# Offered Theses

Please contact the doctoral researchers directly if you are interested in a Bachelor or Master thesis, a student job, an "Ingenieurspraxis" or a "Forschungspraxis". It is also usually possible to find a topic that matches 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's Theses

Analysis of Identification for the Binary Symmetric Channel and a comparison to decoding problem

## Analysis of Identification for the Binary Symmetric Channel and a comparison to decoding problem

**Keywords: **

Identification, Binary Symmetric Channel, Communication Complexity

**Short Description: **

Problem of transmission and Identification over the BSC is investigated and analysed. Further it will be shown that identification would be easier than decoding problem in terms of minimum number of bits of communication

#### Description

Assuming that the communication channel between two processors P1 and P2 makes an error with probability ε>0, the identification problem is to determine whether P1 and P2 have the same n-bit integer. The decoding problem is for P2 to determine the n-bit integer of P1. For the latter problem we show that given any arbitrarily large constant λ>0, there exists an ε, 0<ε<1/2, for which no scheme requiring less than λn bits of communication can guarantee (for large n) any bound q<1 on the error probability. On the other hand, given any arbitrarily small constant γ>0 and any ε, 0<ε<1/2, the identification problem can be solved with (1+γ)n bits of (one-way) communication with an error probability bounded by c2^{-αn}, where c and α are positive constants.

#### Prerequisites

- Elementary Knowledge of Communication Complexity
- Familiarity with facts from Information Theory such as capacity, rate, decoding error, code size, hamming distance.
- Elementary knowledge of combinatorial inequlities

#### Supervisor:

Identification Without Randomization for the Discrete Memoryless Channel

## Identification Without Randomization for the Discrete Memoryless Channel

**Keywords: **

Identification, Identification Without Randomization, Complexity of Distributive Computing, One-Way/Two-Way Probabilistic Communications

**Short Description: **

Identification without randomization for a general DMC would be studied and investigated. Method of coding, decoding sets, type I/II errors and a closed-form solution of non-randomized identification capacity will be considered and analysed.

#### Description

In theory of Identification introduced by Ahlswede and Dueck the perspective of communications is changed from decoding to identification, i.e., the receiver is only interested to check whether or not his message was sent by transmitter. Ahslwede and Dueck proved that by means of local randomness (at encoder) they can achieve doubly exponential gain in code size which outperfrom substantially the classical scheme of Shannon transmission. (only exponential gain in code size). However, in many cases, there is no need to exploit the Randomization at encoder and thus the view of identification without randomization is introduced.

On the other hand to derive probabilistic complexity of models for one/two way communications for distributive computing (communication between two processors for determine copperatively value of an identification function) similar ideas were discussed. The student should understand those ideas and try to find the link between them and idea of Identification of Ahlswede and Dueck. Ideally the student attempt to derive forward or/and backward proof for non-randomized identification capacity of a general DMC.

#### Prerequisites

- Background in fundamentals of Information Theory, such as Entropy, Mutual Information, Hamming Distance, Rate, Probability of Error, The Binary Symmetric Channel etc)
- Familiarity with fundamentals of Identification Theroy

#### Supervisor:

Two-sided search

## Two-sided search

#### Description

In the most studied models in the literature, it is assumed that the target of the search is either stationary with its hidden position being chosen according to someknown distribution, or it is moving and its movements follow some known rules. In such cases, we talk about one-sided search, meaning that the target’s behaviour is somehow independent of the searcher’s attempt to catch it. Conversely, if the target can attempt to contrast the searcher’s activity and react in some intelligent way in order not to be found, the model is referred to as two-sided search. Two-sided search was introduced by Koopman. The goal is to implement a two-sided search algorithm.

#### Supervisor:

### Master's Theses

Protograph-based LDPC Code Design for Finite Number of Iterations

## Protograph-based LDPC Code Design for Finite Number of Iterations

#### Description

Low-density parity-check (LDPC) codes are usually designed using an extrinsic information transfer (EXIT) analysis to compute the asymptotic iterative decoding threshold for a given code ensemble. The iterative decoding threshold over an additive white Gaussian noise (AWGN) channel is thereby defined as the minimum signal-to-noise ratio (SNR) for which the a posteriori mutual information converges to one as the number of decoding iterations goes to infinity.

For practical applications, however, decoding is often performed using only a small number of iterations. Mulholland *et al.* investigated a code design for protograph-based LDPC codes where the protograph-based EXIT (PEXIT) analysis [1] is run for the targeted number of decoding iterations only [2]. They showed that for the binary erasure channel (BEC), the obtained *iteration-constrained threshold* does not match the bit error rate (BER) threshold of finite-length codes.

