# 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).

### Bachelorarbeiten

Computation of Identification Function Over Faulty Channels

## Computation of Identification Function Over Faulty Channels

**Stichworte: **

Identification via channels, Identification Function,

**Kurzbeschreibung: **

Identification problem over certain noisy channel is addressed.

#### Beschreibung

Identification problem for certain noisy channel is studied and the capacity is derived.

#### Voraussetzungen

Familiarity with basics of information theory and channel coding.

#### Betreuer:

A Jupyter Notebook for Line Coding in Access Networks (LB)

## A Jupyter Notebook for Line Coding in Access Networks (LB)

#### Beschreibung

yle="margin-bottom: 0cm; line-height: 100%;">For the access network case, the spectrum of the transmit signal has to be adapted to the channel properties. This can either be achieved by choosing suitable transmit pulse shapes or by encoding the (redundancy free) source symbols [1].

yle="margin-bottom: 0cm; line-height: 100%;">The students task is to implement a demonstration of two line coding schemes in Python [2] (Jupyter Notebook) and visualize the results. Additionally, the student also has to arrange code and surrounding text, such that the content becomes self-explanatory.

yle="margin-bottom: 0cm; line-height: 100%;">[1] Skript "Physical Layer Methods“

yle="margin-bottom: 0cm; line-height: 100%;">[2] "Python in 30 minutes" (https://www.programiz.com/python-programming/tutorial)

#### Voraussetzungen

Since the Jupyter Notebook is to be written in german language, the student should be able to write in german at least on a basic level.

While some basics in any programming language are beneficial, this is also a great opportunity for programming beginners, wishing to expand their programming skills.

For this topic students of the "Lehramtsstudiengänge" are preferred.

#### Betreuer:

Deterministic Identification Over the Binary Symmetric Channel

## Deterministic Identification Over the Binary Symmetric Channel

**Stichworte: **

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

**Kurzbeschreibung: **

Identification without randomization over the binary symmetric channel (BSC) would be studied and investigated. Method of coding, decoding sets, type I/II errors and a closed-form solution of non-randomized (deterministic) identification capacity will be considered and analysed.

#### Beschreibung

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 the Binary Symmetric Channel (BSC).

#### Voraussetzungen

- Familiarities with fundamental concepts 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

#### Betreuer:

### Masterarbeiten

Semantic security of infinite-dimensional classical-quantum channels

## Semantic security of infinite-dimensional classical-quantum channels

#### Beschreibung

Generalize semantic security of classical-quantum channels to infinite dimensional channel (not necessarily gaussian)

- [1] finite dimensional classical-quantum case

https://arxiv.org/abs/2001.05719 - finite and infinite dimensional classical case

https://arxiv.org/abs/1811.07798

- [this subpoint can be a project by itself] the finite dimesional case needs to be recast into smooth-max information (instead than Lemma 5.7 of [1]) as the classical case does, this paper proves properties of the smooth-max-inf in finite dimension that we would need for that

https://arxiv.org/abs/2001.05719

- papers regarding the capacity for infinite dimensional channels

http://arxiv.org/abs/quant-ph/9912067v1

http://arxiv.org/abs/quant-ph/0408009v3

http://arxiv.org/abs/quant-ph/0408176v1

#### Voraussetzungen

quantum information theory

#### Betreuer:

Asymptotic continuity of restricted quantum relative entropies under general channels

## Asymptotic continuity of restricted quantum relative entropies under general channels

**Stichworte: **

quantum, relative entropy, Pinsker, reverse, inequality, information thoery, asymptotic, continuity

#### Beschreibung

Asypmtotic continuity is a property in the form of inequalities (classically known also as inequalities of the reverse-Pinker type) that is necessary to prove upper bounds on operational capacities.

The (quantum) relative entropy (also known as quantum divergence and classically also known as Kullbackt-Leibler divergence), can be used to define various entanglment measures many of which have a proven asymptotic continuity.

Of particular interest are the restricted quantum relative entropies defined by Marco Piani (https://arxiv.org/abs/0904.2705), many of which satisfy asymptotic continuity (A.S.)

- https://arxiv.org/abs/quant-ph/9910002
- https://arxiv.org/abs/quant-ph/0203107
- https://arxiv.org/abs/quant-ph/0507126
- https://arxiv.org/abs/1210.3181
- https://arxiv.org/abs/1507.07775
- https://arxiv.org/abs/1512.09047

In the above there are maybe 2-3 different proof styles.

