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This work covers the implementation and theoretical analysis of sliding window decoding of spatially coupled product-like codes. The student will explore the performance-complexity tradeoff for eBCH component codes and precoded polar component codes under suboptimal component decoders like the Chase decoder or the SCL decoder. We consider adaptive coding for channels with state known at the transmitter and compute iterative decoding thresholds of corresponding code ensembles.

You may also contact me with your own project idea related to iterative decoding.

Voraussetzungen

The Gerchberg-Saxton algorithm is an iterative phase retrieval method originally developed in optics, and it has been adapted for electronic dispersion compensation in optical communication systems. The student will implement the algorithm and apply it to intensity-modulation/direct-detection (IM/DD) systems to explore its potential for waveform optimization. The focus lies on simulating the algorithm's behavior in the presence of fiber dispersion and analyzing convergence properties and performance.

Please reach out if you are interested in a thesis in any of my research fields. Possible areas include optical communications, particularly physical modeling and nonlinearity mitigation for single-mode fiber, and aspects of receiver design, such as receivers for channels with memory.
A good background in optical communication systems and applied information theory is preferable, but the requirements generally depend on your interests.
Please include a description of your interests and corresponding academic background in your application. If you have a thesis idea, I am happy to discuss your suggestions. Also, I am available to supervise external theses as long as they are in my field of expertise.

This thesis investigates how to optimally monitor and estimate real-time information from remote systems when communication resources are limited or delayed. In modern networked systems—such as sensor networks, autonomous agents, or industrial control applications—measurements often traverse unreliable or congested channels before reaching a central estimator. This raises a fundamental question: When should data be sampled and transmitted to ensure accurate and timely understanding of the system state?

The thesis will explore strategies that balance the freshness of information (often quantified by metrics like the Age of Information) with the quality of estimation. It will involve studying optimal sampling policies, understanding the impact of transmission delays, and characterizing how these factors affect overall system performance. The student will engage with both theoretical models and simulation tools to gain insights relevant to real-world applications in remote monitoring, edge computing, and cyber-physical systems.

Voraussetzungen

A foundational concept in information theory is Shannon entropy. However, Shannon entropy does not always provide sufficient flexibility when dealing with various optimization problems, robustness considerations, or scenarios where fine control over uncertainty quantification is required. In 1961, Rényi provided a parametric generalization of Shannon entropy [1], allowing for a more nuanced analysis of information measures. 

Rényi entropy has found applications in diverse fields such as hypothesis testing, machine learning, privacy and security (e.g., differential privacy), and statistical physics. The target of this project is to understand the difference between Shannon and Rényi entropy, conditional entropy, and divergence, as well as its applications in both theoretical and applied research.

[1] A. Rényi, “On measures of entropy and information,” in Proc. 4th Berkeley Symp. Mathematics, Statistics, and Probability, vol. 1, Berkeley, CA, USA, 1961, pp. 547–561.

I may not always have prepared thesis topics available. Please feel free to reach out if you are interested in working on a thesis within any of my research areas.

Voraussetzungen

I may not always have prepared thesis topics available. Please feel free to reach out if you are interested in working on a thesis within any of my research areas.

In a distributed learning setting, multiple worker machines are hired to help a main server with the expensive training of a machine learning model. Each worker is assigned a subtask, from which the main server tries to reconstruct the total computation result.

In the presence of faulty or malicious workers, called Byzantine workers, a common strategy is to distribute subtasks redundantly [3]. Since the redundancy introduces large computation overheads for the workers, strategies to reduce this overhead are required. One approach is to use interactive consistency checks at the main server, which can reduce the redundancy by up to 50% [1].

The interactive consistency checks are not for free, but cause additional computation and communication cost. For specific parameter regimes, this cost is well-studied. However, it is unkown how large this cost is in general. Therefore, we ask the following research questions:

1) How much computation is needed to guarantee error-free reconstruction of the computation result?

2) How much communication is needed?

3) What is the best trade-off between communication and computation cost?

