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In this work, we investigate and compare selected gradient compression schemes and their impact on the performance of the underlying machine learning algorithm.

We study the impact of different measures of fairness on the privacy guarantees for individual clients in federated learning.

We study the usage of channel codes for the setting of federated learning with over-the-air computation so that the sum of codewords over reals can be efficiently and reliably decoded at the federator to obtain the average of partial model updates.

Gradient boosting tree model is widely used in practical applications, and its optimized implementation XGBoost is one of the most popular machine learning algorithms. If the data is centralized, It has been well implemented. When the data is decentralized and to preserve privacy, federated learning (FL) is used. FL is widely divided into ‘horizontal FL’ and ‘vertical FL,’ which differ from the partition methods of datasets. Previous works have focused more on horizontal FL, while vertical FL remains unexplored. Existing works in vertical federated XGBoost have some limitations, such as intermediate data leakage, computation overhead, etc. GPU acceleration is quite common in machine learning and is not applied to privacy-preserving XGBoost. This project aims to build an efficient privacy-preserving vertical federated XGBoost using GPUs.

The main aim of the thesis is to make a comparison between different multicarrier modulations, in particular OFDM and OTFS, inside a wireless system.

The considered wireless system consists in a Delay-Doppler channel, which is typical in vehicular communications. A Hybrid IRS is considered in order to be able to achieve Integrated Sensing and Communications.

In paper 

"Correcting a Single Error in Feedback Channels" the problem of correcting a single error with feedback was investigated. It was mainly devoted to binary channels, namely, binary symmetric and asymmetric channels. A general theorem, which allows constructing codes correcting one error with one feedback, was proved. For the symmetric channel with one error, it was proved that with two feedbacks one can transmit as many messages as with complete feedback.

In this project, it is proposed to generalize these results to the case of two errors. Namely, it is required to prove the theorem, which describes optimal codes, correcting 2 errors with one feedback. After that, some optimization problems should be solved to find the parameters of optimal codes.

This work shall deal with post-quantum secure schemes utilizing the Lee metric. The student's task is to get familiar with this metric and to design a signature scheme. The student shall show that known attacks in the Hamming metric are not applicable for the Lee metric.

Channel Coding

Due to the recent advances in quantum computers, the search for cryptosystems that survive quantum attacks is of great interest. Code-based cryptography is a promising candidate, since it is build on the NP-hard problem of decoding a random code [1].

Recently, different variants of the classical syndrome decoding problem (SDP) in the Hamming metric have been proposed [2,3].
The main reason for this is that it appears hard to build an efficient digital signature scheme around the classical SDP.
One such variant is the restricted syndrome decoding which was introduced in [2].

The goal of this the construction of codes for this error model, which has not been done before.
For this, a first approach is to follow the general idea given in [4].

Open questions are:

- discussion of the appropriate choice of the error set of a McEliece-type cryptosystem
- optimality bounds for codes in the restricted setting
- construction of short codes that are efficiently decodable and/or optimal
- construction of longer codes from short codes and the evaluation of their perfomance

References:

[1] Weger, V., Gassner, N., & Rosenthal, J. (2022). A Survey on Code-Based Cryptography. arXiv preprint arXiv:2201.07119.

[2] Baldi, M., Battaglioni, M., Chiaraluce, F., Horlemann-Trautmann, A. L., Persichetti, E., Santini, P., & Weger, V. (2020). A new path to code-based signatures via identification schemes with restricted errors. arXiv preprint arXiv:2008.06403.

[3] Baldi, M., Bitzer, S., Pavoni, A., Santini, P., Wachter-Zeh, A., & Weger, V. (2023). Generic Decoding of Restricted Errors. arXiv preprint arXiv:2303.08882.

[4] Rohweder, D., Freudenberger, J., & Shavgulidze, S. (2018). Low-density parity-check codes over finite Gaussian integer fields. In ISIT.