We can group the results in the above as follows:

- A.S. for entropy, conditional entropies, mutual information, conditional mutual information
- A.S. for relative entropies with infimum over states on the second argument
- A.S. relative entropies with infimum over state *and maximization over measurement channels*

The goal of the project is to generalize the last case to asymptotic continuity for relative entropies with infimum over state and maximization over *general* channels

- Partial results toward this goal can be found in the appendix of my PhD thesis: http://web.math.ku.dk/noter/filer/phd18rf.pdf
- Such a result would have immediate applications to this paper: https://arxiv.org/abs/1801.02861
- Possible new proof directions could involve the use of Renyi α-realtive entropies with the limit α->1

#### Voraussetzungen

Knowledge of quantum information is highly recommended/required.

Knowledge of matrix analysis will be a strong advantage.

#### Kontakt

roberto.ferrara@tum.de

#### Betreuer:

Practical protocols for quantum synchronization in classical network

## Practical protocols for quantum synchronization in classical network

**Stichworte: **

quantum, network, synchronization

#### Beschreibung

relevant papers

https://arxiv.org/abs/1310.6043

https://arxiv.org/abs/1304.5944

https://arxiv.org/abs/1310.6045

https://arxiv.org/abs/1703.05876

https://arxiv.org/abs/1303.6357

background papers

https://ieeexplore.ieee.org/document/7509657

#### Voraussetzungen

Knowledge of quantum theory as provided by the course Algorithms in Quantum Theory or similar

#### Betreuer:

Entanglement-measures upper bounds on device-independent distillable key

## Entanglement-measures upper bounds on device-independent distillable key

**Stichworte: **

quantum, qkd, entanglement

#### Beschreibung

The goal of this work is to try to upper bound the device-independent distillable key in terms of locally restricted relative entropy of entanglement (an entanglement measure).

The following are relevant works/articles

- works toward even *a definition* of device independent distillable key

https://arxiv.org/abs/2005.13511

https://arxiv.org/abs/2005.12325

https://arxiv.org/abs/1810.05627 - works relating distillable entanglement and distillable key to locally restricted relative entropy measures

https://arxiv.org/abs/1609.04696

https://arxiv.org/abs/1402.5927 - the first definition of restricted relative entropies

https://arxiv.org/abs/0904.2705 - important properties of restricted relative entropies, and some overview of entanglement measures

https://arxiv.org/abs/1210.3181 - my PhD thesis

http://web.math.ku.dk/noter/filer/phd18rf.pdf

#### Voraussetzungen

Strong background in quantum theory is required, preferably in quantum information theory, which is not covered by the course Algorithms in Quantum Theory

#### Betreuer:

Intelligent Reflecting Surface -aided Beam Alignment for mmWave Communications

## Intelligent Reflecting Surface -aided Beam Alignment for mmWave Communications

**Stichworte: **

Intelligent refelecting surface (IRS), mmWave beam alignment

#### Beschreibung

The future generation communication networks will be operated mainly at millimeter wave (mmWave) or even higher frequency bands in order to achieve high spectral efficiency as well as accurate localization/positioning, necessary for emerging autonomous applications. At such a high frequency bands, beamforming both at the transmitter and the receiver, or beam alignment (BA), is considered essential to compensate the high propagation and penetration loss. The design of BA achieving a good tradeoff between alignment accuracy and resource overhead has been extensively studied in the literature [1,2]. In particular, a number of recent works proposed to exploit some side information, such as location [3,4], database [5], or radar [6], at the base station side to speed up the initial acquisition time.

Intelligent reflecting surface (IRS) consists of a large number of passive reflecting elements that can be easily controlled at a base station or access points to cooperatively beamform without the need of any radio-frequency (RF) chains. So far, a number of recent works showed that IRS can be used as an external fixed helper to increase the coverage, mitigate the interference of the network [7] and references therein). Due to its low cost together with the advanced, future user terminals can be also equipped with small IRS. This IRS-integrated device provides a new opportunity that we wish to exploit to speed up the BA protocol.

In this mater thesis, we study IRS-aided BA and quantify how much the resource can be saved as a function of the IRS parameters. To this end, we aim to organize the work as follows:

- Understand the basic of IRS and mmWave BA.
- Study various types of IRS space-time (coding) functions to control passive reflecting elements [8].
- Study the tradeoff between the alignment accuracy and the required resource.

References

[1] X. Song, S. Haghighatshoar, and G. Caire, ``Efficient Beam Alignment for Millimeter Wave Single-Carrier Systems With Hybrid MIMO Transceivers," IEEE Trans. Wireless Commun., vol. 18, no. 3,pp. 1518-1533, 2019.

