenated coding schemes using Polar codes and other codes like BCH or CRC codes and to analyse and discuss the distance properties and the performance of the schemes.

[1] E. Arikan, "Channel Polarization: A Method for Constructing Capacity-Achieving Codes for Symmetric Binary-Input Memoryless Channels," in IEEE Transactions on Information Theory, vol. 55, no. 7, pp. 3051-3073, July 2009.<br />

[2] I. Tal and A. Vardy, "List Decoding of Polar Codes," in IEEE Transactions on Information Theory, vol. 61, no. 5, pp. 2213-2226, May 2015. <br />

[3] ZYABLOV, Victor; SHAVGULIDZE, Sergo; BOSSERT, Martin. An introduction to generalized concatenated codes. European Transactions on Telecommunications, 1999, 10. Jg., Nr. 6, S. 609-622.

#### Voraussetzungen

- Channel coding
- basic knowledge in Information Theory

#### Betreuer:

Simulation of Improved Staircase Code Decoding

## Simulation of Improved Staircase Code Decoding

#### Beschreibung

Staircase codes, as introduced in 2011 by Smith et. al. [1], are a hardware friendly code design for error correction in optical communication systems. However, the choices of parameters such as block size and code rate that achieve a desired output bit error rate are limited by the error floor of the decoder. A new and improved decoder has been devised [2], allowing for staircase codes with a scope of new parameters to be considered for optical communication. While estimations show the significant improvements, the high throughput required to simulate the error floor can only be achieved with an efficient and parallelisable implementation. The main goal of the thesis is the implementation in VHDL and simulation on an FPGA of the new decoder in order to provide further evidence for the estimated performance.

[1] https://arxiv.org/abs/1201.4106

[2] https://arxiv.org/abs/1704.01893

#### Voraussetzungen

interest in channel coding, knowledge in VHDL

#### Betreuer:

Synchronization error correcting codes

## Synchronization error correcting codes

#### Beschreibung

Synchronization errors occur when the transmitter and receiver of a communication system are not perfectly synchronized and result in insertions or deletions of symbols from the transmited word. These errors are fundamentally different from the well-researched substitution errors and conventional error correcting codes cannot be applied on these kinds of errors. Although synchronization errors can significantly impact the performance of conventional codes, still little is known about these errors and basic questions like the capacity of the binary deletion channel remain unknown. Current research, and the topic of this thesis, is directed towards finding the minimum redundancy of such codes and developing constructions that can correct insertion and deletion errors.

#### Voraussetzungen

You should have good knowledge in linear Algebra and interest in coding theory.

#### Betreuer:

MIMO Multiport Communications

## MIMO Multiport Communications

#### Beschreibung

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.

#### Betreuer:

Rate-Distortion Theory for Sparse Sources

## Rate-Distortion Theory for Sparse Sources

#### Beschreibung

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: <br/>

#### Voraussetzungen

- Information Theory (must)
- Pleasure with mathematics (must)
- Multiuser information theory (beneficial)

#### Betreuer:

Analysis of Deep Neural Networks using Information Theory

## Analysis of Deep Neural Networks using Information Theory

#### Beschreibung

The aim of this thesis is to take the recently introduced methods for explaining individual predictions of DNNs and adapt them to build statistical methods using information theoretic quantities that can help in understanding the internal functionality of the DNN. This can later be used to improve the performance of the DNN or to reduce the inference complexity by pruning the parts which do not play a significant role in the operation of DNN.

The work will consist of both theory and experimentation.

#### Voraussetzungen

- Basic knowledge information theory

- Basic knowledge of DNNs and their operation.

#### Betreuer:

GPU-Implementation of the Split-Step Fourier Method with CUDA

## GPU-Implementation of the Split-Step Fourier Method with CUDA

**Stichworte: **

split-step Fourier method, parallel programming, programming in C, CUDA, code performance optimization and evaluation

**Kurzbeschreibung: **

In this thesis the split-step Fourier method has to be implemented utilizing GPU computation via CUDA.