In this thesis, the student will understand and reproduce the results from [2], apply these tools to the AWGN channel, and compare them to code design tools developed at the institute.

[1] G. Liva and M. Chiani, “Protograph LDPC codes design based on EXIT analysis,” in *Proc. IEEE Global Telecommun. Conf. (GLOBECOM)*, Nov. 2007, pp. 3250–3254.

[2] I. P. Mulholland, E. Paolini, and M. F. Flanagan, “Design of protograph-based LDPC code ensembles with fast convergence properties,” in *Proc. Int. ITG Conf. Syst. Commun. Coding (SCC)*, Feb. 2017, pp. 1–6.

#### Prerequisites

- Channel codes for iterative decoding

#### Supervisor:

Joint Beam Alignment and Multi-target Tracking

## Joint Beam Alignment and Multi-target Tracking

**Keywords: **

Multi-target tracking, mmWave beam alignment

#### Description

The key-enabler of mobility-driven networks such 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.

Joint radar and vehicular communication based on IEEE 802.11 has been proposed in the literature, where the same mmWave frequency bands (e.g. 60GHz) are considered for both radar and communication.

At such a high frequency bands, beamforming both at the transmitter and the receiver is considered essential to compensate the high propagation loss over mmWave frequencies.

In this master thesis, we study beam alignment for a joint radar and communication system. In particular, we are interested in the multi-target detection (or estimation) problem such that the transmitter wishes to detect targets reliably (or estimate the multi-target parameters accurately) in a given angular area. A natural question arises as whether it is better to choose a wide beam to perform multi-target detection or scan sub-areas successively with narrow beam to perform hypothesis testing in each sub-area such that the detection/estimation performance is maximized.

Possible research directions include:

- Understand the basic of radar detection and hypothesis testing for a single-target case.
- Study the multi-target detection/estimation using various waveforms.
- If time allows, extend to the mobility scenario.

Reference:

M. A. Richards, ``Fundamentals of radar signal processing'', Tata McGraw-Hill Education, 2005.

#### Prerequisites

Solid background in wireless communications, signal processing, and optimization.

#### Contact

Mari Kobayashi

mari.kobayashi@tum.de

#### Supervisor:

Adaptive List Decoding for Polar Codes

## Adaptive List Decoding for Polar Codes

#### Description

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.

Reference:

[1] I. Tal and A. Vardy. "List decoding of polar codes." IEEE Transactions on Information Theory 61.5 (2015): 2213-2226.

[2] P. Yuan and F. Steiner. "Efficient Decoding Algorithms for Polar Codes based on 2×2 Non-Binary Kernels." International Symposium on Turbo Codes & Iterative Information Processing. 2018.

#### Prerequisites

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

#### Supervisor:

### Forschungspraxis or MSCE Internships

Two-sided search

## Two-sided search

#### Description

In the most studied models in the literature, it is assumed that the target of the search is either stationary with its hidden position being chosen according to someknown distribution, or it is moving and its movements follow some known rules. In such cases, we talk about one-sided search, meaning that the target’s behaviour is somehow independent of the searcher’s attempt to catch it. Conversely, if the target can attempt to contrast the searcher’s activity and react in some intelligent way in order not to be found, the model is referred to as two-sided search. Two-sided search was introduced by Koopman. The goal is to implement a two-sided search algorithm.

#### Supervisor:

Simmulation eines Quantenrepeaters

## Simmulation eines Quantenrepeaters

**Keywords: **

Simmulation, Quantenrepeater

**Short Description: **

Ein Quantenrepeater ist wichtiger Baustein für Quantenkommunikation über große Distanzen. Hier soll ein Quantenrepeater der 1. Generation simmuliert werden.

#### Description

Im Gegensatz zu klassischen Signalen ist bei einem quantenmechanischen Zustand das Verstärken oder Kopieren des Signals nicht möglich, Der Quantenrepeater (1. Generation) basiert auf Verschränkung, und der Destillation. Die einzelnen Komponenten des Repeaters können unterschiedlich realisiert werden. Ziel der Simmulation ist es Vor- und Nachteile der verschiedenen möglichen Komponenten heraus zu finden.

#### Prerequisites

Grundwissen in Quanteninformationstheorie

#### Supervisor:

Adaptive List Decoding for Polar Codes

## Adaptive List Decoding for Polar Codes

#### Description

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.

Reference:

[1] I. Tal and A. Vardy. "List decoding of polar codes." IEEE Transactions on Information Theory 61.5 (2015): 2213-2226.

[2] P. Yuan and F. Steiner. "Efficient Decoding Algorithms for Polar Codes based on 2×2 Non-Binary Kernels." International Symposium on Turbo Codes & Iterative Information Processing. 2018.

#### Prerequisites

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