[2] S. Chiu, N. Ronquillo, and T. Javidi, ``Active Learning and CSI Acquisition for mmWave InitialAlignment," IEEE J. Sel. Areas Commun., vol. 37, no. 11, pp. 2474-2489, 2019.

[3] V. Va, T. Shimizu, G. Bansal, and R. W. Heath, ``Position-aided millimetre wave V2I beam alignment:A learning-to-rank approach," in 2017 IEEE 28th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC). IEEE, 2017, pp. 1-5.

[4] A. U. Rahman and M. Biswal, ``Error-tolerant Beam Steering of mmWave Antennas by Trajectory Estimation of Highway Vehicles," in 2019 11th International Conference on Communication Systems Networks (COMSNETS), 2019, pp. 530-531.

[5] V. Va, J. Choi, T. Shimizu, G. Bansal, and R. W. Heath, ``Inverse multipath fingerprinting for millimeter wave V2I beam alignment," IEEE Trans. Veh. Technol., vol. 67, no. 5, pp. 4042-4058, 2018.

[6] Nuria Gonzalez-Prelcic, Roi Mendez-Rial, and Robert W. Heath, ``Radar aided beam alignment in mmwave V2I communications supporting antenna diversity," in Information Theory and Applications Workshop (ITA), 2016. IEEE, 2016, pp. 1-7.

[7] Qingqing Wu, Shown Zhang, Beixiong Zheng, Changsheng You, and Rui Zhang, ``Intelligent reflecting surface aided wireless communications: A tutorial," IEEE Trans. Wireless Commun., 2021.

[8] Lei Zhang et al., ``Space-time-coding digital metasurfaces,” Nature communications, vol. 9, no. 1, pp. 1-11, 2018.

#### Voraussetzungen

- Solid background in signal processing and optimization.
- Matlab programming skills.

#### Kontakt

Mari Kobayashi (mari.kobayashi@tum.de)

#### Betreuer:

Joint Sensing and Communications for Future Autonomous Applications

## Joint Sensing and Communications for Future Autonomous Applications

**Stichworte: **

Joint sensing and communication, capacity-distortion-cost tradeoff

#### Beschreibung

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. Motivated by such applications, the joint sensing and communication, where a transmitter equipped with on-board sensors wishes to communicate data to its receivers and simultaneously estimate/track the states, has been extensively studied in the literature. Although common waveforms to perform both communication and sensing tasks have been proposed for specific scenarios, the fundamental limit of such a system is not well understood yet.

In this master thesis, we aim to study the fundamental tradeoff between state sensing and communications in simple point-to-point channels. Our preliminary results were restricted to the memoryless channels with identically and identically distributed (i.i.d.) states, which is unrealistic in practical wireless channels. Therefore, the focus is to extend the preliminary results to temporally correlated channels such that the transmitter can predict the upcoming channels from the previous observations in order to enhance further both sensing and communication performance. If time allows, we will consider other types of channels such as block-fading channels, multiple-input-multiple-output (MIMO) channels.

#### Voraussetzungen

- Solid background in signal processing, optimization or information theory.
- Matlab programming skills.

#### Kontakt

Mari Kobayashi (mari.kobayashi@tum.de)

#### Betreuer:

Explicit Construction of Deterministic Identification Codes

## Explicit Construction of Deterministic Identification Codes

**Stichworte: **

Identification via channels, identification codes,

#### Beschreibung

In this thesis, the student after studying deterministic identification will construct the explicit codes for certain channels.

#### Voraussetzungen

Background in **Information Theory** and **Channel Coding**

Familiarity in fundamentals of **Identification Theory**

#### Betreuer:

Group testing techniques based on sparse graphs for large-scale population screening

## Group testing techniques based on sparse graphs for large-scale population screening

#### Beschreibung

Group testing is a combinatorial technique (developed by R. Dorfman in 1943) which allows to detect infected individuals by running “pooled” tests on (blood) samples. More specifically, by merging the samples of a subset of individuals into a pool, a test is carried out to verify the positivity (or negativity) of the pool. By repeating the test on different subsets, it is eventually possible to detect the individuals carrying the infection, possibly with very few tests compared with the test population. The approach is currently scouted to speed-up the testing in the context of the COVID-19 pandemic (see https://www.nature.com/articles/d41586-020-02053-6 and [1-2]). The technique admits a description which shares several similarities with the syndrome-based error correction problem via linear block codes. It is not a surprise that major contributions in the area of group testing have been given by coding and information theorists.

