Es spielt keine Rolle zu welchem Sie sich anmelden (bitten wählen sie *eines*), wir werden Sie dann entsprechend zuweisen falls Sie einen Platz nach der Bewerbugsphase erhalten.
Sie müssen sich für Themen bewerben, die Sie interessieren. Wählen Sie bitte mehr als ein Thema, aber nicht mehr als 4. Schreiben Sie die entsprechenden Betreuer direkt an und setzen den Seminarleiter auf CC (firstname.lastname@example.org).
Hier finden Sie eine Übersicht der angebotenen Themen der drei Seminare.
Recent applications of Levenshtein's reconstruction problem
The student will familiarize themselves with the reconstruction problem, choose a recent work applying its principles, and present it to their peers.
Levenshtein presented in 2001 his reconstruction problem: given multiple noisy observations of the same information, can the original be deduced, and how? It is a problem applicable to many data storage and transmission scenarios, where multiple transmissions and/or reads are inherently available or else cheaper to obtain than the cost of added redundancy required for tranditional error-correction.
This framework has since seen many adaptations and applications in various contexts, for various channels. It is especially applicable to some novel storage technologies such as cloud storage, racetrack memories and DNA storage.
The student's taks is to research Levenshtein's seminal paper in addition to any recent application of their choosing (some suggestions herein), and present (an introduction to / a summary of) the underlying principles to their peers.
 V. I. Levenshtein, “Efficient reconstruction of sequences,” IEEE Trans. on Inform. Theory, vol. 47, no. 1, pp. 2–22, Jan. 2001.
 Y. Cassuto and M. Blaum, “Codes for symbol-pair read channels,” IEEE Trans. on Inform. Theory, vol. 57, no. 12, pp. 8011–8020, Dec. 2011.
 Y. M. Chee, H. M. Kiah, A. Vardy, V. K. Vu, and E. Yaakobi, “Coding for racetrack memories,” IEEE Trans. on Inform. Theory, vol. 64, no. 11, pp. 7094–7112, Nov. 2018.
 E. Yaakobi and J. Bruck, “On the uncertainty of information retrieval in associative memories,” IEEE Trans. on Inform. Theory, vol. 65, no. 4, pp. 2155–2165, Apr. 2019.
 Y. Yehezkeally and M. Schwartz, “Uncertainty of Reconstruction with List-Decoding from Uniform-Tandem-Duplication Noise,” IEEE Trans. on Inform. Theory, accepted for publication, Feb. 2021.
Basic knowledge of error-correcting codes and their applications. Control of basic mathematic notions (linear and abstract algebra) is assumed.
Massive Random Access
With with the increasing number of devices connected to the internet and the growing number of M2M type communications, massive random access has become a crucial topic in the design of communication systems. The student's task is to understand the concepts of massive random access. The Two main resources are  and .
 Y. Polyanskiy, “A perspective on massive random-access,” in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Aachen, Germany, Jun. 2017, pp. 2523–2527.
 K.H. Ngo, A. Lancho, G. Durisi, A. Graell i Amat, "Massive Uncoordinated Access With Random User Activity," arXiv:2103.09721, Mar 2021.
Multi User Information Theory
Polarization-adjusted convolutional codes
The student's task is to understand a recently introduced coding scheme, namely polarization-adjusted convolutional (PAC) codes . In addition to encoding and decoding schemes presented in the papers below [2,3], the students asked to study the error exponent for concatenated code ensembles , which is closely related to the good performance of not only concatenated polar codes but also PAC codes.
-  https://arxiv.org/pdf/1908.09594.pdf
-  https://arxiv.org/pdf/2002.06805.pdf
-  https://arxiv.org/pdf/2003.08640.pdf
-  http://yoksis.bilkent.edu.tr/pdf/files/13637.pdf
Channel Codes for Iterative Decoding
Interleaver Design of Turbo Codes
The LTE standard adopted a Turbo Code (TC) as channel code. And TCs could remain promising channel coding candidates for 5G. A typical TC is constructed by parallel concatenating two convolutional codes via an interleaver. The design of the interleaver is critical to the performance of the TC, particularly for short frame sizes. They can in general be separated into two classes: random interleavers and deterministic interleavers. The task of the student is to give an overview of three kinds of deterministic interleavers: Quadratic Polynomial Permutation (QPP) , Almost Regular Permutation (ARP)  and Dithered Relative Prime (DRP) lnterleavers . References:  yle="color: #3070b3; text-decoration: none; border-bottom-width: 1px; border-bottom-style: solid; border-bottom-color: gray; padding-bottom: 1px; transition: all 188ms ease;" href="http://ieeexplore.ieee.org/document/1377495/" rel="noopener" target="_blank">http://ieeexplore.ieee.org/document/1377495/  yle="color: #3070b3; text-decoration: none; border-bottom-width: 1px; border-bottom-style: solid; border-bottom-color: gray; padding-bottom: 1px; transition: all 188ms ease;" href="http://ieeexplore.ieee.org/document/1312507/" rel="noopener">http://ieeexplore.ieee.org/document/1312507/  yle="color: #3070b3; text-decoration: none; border-bottom-width: 1px; border-bottom-style: solid; border-bottom-color: gray; padding-bottom: 1px; transition: all 188ms ease;" href="http://read.pudn.com/downloads155/doc/project/686322/DRP.pdf" rel="noopener" target="_blank">https://ieeexplore.ieee.org/document/957178
Forward Error Correction (FEC) for High-Throughput Optical Communication
Forward Error Correction (FEC) for high-throughput optical communication has gained growing interest in the research community. The always-growing data rate (soon expected to reach 1 Tb/s) makes it necessary to look for low-complexity and low-power consumption solutions. Soft-decision (SD) decoding can guarantee top performances but it is not feasible in this setting due to its high complexity. Hard-decision (HD) decoding, especially of product codes and product-like codes, is regarded as an appealing solution due to its good performance-complexity trade-off. During the recent years, many researcher have tried to fill the performance gap between HD and SD decoding performances while keeping the complexity low.