Security in Communications and Storage

Channel Coding

Sustainability is an essential part of every industrial field in today’s world. Thus, the importance of energy-efficient software cannot be overstated. In this master's thesis, the student examines the hardware-related metrics of a consumer computing device and estimate the energy consumption of specific applications by analysing their metrics. With this analysis, we aim to find a universally applicable mathematical method to estimate the energy consumption of individual applications by using only their resource consumption metrics without the need for an additional power measurement tool. This includes the determination of useful metrics that affect the energy consumption of a consumer computing device.

Compared with traditional frame-based cameras, an event-based camera has the advantages of low latency, high dynamic range, (almost) no motion blur, etc., and can respond fast to a brightness change at the image plane with thresholds determined by the previous state of brightness. It can generate event data of structural features without signal processing, such as edges and corners, which saves time, energy and computing effort.

However, it still lacks standard processes for analyzing, characterizing and evaluating event-based camera information. Moreover, data acquisition of this camera demands changes in brightness on a respective pixel. This can be introduced artificially by relative movement of the camera to the object. This might miss out part of the data due to linear translation along structural elements like edges or introduce some error due to error motion or vibration.

This thesis aims to ensure safety and quality when implementing event-based cameras in the field of industrial inspection, by dedicated experiments and related discussion of results. Event based camera imageswill be characterized and evaluated. New methods for event generation and signal processing will be proposed which will make use of the special characteristics of event-based cameras and their special characteristics arising from their working principle.

In theory, the check nodes operations of belief propagation rely on tanh() and arctanh() functions which require high computational power. Hence, in most of the practical applications, an approximation called “MinSum” is used. This method aims to exploit the structure of tanh() function where the absolute value of output sufficiently converges to 1 with increasing absolute value of input. Hence, in a series multiplication of absolute outputs, the most dominant effect comes from the minimum element and other contributions are considered negligible. However, neglection of other attenuation factors cause overcalculated outputs in “MinSum” algorithm which can accumulated by multiple iterations. This drawback can be compensated through adding attenuation or/and offset factors. These factors are mostly iteration specific and intuitively determined, which means one factor which is determined by educated guess is applied to all leaving edges. However, every edge in an unfolded Tanner graph has its own unique identity corresponding to the previous nodes and edges that the message is transmitted.

In addition to approach aiming to close the performance gap between main algorithm and “MinSum ” approximation, we can intend to improve the qualities of main algorithm. Even though belief propagation decoding in LDPC codes is considered as highly successful, it is still a “suboptimal” method compared to very expensive but accurate Maximum A posteriori Probability (MAP) estimation. It means there might be some room for improvement in performance. Additionally, belief propagation requires multiple iterations to converge and the required number of iterations can dramatically increase by decreasing signal-to-noise ratio (SNR). Additional correction weights imposed on iterated messages can be a candidate to improve performance in overall.

5G specification for channel coding is using protograph based LDPC codes. Every node duplicated from same base matrix node is keen to show similar properties, it may be possible to use same weights for these nodes by preserving the good decoding results. This detail can help us to using additional correction weights by minimum additional memory burden.

The degree of damage to a Flash cell’s oxide layer caused by program and erase (P/E) operations is directly related to the volume of charge traveling through the oxide layer [2]. While the channel degradation caused by by P/E operations is often modeled as a function of the number of P/E cycles, the model in [3] essentially assumes that approximately the same volume of charge travels through the oxide layer during each P/E cycle. Intended threshold voltages themselves can be varied over time so that less charge travels through the oxide layer during early P/E cycles when the channel is favorable. In [3], the authors consider the degradation as a function of the cumulative effect of the charge written and erased from the cell and use Dynamic Voltage Allocation of Write (DVA) as a solution.

[1] T. Parnell, N. Papandreou, T. Mittelholzer, and H. Pozidis, “Modelling of the threshold voltage distributions of sub-20nm NAND flash memory,” in Proc. 2014 IEEE Global Commun. Conf. (GLOBECOM), 2014, pp. 2351–2356 [2] M. Gill and S. Lai, “Flash reliability issues,” in Nonvolatile semiconductor memory technology: a comprehensive guide to understanding and to using NVSM devices, W. D. Brown and J. Brewer, Eds. New York, NY: IEEE Press, 1998, ch. 4, sec. 6, pp. 255–281. [3] H. Wang, N. Wong, T. Chen, and R. D. Wesel, “Using dynamic allocation of write voltage to extend Flash memory lifetime”, IEEE Transactions on Communications, vol. 64, no. 11, pp. 4474–4486, November 2016.