The scope of the thesis is to investigate the adoption of capacity-approaching codes based on sparse graphs (e.g., low-density parity-check codes) to attack the group testing problem. The use of sparse-graph codes for this purpose has been already envisaged in [3-4]. In this work, we will address the design of adaptive/non-adaptive and quantitative/non-quantitative group testing techniques based on sparse graphs, under various detection algorithms (belief propagation, as well as combinatorial orthogonal matching pursuit).

[1] Mutesa, Leon, et al. "A strategy for finding people infected with SARS-CoV-2: optimizing pooled testing at low prevalence." *arXiv preprint arXiv:2004.14934* (2020). [2] Narayanan, Krishna R., Anoosheh Heidarzadeh, and Ramanan Laxminarayan. "On Accelerated Testing for COVID-19 Using Group Testing." *arXiv preprint arXiv:2004.04785*(2020). [3] K. Lee, R. Pedarsani and K. Ramchandran, "SAFFRON: A fast, efficient, and robust framework for group testing based on sparse-graph codes," *2016 IEEE International Symposium on Information Theory (ISIT)*, Barcelona, 2016 - available at https://arxiv.org/abs/1508.04485 [4] Aldridge, Matthew, Oliver Johnson, and Jonathan Scarlett. "Group testing: an information theory perspective,: NOW Published, 2020 - available at https://arxiv.org/pdf/1902.06002.pdf

#### Voraussetzungen

The student should have successfully passed the Channel Coding course and should exhibit a good understanding of probability theory. The Channel Codes for Iterative Decoding and Information Theory courses are plus.

#### Kontakt

mustafa.coskun@tum.de

#### Betreuer:

Efficient Implementation of Decryption Algorithms in Rank-Based Cryptography

## Efficient Implementation of Decryption Algorithms in Rank-Based Cryptography

#### Beschreibung

Many Rank-based cryptosystems require decoding of Gabidulin codes in their decryption algorithm. In this work, the student should compare the theoretical complexity of different Gabidulin code decoders. Based on the theoretical complexity analysis, the students should decide on the most promising decoding algorithms. Then, the algorithms should be implemented in C and their performance should be compared on a microcontroller.

#### Voraussetzungen

- Good knowledge about rank-metric codes (e.g. by taking the course Coding Theory for Storage and Networks)

- Good knowledge about cryptography (e.g. by taking the course Security in Communications and Storage)

- Very good knowledge of the Programming language C

#### Betreuer:

The coin weighing problem

## The coin weighing problem

#### Beschreibung

The question of finding a small subset of defective coins from a set of regular coins in the fewest number of weighings has been a notorious problem.

Suppose there is a collection of *n* coins so that some of them are defective. In other words, we know that the weight of regular coins is *A*, and the weight of the remaining coins is *B*, where integers *A* and *B* are given. The problem is to determine the weight of each coin by weighing subsets of coins in a spring scale. The main figure of merit when studying adaptive coin weighing algorithms is the number of required weighings in the worst-case and in the average-case. In this project, we design and implement an efficient algorithm which works for two coins.

#### Voraussetzungen

Coding theory, combinatorics

Good programming skills

#### Kontakt

#### Betreuer:

Error Correction in DNA Storage

## Error Correction in DNA Storage

**Stichworte: **

DNA storage, Error Correction, Deletion, Insertion, Substitutions

#### Beschreibung

DNA storage is an uprising topic in the research field of storage systems. Due its natural longetivity, robustness, and density properties the main application would arise in high-dense long-term storage systems. The interest has become larger and larger due the large amount of data nowadays and the relative new biological advances in DNA synthesis and sequencing processes (e.g. polymerase chain reaction). In contrary to conventional storing methods, due to the nature of DNA and the involved biological processes special error patterns such as insertion, deletion, and substitution errors occur. To tackle these errors novel methods for correction have to be investigated. Moreover, the model of the DNA storage channel needs to be investigated thorougly, e.g. capacity statements.

#### Voraussetzungen

- Linear Algebra
- Channel Coding
- Coding Theory for Storage and Networks (optional)

#### Betreuer:

How to guess an n-digit number

## How to guess an n-digit number

#### Beschreibung

In a deductive game for two players, Alice and Bob, Alice conceals an *n*-digit number *x*, and Bob, who knows *n*, tries to identify *x* by asking a number of questions, which are answered by Alice. Each question is an *n*-digit number *y*, and each answer is the number of positions at which the corresponding symbols of *x* and *y* are different. Moreover, we require Bob to ask all questions at once. The goal of this project is to design and implement an efficient coding scheme for Bob with an asymptotically optimal number of questions.