#### Beschreibung

Within the scope of this thesis, the split-step Fourier method (SSFM), a numerical method solving the nonlinear Schrödinger equation (NLSE), will be implemented. The implementation has to be conducted, using the CUDA framework for parallel implementation on graphical processing units (GPUs), in the programming language C. The main focus is on reducing the computation time for the SSFM, by utilizing the massive parallel computational capabilities of GPUs. Even though Matlab can natively utilize GPU hardware for certain operations, the reduction in overall computation time is far below the expected reduction with an implementation fully written in C and called from Matlab (e.g. via Mex). Over the course of this thesis, the student will get familiar with the following concepts: split-step Fourier method, parallel programming, programming in C, CUDA, code performance optimization and evaluation.

#### Voraussetzungen

There are no special requirements needed to apply for this thesis. Still some knowledge in the following fields is beneficial: Optical Communication Systems, Basics in C programming (or basics in any other programming language), Matlab (Mex)

#### Kontakt

benedikt.leible@tum.de (Please attach an overview of your current grades to the email)

#### Betreuer:

The Weight Enumerators of Product Codes

## The Weight Enumerators of Product Codes

**Stichworte: **

weight enumerator, input-output weight enumerator, input-redundancy weight enumerator, distance spectrum

#### Beschreibung

For product codes (PCs), it is very easy to find the minimum distance and its multiplicity once those of the component codes are known. However, the characterization of its complete distance spectrum is a largely open problem even if those of the component codes are given. In [1], they provide a feasible method to compute the weight enumerators (WEs) of PCs where at least one component code is a single parity check (SPC) code. In addition, an extension to compute the exact input-output weight enumerator (IO-WE) for 2-dimensional PCs with SPC component codes and a lower bound for those with more dimensions are available in [2].

The student will understand the ideas presented there and develop a software to compute them efficiently.

References:

[1] http://ieeexplore.ieee.org/document/512606/

[2] ttps://dspace.library.uvic.ca/bitstream/handle/1828/5487/Rankin_DavidM_EURASIPJAdvSignalProcess_2005.pdf?sequence=1&isAllowed=y

#### Voraussetzungen

**Necessary:**

- Basics of channel coding
- C++ (The applicant can suggest an alternative with a good reason)

**Related Courses:**

- Channel Coding
- Channel Codes for Iterative Decoding
- Coding Theory for Storage and Networks

#### Kontakt

mustafa.coskun@tum.de

#### Betreuer:

Code design for Physical Layer Security

## Code design for Physical Layer Security

#### Beschreibung

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.

#### Betreuer:

Information Theoretic Security: Code Construction for PUFs and Biometric Security

## Information Theoretic Security: Code Construction for PUFs and Biometric Security

#### Beschreibung

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.

#### Voraussetzungen

Information theory and channel coding

#### Betreuer:

The Weight Enumerators of Product Codes

## The Weight Enumerators of Product Codes

**Stichworte: **

weight enumerator, input-output weight enumerator, input-redundancy weight enumerator, distance spectrum

#### Beschreibung

For product codes (PCs), it is very easy to find the minimum distance and its multiplicity once those of the component codes are known. However, the characterization of its complete distance spectrum is a largely open problem even if those of the component codes are given. In [1], they provide a feasible method to compute the weight enumerators (WEs) of PCs where at least one component code is a single parity check (SPC) code. In addition, an extension to compute the exact input-output weight enumerator (IO-WE) for 2-dimensional PCs with SPC component codes and a lower bound for those with more dimensions are available in [2].

The student will understand the ideas presented there and develop a software to compute them efficiently.

References:

[1] http://ieeexplore.ieee.org/document/512606/

[2] ttps://dspace.library.uvic.ca/bitstream/handle/1828/5487/Rankin_DavidM_EURASIPJAdvSignalProcess_2005.pdf?sequence=1&isAllowed=y

#### Voraussetzungen

**Necessary:**

- Basics of channel coding
- C++ (The applicant can suggest an alternative with a good reason)

**Related Courses:**

- Channel Coding
- Channel Codes for Iterative Decoding
- Coding Theory for Storage and Networks

#### Kontakt

mustafa.coskun@tum.de