The focus of this project is to study these research questions fundamentally. That is, we aim at understanding what the least amount of communication and computation possible is. The student will analyze these questions through mathematical tools, such as graph theory or information theory. The findings shall be compared against existing schemes [1,2] to evaluate their (sub-)optimality.

[1] C. Hofmeister, L. Maßny, E. Yaakobi and R. Bitar, "Byzantine-Resilient Gradient Coding Through Local Gradient Computations," in IEEE Transactions on Information Theory, vol. 71, no. 4, pp. 3142-3156, April 2025, doi: 10.1109/TIT.2025.3542896.

[2] S. Jain, L. Maßny, C. Hofmeister, E. Yaakobi and R. Bitar, "Interactive Byzantine-Resilient Gradient Coding for General Data Assignments," 2024 IEEE International Symposium on Information Theory (ISIT), Athens, Greece, 2024, pp. 3273-3278, doi: 10.1109/ISIT57864.2024.10619596.

[3] R. Tandon, Q. Lei, A. G. Dimakis, N. Karampatziakis, "Gradient Coding: Avoiding Stragglers in Distributed Learning", in Proceedings of the 34th International Conference on Machine Learning, PMLR 70:3368-3376, 2017.

Voraussetzungen

Please reach out if you are interested in a thesis in any of my research fields. Possible areas include optical communications, particularly physical modeling and nonlinearity mitigation for single-mode fiber, and aspects of receiver design, such as receivers for channels with memory.
A good background in optical communication systems and applied information theory is preferable, but the requirements generally depend on your interests.
Please include a description of your interests and corresponding academic background in your application. If you have a thesis idea, I am happy to discuss your suggestions. Also, I am available to supervise external theses as long as they are in my field of expertise.

I may not always have prepared thesis topics available. Please feel free to reach out if you are interested in working on a thesis within any of my research areas.

Voraussetzungen

The entropy rate of a stochastic process quantifies the average uncertainty per time step. In the context of Hidden Markov Models (HMMs)—where we observe a sequence of outputs generated by an underlying Markov process—this notion becomes particularly intriguing. While standard Markov chains have a well-defined structure for computing entropy rates, the introduction of a hidden layer complicates matters significantly. The entropy rate of an HMM reflects the long-term unpredictability of its observable outputs, capturing both the randomness of the state transitions and the ambiguity introduced by the observation process.

Understanding the entropy rate of HMMs has broad implications, from speech recognition and bioinformatics to machine learning and signal processing. Despite their practical importance, entropy rates of HMMs are notoriously hard to compute exactly, often requiring approximate methods or asymptotic analysis. This challenge opens up interesting theoretical questions and motivates efficient computational approaches. In this project, we investigate how structure, memory, and noise in the model impact entropy rate, and what this reveals about the information limits of systems modeled by HMMs.

Voraussetzungen

I may not always have prepared thesis topics available. Please feel free to reach out if you are interested in working on a thesis within any of my research areas.

Motivated by the cell-free and massive MIMO (multiple input multiple outputs) communication scenarios, the number of power amplifiers (PA), digital to analog converters (DAC), etc., is increased. Thus, using coarse quantized transmission reduces the channel's hardware cost and nonlinear effects. More details can be found here.

In this project, we investigate algorithms for mapping modulated data to coarsely quantized signals and compare their information rates. 

The student needs an understanding of information theory and communication systems.

This thesis is concerned with developing code constructions for a new weight function (and associated metric) on (Z/qZ)^n called the unit-burst weight, suitable for measuring same-symbol burst errors. A unit burst is defined as a vector that has some consecutive positions of ones and is zero otherwise.

Any vector v in (Z/qZ)^n can be written as a (not necessarily unique) linear combination of these bursts. The burst weight is then the minimum number of bursts that need to be added or subtracted to produce v.

This metric has a connection to the A_n root lattice, a special lattice in Z^n+1 of vectors whose entries sum to zero. More precisely, the unit bursts relate to the shortest vectors of A_n called roots, and the burst weight corresponds to the smallest decomposition of a lattice point into roots.