#### Voraussetzungen

Coding theory, combinatorics, analysis

Good programming skills

#### Kontakt

#### Betreuer:

DNA Storage Channel Modeling and Error Correction

## DNA Storage Channel Modeling and Error Correction

#### Beschreibung

DNA-based data storage is a novel approach for long term data archiving.

Due to the unique nature of writing and reading DNA, the channel associated with these processes is still realtively poor understood and varies over different synthesis (writing) and sequencing (reading) technologies. The task of the student is to analyze different sequencing methods and the associated errors and formulate associated channel models. Based on these models, error-correcting schemes shall be evaluated.

#### Voraussetzungen

- Basic principles of stochastic and algebra

- Channel Coding

#### Betreuer:

Algebraic Coding for Distributed Storage

## Algebraic Coding for Distributed Storage

#### Beschreibung

Distributed storage systems with a large number of storage commonly rely on MDS codes, such as Reed-Solomon codes, to protect the system from data loss in the event of node failures while keeping the storage overhead low. In the event of such a failure, the reconstruction of failed nodes induces a large amount of network traffic. In recent years several solutions to this problem have been proposed, most notably locally repairable codes and regenerating codes. We investigate the properties of specific subclasses of these codes, as well as the combination of the two properties.

Further, with the increased demand for data privacy, we develop methods for protecting users' data from the eyes of curious servers in distributed storage systems.

#### Betreuer:

Homomorphic encryption

## Homomorphic encryption

**Stichworte: **

Cryptography

#### Beschreibung

Consider that a client would like to a server to do some computations for him but he does not want to give information meaningful information to the server. The client therefore sends encrypted messages c1 = Enc(pk, m1) and c2 = Enc(pk, m2) to the server and the client would like to obtain some function f of the two plaintexts f(m1,m2). It suffices for the client to get Enc(pk, f(m1,m2)) because the client owns the secret key sk. He is able to use the decryption function Dec on the ciphertext and gets Dec(sk, Enc(pk,f(m1,m2=))) = f(m1,m2).

The goal of this internship is to analyze schemes that achieve this property based on code-based cryptography.

#### Voraussetzungen

linear algebra

coding theory

basic understanding of cryptography

#### Betreuer:

Simulation and performance improvement of identification codes

## Simulation and performance improvement of identification codes

#### Beschreibung

Identification is a communication scheme that allows rate doubly exponential in the blocklemght, with the tradeoff that identities cannot be decoded (as messages do) but can only be verified.

The double exponential growth presents various challenges in the finite regime: there are heavy computational costs introduced at the encoder and decoder and heavy trade-offs between the error and the codes sizes.

The ultimate goal is to find a fast, reliable implementation while still achieving large code sizes.

Your task will be implementing and testing new ideas toward this goal.

The coding will be in Matlab. Some existing code needs conversion from Sagemath to Matlab.

This work can accomodate multiple students.

The working language will be in English.

Environment: we collaborate with LTI. At LNT and LTI there is currently a lot of funding for research in identification. Therefore you will find a large group of people that might be available for discussion and collaboration.

#### Voraussetzungen

Nachrichtentechnik 2

#### Betreuer:

Two-sided search

## Two-sided search

#### Beschreibung

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.

#### Betreuer:

Learning Aided SC Flip Decoding for Polar Codes

## Learning Aided SC Flip Decoding for Polar Codes

#### Beschreibung

Polar codes achieve the capacity of binary-input discrete memoryless channels asymptotically in the block length under successive cancellation (SC) decoding. Polar codes have been adopted for the control channel in 5G enhanced mobile broadband (eMBB).

Due to the serial nature of SC decoding, an erroneous bit decision can be caused by the channel noise or previous erroneous bit estimates. The main idea of SC flip decoding is trying to correct the first erroneous bit decision by sequentially flipping the unreliable decisions.

The optimal flipping strategy is considered difficult due to lack of an analytical solution. Alternatively, (deep) learning aided SC flip algorithm are investigated in this thesis.

[1] O. Afisiadis, A. Balatsoukas-Stimming, and A. Burg, “A low-complexity improved successive cancellation decoder for polar codes,” in Proc. 48th Asilomar Conf. Signals, Systems and Computers, pp. 2116-2120, 2014.

[2] L. Chandesris, V. Savin, and D. Declercq, “Dynamic-SCFlip Decoding of Polar Codes,” IEEE Trans. Commun., vol. 66, no. 6, pp. 2333-2345, Jun., 2018.

[3] X. Wang, et al. "Learning to Flip Successive Cancellation Decoding of Polar Codes with LSTM Networks." *arXiv preprint arXiv:1902.08394* (2019).