- Channel Coding lecture.

- Basic knowledge about storage devices.

- Combinatoric and algebra plus probability.

In this project the student should calculate the zero-error capacity for 

a multi-user model with feedback.

Information theory

In this internship, the student will read and summarize the recent progress on codes for privacy and security in federated learning.

Depending on the student's progress, we can investigate new ideas for security in private federated learning that improve upon the state0of0the-art.

We study the bias-variance trade-off in gradient compression in the setting of federated learning. In particular, we investigate if biased and low-variance estimates of indivial clients' gradients can still lead to unbiased averaged gradients while reducing the overall variance, and hence the distortion of the compression scheme.

We theoretically study the impact of gradient compression schemes on the regularization properties of the underlying machine learning algorithm.

Due to the recent advances in quantum computers, the search for cryptosystems that survive quantum attacks is of great interest. Code-based cryptography is a promising candidate, since it is build on the NP-hard problem of decoding a random code [1].

The McEliece cryptosystem is a promising candidate for asymmetric encryption.
However, many attempts at constructing a code-based signature scheme have resulted in impractical parameters or security problems.

NIST's announcement of a competetion dedicated to standardizing post-quantum signatures has lead to the publication of several new code-based schemes

In this work we consider a proposals based on quasi-cyclic low-density parity-check codes [2].
We investigate possible information leakage through the signatures, since for related signature schemes, such leakages have lead to efficient key recovery attacks.

References:

[1] Weger, V., Gassner, N., & Rosenthal, J. (2022). A Survey on Code-Based Cryptography. arXiv preprint arXiv:2201.07119.

[2] Picozzi, C., Meneghetti, A., & Tognolini, G. (2022). A Post-Quantum Digital Signature Scheme from QC-LDPC Codes. Cryptology ePrint Archive.

[3] Persichetti, E. (2018). Efficient one-time signatures from quasi-cyclic codes: A full treatment. Cryptography, 2(4), 30

[4] Santini, P., Baldi, M., & Chiaraluce, F. (2019, July). Cryptanalysis of a one-time code-based digital signature scheme. In 2019 IEEE International Symposium on Information Theory (ISIT) (pp. 2594-2598). IEEE.

Channel coding

Security in Communications and Storage

Since the introduction of federated learning in [1], we can observe a rapidly growing body of research. In particular, we face challenges with respect to privacy, security and efficiency. We build upon an existing generic framework for simulating decentralized optimization procedures in a federated learning setting. With the help of that framework, the student should analyze the performance of selected state-of-the-art schemes and investigate different protocols that utilize local updates and the effect of straggling clients.

Due to the recent advances in quantum computers, the search for cryptosystems that survive quantum attacks is of great interest. Code-based cryptography is a promising candidate, since it is build on the NP-hard problem of decoding a random code [1].

The McEliece cryptosystem is a promising candidate for asymmetric encryption.
However, many attempts at constructing a code-based signature scheme have resulted in impractical parameters or security problems.

NIST's announcement of a competetion dedicated to standardizing post-quantum signatures has lead to the publication of several new code-based schemes

In this work we consider LESS [2] a signature scheme based on the hardness of the code equivalence problem [3].
State-of-the-art solvers of the problem [4] are analysed and modifications are made to improve their performance.

References:

[1] Weger, V., Gassner, N., & Rosenthal, J. (2022). A Survey on Code-Based Cryptography. arXiv preprint arXiv:2201.07119.

[2] Barenghi, A., Biasse, J. F., Persichetti, E., & Santini, P. (2021). LESS-FM: fine-tuning signatures from the code equivalence problem. In Post-Quantum Cryptography: 12th International Workshop, PQCrypto 2021, Daejeon, South Korea, July 20–22, 2021, Proceedings 12 (pp. 23-43). Springer International Publishing.