Staircase codes are a class of product-like codes introduced in  with their HD decoding algorithm. They offer a good performance-complexity trade off, and they are adopted in recent optical standardizations (e.g. 400ZR standard). To enhance further their performances, they can be used as outer code of a concatenation scheme - with an inner SD decoded code.
The task of the student is to learn about performance-complexity trade-off in FEC for optical communications, to understand the structure and HD decoding of staircase codes and their application in the concatenated structure.
“Staircase Codes: FEC for 100 Gb/s OTN” Benjamin P. Smith, Arash Farhood, Andrew Hunt, Frank R. Kschischang
“Low-Complexity Soft-Decision Concatenated LDGM-Staircase FEC for High-Bit-Rate Fiber-Optic Communication” Lei M. Zhang, Frank R. Kschischang
“Low-Complexity Concatenated LDPC-Staircase Codes” Masoud Barakatain, Frank R. Kschischang
Channel Coding, Advanced Topics (Graell i Amat) or Channel Codes for Iterative Decoding
Trapping Sets of LDPC Codes
yle="margin-bottom: 0.1in; line-height: 1.15px; font-size: medium; font-variant-numeric: normal; font-variant-east-asian: normal;">Investigation of the stopping/trappi construct LDPC
yle="margin-bottom: 0.1in; line-height: 1.15px; font-size: medium; font-variant-numeric: normal; font-variant-east-asian: normal;">
yle="margin-bottom: 0.1in; line-height: 1.15px; font-size: medium; font-variant-numeric: normal; font-variant-east-asian: normal;">codes and study algorithms to construct
yle="margin-bottom: 0.1in; line-height: 1.15px; font-size: medium; font-variant-numeric: normal; font-variant-east-asian: normal;">LDPC codes without small stopping/trapping sets.
yle="font-size: medium; font-variant-numeric: normal; font-variant-east-asian: normal; font-weight: normal;">https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6211373
yle="font-size: medium; font-variant-numeric: normal; font-variant-east-asian: normal; font-weight: normal;">https://arxiv.org/pdf/1705.05996.pdf
yle="font-size: medium; font-variant-numeric: normal; font-variant-east-asian: normal; font-weight: normal;">https://hal.archives-ouvertes.fr/hal-01338688/document
yle="font-size: medium; font-variant-numeric: normal; font-variant-east-asian: normal; font-weight: normal;">https://ieeexplore.ieee.org/document/4039670
Channel codes for iterative decoding
Graph Capacity (Intro.)
Shannon Capacity of A Graph, Confusability Graph, Graph Powers.
The student study the problem of transmission over a channel (communication) through the lens of graphs. Hence, S/he learn some graph language and alphabets and later study the known results for the graph capacities.
Specifically the following topics will be touched:
- Shannon Capacity of A Graph
- Zero-Error Capacity
- Zero-Error Applications (Perfect Hash Function, Superimposed Codes)
- Sperner Capacity
- Lovasz Number
- Haemers Bound
- Confusability Graph
- Hyper-graph Capacity
- Graph Alphabets:
- Independenc Number
- Chromatic Number
- Graph Entropy
- Graph Powers
Basics of the following:
- Information Theory
- Graph Theory
- Coding Theory
- Channel Coding
- Alon, N. "The Shannon Capacity of a Union." Combinatorica 18, 301-310, 1998.
- Haemers, W. "An Upper Bound for the Shannon Capacity of a Graph." In Algebraic Methods in Graph Theory. Szeged, Hungary: pp. 267-272, 1978.
- Lovász, L. "On the Shannon Capacity of a Graph." IEEE Trans. Inform. Th. IT-25, 1-7, 1979.
- Shannon, C. E. "The Zero-Error Capacity of a Noisy Channel." IRE Trans. Inform. Th. 2, 8-19, 1956.
- Cohen, G., Körner, J. and Simonyi, G., 1990. "Zero-error capacities and very different sequences." In Sequences (pp. 144-155). Springer, New York, NY.
- Korner, Janos, and Alon Orlitsky. "Zero-error information theory." IEEE Trans. Inform. Th. IT-25, no. 6 (1998): 2207-2229.
Computing discrete eigenvalues by contour integrals in the nonlinear Fourier domain
In an attempt to improve achievable rates for optical communication systems in the high input power regime, modulation via the nonlinear Fourier transform (NFT) has attracted some attention in recent years. Many NFT algorithms however still exhibit high computational complexity that has to be addressed. One very recent approach focuses on the computation of the discrete eigenvalues of a received pulses nonlinear Fourier spectrum by using the well-known Delves-Lyness zero-search algorithm [1-2].
The students task would be to first get a basic grasp of the NFT by having a look at  and an overview on existing methods from . Subsequently, by studying references [1-2] (mostly ) the student should get a good understanding of the described contour integral method.
At the end of the seminar the student should be able to give a basic introduction into NFT-aided optical communication systems and give an explanation of the method from [1-2] (mostly using ), identify benefits and drawbacks compared to other existing methods and also discussing the simulation results for the test cases presented in the paper.
Optical Communication Systems, Nonlinear Optics (both are not stricly necessary but highly beneficial for this topic)