[4] N. Doan, et al. "Neural Dynamic Successive Cancellation Flip Decoding of Polar Codes." *arXiv preprint arXiv:1907.11563* (2019).

#### 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:

### Forschungspraxis oder MSCE Forschungspraxis

Fano's Inequality: Applications in Communications and Beyond the Communication Problem

## Fano's Inequality: Applications in Communications and Beyond the Communication Problem

#### Beschreibung

Information theory plays an indispensable role in the development of algorithm-independent imposibility results, both for communication problems and for seemingly distinct areas such as statistics and machine learning. While numerous information-theoretic tools have been proposed for this purpose, the oldest one remains arguably the most versatile and widespread: Fano's inequality.

References:

[1] An Introductory Guide to Fano's Inequality with Applications in Statistical Estimation. Jonathan Scarlett, Volkan Cevher. (and references within).

https://arxiv.org/abs/1901.00555

Please contact the supervisor for possible additional references, too.

#### Voraussetzungen

-Background and interest in Probability theory and stochastic processes, statistics and Information theory.

-An interest in a possible numerical simulation using MATLAB or any other numerical simulation environment (Python, Julia..etc)

-The exact starting date is flexible. But it should be sometime around summer 2021.

#### Betreuer:

Decoding of product codes

BCJR Algorithm

Construction of Identification Codes via Prime Numbers

## Construction of Identification Codes via Prime Numbers

**Stichworte: **

Identification via channels, Prime Number Encryption

**Kurzbeschreibung: **

An approach for construction of identification codes for noiseless channel by means of the prime number encryption would be studied.

#### Beschreibung

In original scheme of **identificaion via channels** (*Ahlswede and Dueck, 1989*), a non-constructive method for coding for noiseless channel was studied. To address the explicit construction of identificaion codes, foremost *Ahlswede and Verboven, 1991* provide a number theoretic approach based on the two successive prime number encryption. This method require the knowledge of first** 2^n** prime numbers for a block-length of n codeword. In this research internship, this method along with related prime number encryption tools and theorems would be investigated. Further, the extension of this scheme to a general DMC will be analyzed.

#### Voraussetzungen

Background in Information Theory and Channel Coding

Familiarity with Fundamental of Identificaion Theory

Familiarity with Prime Number Theorem (Chebyshev)

#### Betreuer:

On the Equivalence of Identification and Authentication

## On the Equivalence of Identification and Authentication

**Stichworte: **

Identification via channel, identification codes, authentication, authentication codes

**Kurzbeschreibung: **

A Certain equivalence of identification and authentication would be shown.

#### Beschreibung

It would be shown that under suitable formulations (preserving all salient features) the two problem of **Identification** (*Ahlswede and Dueck, 1989*) and **Authentication **(*Simmons, G. J. 1984*)** **are in essence very close to each other. This equivalency was conjectured first by **M. S. Pinsker**. In this research internship the student is expected to address this conjecture. Both problems must be studied separately and then the similar essence of them should be drawn out. In particular the identification codes and authentication codes along with theire relation will be investigated.

#### Voraussetzungen

- Background in Information Theory and Channel Coding
- Familiarity with fundamentals of Identification Theory

**References:**

- Simmons, G. J. 1984, “Message authentication: a game on hypergraphs,” Congressus Numer. 45:161-192.
- Simmons, G. J. 1982, “A game theory model of digital message authentication,” Congressus Numer., 34, 413-424
- Simmons, G. J. 1985, “Authentication theory/coding theory,” in: Advances in Cryptology: Proceedings of CRYPTO 84, Lecture Notes in Computer Science, vol. 196, Springer-Verlag, Berlin, pp. 411-432.
- E. Gilbert, F. J. MacWilliams and N.J. A. Sloane, 1974, “Codes which detect deception,” Bell System Tech. J., 53, 405-424.
- R. Ahlswede and G. Dueck, “Identification via channels,” in IEEE Trans. on Inf. Theory, vol. 35, no. 1, pp. 15-29, Jan. 1989, doi: 10.1109/18.42172.
- L. A. Bassalygo, M. V. Burnashev, “Authentication, Identification, and Pairwise Separated Measures”, Problems Inform. Transmission, 32:1 (1996), 33–39

#### Betreuer:

Analysis of Criss-Cross Deletion in Arrays

## Analysis of Criss-Cross Deletion in Arrays

#### Beschreibung

yle="font-weight: normal;" lang="de-DE" align="left">In this project we study two dimensional deletion/insertion problem introduced in https://arxiv.org/pdf/2004.14740.pdf. An array of n rows and n columns is transmitted through a specific deletion channel which for example occurs in DNA storage systems and racetrack memories. After transmission the receiver observes an array of dimension (n-1)*(n-1). The goal is to allow the receiver to know exactly which n*n array was transmitted by using error-correction techniques.