[3] Barenghi, A., Biasse, J. F., Persichetti, E., & Santini, P. (2022). On the computational hardness of the code equivalence problem in cryptography. Cryptology ePrint Archive.

[4] Beullens, W. (2021, July). Not enough LESS: An improved algorithm for solving code equivalence problems over F q. In Selected Areas in Cryptography: 27th International Conference, Halifax, NS, Canada (Virtual Event), October 21-23, 2020, Revised Selected Papers (pp. 387-403). Cham: Springer International Publishing.

Channel coding

Security in Communications and Storage

We are interested in computing upper bounds (on capacity) for frequency-selective channels with a memoryless nonlineary at the transmitter/receiver.

One application for these bounds are short-reach fiber-optic communication systems with a single photodiode at the receiver. The photodiode is a memoryless nonlinearity, as it produces an output that is proportional to the squared magnitude of the input signal.

A simple upper bound for the above model is given in [Sec. III D, 2].

D. Plabst et al., "Achievable Rates for Short-Reach Fiber-Optic Channels With Direct Detection," in Journal of Lightwave Technology, vol. 40, no. 12, pp. 3602-3613, 15 June15, 2022, doi: 10.1109/JLT.2022.3149574.

Information Theory

Linear System Theory

Forschungspraxis

The ever-growing need for precise and high-accuracy

localization in 5G and GNSS-based hybrid systems

require methods that are able to overcome the challenges of

cost and time in development. One of the key challenges involves

the multipath effect that has been studied for decades. Classical

methods that can identify Line-of-Sight (LOS) signals and mitigate

non-Line-of-Sight (NLOS) signals are widely available, however,

they perform poorly in comparison to Machine-Learning

(ML) based methods. In this project, we present an ML pipeline

for the extraction of LOS signals from NLOS present under

multipath conditions. The Channel Impulse Response (CIR) of

Frequency Range 1 (FR1) of 5G as well as Global Navigation

Satellite System (GNSS) signals from a real environment data

are virtually recreated and simulated via Ray-Tracing Engine

to identify the presence of LOS. 

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The size of the ball of radius d in Levenstein metric depends on the center of the ball. During this project it is suggested to investigate the distribution of the sizes of Levenstein balls, i.e. estimate the mathematical expectation and variance of the size, and find its maximal and minimum value.

For the case d=1 and 2 this question have already been addressed in papers [1] and [2] correspondingly, where some theoretical results have been obtained. The task of the project is to verify it with numerical computation, and obtain similar estimations for d>2.

[1] Bar-Lev, D., Etzion, T., & Yaakobi, E. (2021, July). On Levenshtein balls with radius one. In 2021 IEEE International Symposium on Information Theory (ISIT) (pp. 1979-1984). IEEE.

[2] He, L., & Ye, M. (2023, June). The size of Levenshtein ball with radius 2: Expectation and concentration bound. In 2023 IEEE International Symposium on Information Theory (ISIT) (pp. 850-855). IEEE.

The DiVincenzo criteria, introduced by theoretical physicist David P. DiVincenzo in 2000, provides a comprehensive framework for identifying the necessary requirements to achieve successful quantum computation. In this project, we search for ideal conditions necessary for buidling distributed quantum devices. 

Enumerative sphere shaping [1] is an efficient method to perform energy-optimal distribution matching for short to medium block lengths. It is an alternative approximate shell mapping schemes based on CCDM [2].

The goal of this thesis is to extend enumerative sphere shaping to general target distributions using the ideas from [3] and compare the performance of this distribution matcher to CCDM-based approximate shell mapping.

1. https://doi.org/10.1109/TWC.2019.2951139
2. https://doi.org/10.1109/TIT.2015.2499181
3. https://doi.org/10.1109/LWC.2018.2890595

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the students should translate functions from Matlab and C to julia. the functions involve calculation of infomation theoretic quantities to basic function of a discrete time transmission chain.

The students task is to learn julia and matlab to a extend that the translation from one to the other language is possible. We furthermore expect the student to learn how to use git and gitlab for managing larger projects.

basic programming knowledge

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