We have already derived some basic properties and algorithms for this new metric and now would like to find some bounds and code constructions achieving those bounds. 

In federated learning, a machine learning model shall be trained on private user data with the help of a central server, the so-called federator. This setting differs from other machine learning settings in that the user data shall not be shared with the federator for privacy reasons and/or to decrease the communication load of the system.

Even though only intermediate results are shared, extra care is necessary to guarantee data privacy. An additional challenge arises if the system includes malicious users that breach protocol and send corrupt computation results.

The goal of this work is to design, implement and analyze coding- and information-theoretic solutions for privacy and security in federated learning.

Voraussetzungen

In a distributed learning setting, multiple worker machines are hired to help a main server with the expensive training of a machine learning model. Each worker is assigned a subtask, from which the main server tries to reconstruct the total computation result.

In the presence of faulty or malicious workers, called Byzantine workers, a common strategy is to distribute subtasks redundantly [3]. Since the redundancy introduces large computation overheads for the workers, strategies to reduce this overhead are required. One approach is to use interactive consistency checks at the main server, which can reduce the redundancy by up to 50% [1].

The interactive consistency checks are not for free, but cause additional computation and communication cost. For specific parameter regimes, this cost is well-studied. However, it is unkown how large this cost is in general. Therefore, we ask the following research questions:

1) How much computation is needed to guarantee error-free reconstruction of the computation result?

2) How much communication is needed?

3) What is the best trade-off between communication and computation cost?

The focus of this project is to study these research questions fundamentally. That is, we aim at understanding what the least amount of communication and computation possible is. The student will analyze these questions through mathematical tools, such as graph theory or information theory. The findings shall be compared against existing schemes [1,2] to evaluate their (sub-)optimality.

[1] C. Hofmeister, L. Maßny, E. Yaakobi and R. Bitar, "Byzantine-Resilient Gradient Coding Through Local Gradient Computations," in IEEE Transactions on Information Theory, vol. 71, no. 4, pp. 3142-3156, April 2025, doi: 10.1109/TIT.2025.3542896.

[2] S. Jain, L. Maßny, C. Hofmeister, E. Yaakobi and R. Bitar, "Interactive Byzantine-Resilient Gradient Coding for General Data Assignments," 2024 IEEE International Symposium on Information Theory (ISIT), Athens, Greece, 2024, pp. 3273-3278, doi: 10.1109/ISIT57864.2024.10619596.

[3] R. Tandon, Q. Lei, A. G. Dimakis, N. Karampatziakis, "Gradient Coding: Avoiding Stragglers in Distributed Learning", in Proceedings of the 34th International Conference on Machine Learning, PMLR 70:3368-3376, 2017.

Voraussetzungen

This work covers the implementation and theoretical analysis of sliding window decoding of spatially coupled product-like codes. The student will explore the performance-complexity tradeoff for eBCH component codes and precoded polar component codes under suboptimal component decoders like the Chase decoder or the SCL decoder. We consider adaptive coding for channels with state known at the transmitter and compute iterative decoding thresholds of corresponding code ensembles.

You may also contact me with your own project idea related to iterative decoding.

Voraussetzungen

The Gerchberg-Saxton algorithm is an iterative phase retrieval method originally developed in optics, and it has been adapted for electronic dispersion compensation in optical communication systems. The student will implement the algorithm and apply it to intensity-modulation/direct-detection (IM/DD) systems to explore its potential for waveform optimization. The focus lies on simulating the algorithm's behavior in the presence of fiber dispersion and analyzing convergence properties and performance.

Please reach out if you are interested in a thesis in any of my research fields. Possible areas include optical communications, particularly physical modeling and nonlinearity mitigation for single-mode fiber, and aspects of receiver design, such as receivers for channels with memory.
A good background in optical communication systems and applied information theory is preferable, but the requirements generally depend on your interests.
Please include a description of your interests and corresponding academic background in your application. If you have a thesis idea, I am happy to discuss your suggestions. Also, I am available to supervise external theses as long as they are in my field of expertise.