The goal of the project is to derive bounds on the deletion ball of any two-dimensional array. A deletion ball of an array X is the set of unique arrays resulting from the deletion of any possible combination of a column and a row in X. Deriving such bounds is not trivial since it depends heavily on the structure of the array. Thus, it is important to investigate useful characteristics representing the structure of an array for this particular setting. Furthermore, having this bound will be helpful to characterize the optimal redundancy of a deletion-correcting code for this setting.

#### Betreuer:

Index Coding & Coded Caching

## Index Coding & Coded Caching

#### Beschreibung

Coded caching problem has two phases, placement phase and delivery phase.

For a fixed placement scheme, designing the delivery protocol is equivalent to the index coding problem.

Transforming a coded caching problem with coded placement to the corresponding index coding problem is a hignly-interested topic and what is the optimal delivery scheme for a coded caching problem with coded placement is still an open problem.

References:

[1] N. S. Karat, S. Samuel, and B. S. Rajan. Optimal error correcting index codes for some generalized index coding problems. IEEE Transactions on Communications, 67(2):929–942, 2019.

[2] Z. Chen, P. Fan, and K. B. Letaief. Fundamental limits of caching: improved bounds for users with small buffers. IET Communications, 10(17):2315–2318, 2016.

#### Voraussetzungen

- Linear Algebra
- Channel Coding (recommended)

#### Betreuer:

Error Correction in DNA Storage

## Error Correction in DNA Storage

**Stichworte: **

DNA storage, Error Correction, Deletion, Insertion, Substitutions

#### Beschreibung

DNA storage is an uprising topic in the research field of storage systems. Due its natural longetivity, robustness, and density properties the main application would arise in high-dense long-term storage systems. The interest has become larger and larger due the large amount of data nowadays and the relative new biological advances in DNA synthesis and sequencing processes (e.g. polymerase chain reaction). In contrary to conventional storing methods, due to the nature of DNA and the involved biological processes special error patterns such as insertion, deletion, and substitution errors occur. To tackle these errors novel methods for correction have to be investigated. Moreover, the model of the DNA storage channel needs to be investigated thorougly, e.g. capacity statements.

#### Voraussetzungen

- Linear Algebra
- Channel Coding
- Coding Theory for Storage and Networks (optional)

#### Betreuer:

Homomorphic encryption

## Homomorphic encryption

**Stichworte: **

Cryptography

#### Beschreibung

Consider that a client would like to a server to do some computations for him but he does not want to give information meaningful information to the server. The client therefore sends encrypted messages c1 = Enc(pk, m1) and c2 = Enc(pk, m2) to the server and the client would like to obtain some function f of the two plaintexts f(m1,m2). It suffices for the client to get Enc(pk, f(m1,m2)) because the client owns the secret key sk. He is able to use the decryption function Dec on the ciphertext and gets Dec(sk, Enc(pk,f(m1,m2=))) = f(m1,m2).

The goal of this internship is to analyze schemes that achieve this property based on code-based cryptography.

#### Voraussetzungen

linear algebra

coding theory

basic understanding of cryptography

#### Betreuer:

Distributed learning on serverless compute services

## Distributed learning on serverless compute services

**Stichworte: **

Distributed machine learning, straggler mitigation, neural networks, coding theory

**Kurzbeschreibung: **

The goal of this project is to implement a neural network on thousands of serverless computing instances. We start by evaluating two existing coding techniques designed to scale stochastic gradient descent for convex loss functions. We then deviate to devise a coding scheme tailored for distributed neural network that scale for convex and non convex loss functions.

#### Beschreibung

Applying machine learning on large data became part of daily life. Scalability of distributed machine learning algorithms requires tolerance of slower computing nodes referred to as stragglers. To mitigate the effect of stragglers, one can add redundancy to the distributed data. However, stochastic gradient descent (SGD) is known to perform well even when computing on a part of the data. It is shown that for convex loss functions, a small redundancy or no redundancy at all is enough to guarantee good performance of SGD.

In this project, we evaluate the existent coding techniques requiring small redundancy on serverless compute functions offered by Amazon Web Services, or equivalently cloud functions offered by Google Computing Platform. Our goal is to devise a coding technique that goes beyond SGD and can be used for non-convex loss functions. The main targeted application is a full implementation of a neural network on serverless functions with straggler tolerance.

#### Voraussetzungen

Knowledge of machine learning algorithms, e.g., linear regression, logistic regression, neural network

Good programming skills

Self-motivation and dedication

Plus: knowledge of probability, statistical pattern recognition, coding theory and convex optimization

#### Kontakt

rawad.bitar@tum.de

https://sites.google.com/site/rawadbitar1

#### Betreuer:

Investigation of polar and Reed-Muller codes under inactivation decoding for distributed computing

## Investigation of polar and Reed-Muller codes under inactivation decoding for distributed computing

#### Beschreibung

Recently, channel codes are proposed to speed up computation in distributed systems by introducing redundant calculations to avoid the latency due to, e.g., straggling nodes (see, e.g., [1]). Since this problem can be casted as coding for erasure channels (where the erasure probability itself might be a random variable), there are works using inactivation decoding, an efficient way of implementing Gaussian elimination, for this problem [2]. In this internship, the task of the student is to understand the advantages of polar codes under successive cancellation (SC) decoding [3] and investigate polar codes and their variants, e.g., Reed-Muller codes, under an inactivation decoder [4] to understand their performance compared to the existing works, e.g., [2].

[1] https://arxiv.org/pdf/1512.02673.pdf

[2] https://arxiv.org/pdf/1712.08230.pdf

[3] https://arxiv.org/pdf/1901.06811.pdf

[4] https://arxiv.org/abs/2004.05969

#### Betreuer:

Two-sided search

## Two-sided search

#### Beschreibung

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.

#### Betreuer:

Learning Aided SC Flip Decoding for Polar Codes

## Learning Aided SC Flip Decoding for Polar Codes

#### Beschreibung

Polar codes achieve the capacity of binary-input discrete memoryless channels asymptotically in the block length under successive cancellation (SC) decoding. Polar codes have been adopted for the control channel in 5G enhanced mobile broadband (eMBB).

Due to the serial nature of SC decoding, an erroneous bit decision can be caused by the channel noise or previous erroneous bit estimates. The main idea of SC flip decoding is trying to correct the first erroneous bit decision by sequentially flipping the unreliable decisions.

The optimal flipping strategy is considered difficult due to lack of an analytical solution. Alternatively, (deep) learning aided SC flip algorithm are investigated in this thesis.

[1] O. Afisiadis, A. Balatsoukas-Stimming, and A. Burg, “A low-complexity improved successive cancellation decoder for polar codes,” in Proc. 48th Asilomar Conf. Signals, Systems and Computers, pp. 2116-2120, 2014.

[2] L. Chandesris, V. Savin, and D. Declercq, “Dynamic-SCFlip Decoding of Polar Codes,” IEEE Trans. Commun., vol. 66, no. 6, pp. 2333-2345, Jun., 2018.

[3] X. Wang, et al. "Learning to Flip Successive Cancellation Decoding of Polar Codes with LSTM Networks." *arXiv preprint arXiv:1902.08394* (2019).

[4] N. Doan, et al. "Neural Dynamic Successive Cancellation Flip Decoding of Polar Codes." *arXiv preprint arXiv:1907.11563* (2019).

#### 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:

### Ingenieurpraxis

A Jupyter Notebook for Line Coding in Access Networks (LB)

## A Jupyter Notebook for Line Coding in Access Networks (LB)

#### Beschreibung

yle="margin-bottom: 0cm; line-height: 100%;">For the access network case, the spectrum of the transmit signal has to be adapted to the channel properties. This can either be achieved by choosing suitable transmit pulse shapes or by encoding the (redundancy free) source symbols [1].

yle="margin-bottom: 0cm; line-height: 100%;">The students task is to implement a demonstration of two line coding schemes in Python [2] (Jupyter Notebook) and visualize the results. Additionally, the student also has to arrange code and surrounding text, such that the content becomes self-explanatory.

yle="margin-bottom: 0cm; line-height: 100%;">[1] Skript "Physical Layer Methods“

yle="margin-bottom: 0cm; line-height: 100%;">[2] "Python in 30 minutes" (https://www.programiz.com/python-programming/tutorial)

#### Voraussetzungen

Since the Jupyter Notebook is to be written in german language, the student should be able to write in german at least on a basic level.

While some basics in any programming language are beneficial, this is also a great opportunity for programming beginners, wishing to expand their programming skills.

For this topic students of the "Lehramtsstudiengänge" are preferred.

#### Betreuer:

## Seminar Topics

The three Seminars "Seminar on Coding and Cryptography", "Seminar on Digital Communications" and "Seminar on Optical Communications" will be organized jointly.

It does not matter for which one you register (please pick *one*), we will assign you to the right one once you passed the application phase.

You can find an overview about the open topics below.