A foundational concept in information theory is Shannon entropy. However, Shannon entropy does not always provide sufficient flexibility when dealing with various optimization problems, robustness considerations, or scenarios where fine control over uncertainty quantification is required. In 1961, Rényi provided a parametric generalization of Shannon entropy [1], allowing for a more nuanced analysis of information measures. 

Rényi entropy has found applications in diverse fields such as hypothesis testing, machine learning, privacy and security (e.g., differential privacy), and statistical physics. The target of this project is to understand the difference between Shannon and Rényi entropy, conditional entropy, and divergence, as well as its applications in both theoretical and applied research.

[1] A. Rényi, “On measures of entropy and information,” in Proc. 4th Berkeley Symp. Mathematics, Statistics, and Probability, vol. 1, Berkeley, CA, USA, 1961, pp. 547–561.

I may not always have prepared thesis topics available. Please feel free to reach out if you are interested in working on a thesis within any of my research areas.

Voraussetzungen

I may not always have prepared thesis topics available. Please feel free to reach out if you are interested in working on a thesis within any of my research areas.

This thesis is concerned with developing code constructions for a new weight function (and associated metric) on (Z/qZ)^n called the unit-burst weight, suitable for measuring same-symbol burst errors. A unit burst is defined as a vector that has some consecutive positions of ones and is zero otherwise.

Any vector v in (Z/qZ)^n can be written as a (not necessarily unique) linear combination of these bursts. The burst weight is then the minimum number of bursts that need to be added or subtracted to produce v.

This metric has a connection to the A_n root lattice, a special lattice in Z^n+1 of vectors whose entries sum to zero. More precisely, the unit bursts relate to the shortest vectors of A_n called roots, and the burst weight corresponds to the smallest decomposition of a lattice point into roots.

We have already derived some basic properties and algorithms for this new metric and now would like to find some bounds and code constructions achieving those bounds. 

In federated learning, a machine learning model shall be trained on private user data with the help of a central server, the so-called federator. This setting differs from other machine learning settings in that the user data shall not be shared with the federator for privacy reasons and/or to decrease the communication load of the system.

Even though only intermediate results are shared, extra care is necessary to guarantee data privacy. An additional challenge arises if the system includes malicious users that breach protocol and send corrupt computation results.

The goal of this work is to design, implement and analyze coding- and information-theoretic solutions for privacy and security in federated learning.

Voraussetzungen

This work covers the implementation and theoretical analysis of sliding window decoding of spatially coupled product-like codes. The student will explore the performance-complexity tradeoff for eBCH component codes and precoded polar component codes under suboptimal component decoders like the Chase decoder or the SCL decoder. We consider adaptive coding for channels with state known at the transmitter and compute iterative decoding thresholds of corresponding code ensembles.

You may also contact me with your own project idea related to iterative decoding.

Voraussetzungen

A foundational concept in information theory is Shannon entropy. However, Shannon entropy does not always provide sufficient flexibility when dealing with various optimization problems, robustness considerations, or scenarios where fine control over uncertainty quantification is required. In 1961, Rényi provided a parametric generalization of Shannon entropy [1], allowing for a more nuanced analysis of information measures. 

Rényi entropy has found applications in diverse fields such as hypothesis testing, machine learning, privacy and security (e.g., differential privacy), and statistical physics. The target of this project is to understand the difference between Shannon and Rényi entropy, conditional entropy, and divergence, as well as its applications in both theoretical and applied research.

[1] A. Rényi, “On measures of entropy and information,” in Proc. 4th Berkeley Symp. Mathematics, Statistics, and Probability, vol. 1, Berkeley, CA, USA, 1961, pp. 547–561.

I may not always have prepared thesis topics available. Please feel free to reach out if you are interested in working on a thesis within any of my research areas.