Seminar Themen

Die drei Seminare "Seminar on Coding and Cryptography", "Seminar on Digital Communications" und "Seminar on Optical Communications" werden zusammen organisiert und abgehalten.

Es spielt keine Rolle zu welchem Sie sich auf TUM Online anmelden (bitten wählen sie *eines*), wir werden Sie dann entsprechend zuweisen falls Sie einen Platz nach der Bewerbugsphase erhalten. 

Sie müssen sich bis spätestens 24.04.2022 bewerben. Wählen Sie bitte mehr als ein Thema, aber nicht mehr als 4. Schreiben Sie die entsprechenden Betreuer direkt an und setzen den Seminarleiter (diego.lentner@tum.de) auf CC.

Es ist nicht erforderlich einen Lebenslauf und/oder Notenauszug mitzusenden.

Unten finden Sie die angebotenen Arbeiten.

Seminar on Coding and Cryptography

Seminare

String Reconstruction from Substring Compositions: Application to Polymer-Based Storage

Stichworte:
Polymer-based data storage, string reconstruction, composition errors, insertions, deletions

Beschreibung

Polymer-based storage involves storing information strings as a chain of molecules, the masses of which indicate whether the encoded bit is a 0 or 1. The readout mechanism requires tandem mass spectrometers which output compositions of all possible substrings, i.e. the number of 0s and 1s in a particular substring. The authors of [1] demonstrated that unique string reconstruction is only possible for specific string lengths, and also presented an algorithm for the same. In [2-5], code constructions were presented to facilitate this for all string lengths and also to correct substitution errors in the measured compositions.

 

[1] J. Acharya, H. Das, O. Milenkovic, A. Orlitsky, and S. Pan, “String
reconstruction from substring compositions,” SIAM Journal on Discrete
Mathematics, vol. 29, no. 3, pp. 1340--1371, 2015.

[2]  S. Pattabiraman, R. Gabrys and O. Milenkovic, "Coding for Polymer-Based Data Storage", arXiv:2003.02121, 2020

[3] R.Gabrys,   S.Pattabiraman,   and   O.Milenkovic, "Mass error-correction codes for polymer-based data storage,”  IEEE International Symposium on Information Theory, ISIT 2020, Los Angeles, CA, USA, June  21-26,  2020, pp. 25--30, IEEE, 2020.

[4] S.~Pattabiraman,  R.~Gabrys,  and  O.~Milenkovic,  “Reconstruction  and error-correction  codes  for  polymer-based  data  storage,”  in IEEE Information Theory Workshop, ITW 2019, Visby, Sweden, August 25-28,2019, pp. 1--5, IEEE, 2019.

[5] R. Gabrys, S. Pattabiraman and O. Milenkovic, "Reconstructing Mixtures of Coded Strings from Prefix and Suffix Compositions," 2020 IEEE Information Theory Workshop (ITW), 2021, pp. 1-5.

Betreuer:

Anisha Banerjee

Beyond Single-Deletion Correcting Codes: Substitutions and Transpositions

Stichworte:
Deletion Correction, Nonbinary Codes, Transpositions, List Decoding

Beschreibung

DNA is a promising data storing medium due to its longetivity and high storage density. However, due to its biological nature data errors can occur when storing or reading the DNA sequences. Moreover, not only substitution erros but also insertion and deletion errors occur frequently in the storage process. Therefore, it is important to tackle these kind of errors via coding. [1] presents methods how to correct combinations of prominent errors in DNA storage.

The student's task is to understand the coding theme and error models discussed in [1], including the proposed proof method.

For an introduction, the references [2] and [3] may help.

References:

  • [1] R. Gabrys, V. Guruswami, J. Ribeiro, K. Wu, "Beyond Single-Deletion Correcting Codes: Substitutions and Transpositions," arXiv preprint 2112.09971, URL: https://arxiv.org/abs/2112.09971, 2021.
  • [2] N. J. A. Sloane, “On Single-Deletion-Correcting Codes,” 2002.
  • [3] V. I. Levenshtein, “Binary Codes Capable of Correcting Deletions, Insertions, and Reversals.” Soviet Physics-Doklady, Moscow, 1966.

Betreuer:

Seminar on Digital Communications

Seminare

Hierarchical Posterior Matching: An Overall Study

Stichworte:
Posterior Matching, Feedback, RadCom

Beschreibung

The student has to read and understand the paper [1] and present a report in which he/she explains the main elements of the approach. The student has also to go into details about possible applications of the proposed approach.

If it is possible, try to find out alternative approaches with the respect of the proposed one and try to make a theoretical comparison.

 

[1] S. Chiu, N. Ronquillo and T. Javidi, "Active Learning and CSI Acquisition for mmWave Initial Alignment," in IEEE Journal on Selected Areas in Communications, vol. 37, no. 11, pp. 2474-2489, Nov. 2019, doi: 10.1109/JSAC.2019.2933967.

Betreuer:

Anticode (Intro.)

Kurzbeschreibung:
An introduction to anticode and its duality to the code would be given.

Beschreibung

The Anticode is understood in its own merit, then a code is understood as anti-anticode. Code-Anticode duality and known bounds on their size are investigated and presented.

Voraussetzungen

Basics of channel coding

Interested student are encouraged to contact me and send me a CV as well as all the academic transcripts and relevant courses that they have attended.

Betreuer:

Mohammad Salariseddigh

Coding for Caching

Stichworte:
Caching, Coding for computation

Beschreibung

 

The student is needed to understand the basics of coded caching and provide a summary of the topic [1]. Information-theoretic formulation of the problem needs to be studied, where the fundamental limits illustrate possible advantages.

[1] M. A. Maddah-Ali and U. Niesen, "Fundamental Limits of Caching," in IEEE Transactions on Information Theory, vol. 60, no. 5, pp. 2856-2867, May 2014, doi: 10.1109/TIT.2014.2306938.

 

Voraussetzungen

  • Information theory

Betreuer:

Mohammad Mahdi Mahvari Habibabadi

Quantum Identification (Intro.)

Stichworte:
Identification via (classical) channels, Identification via Quantum channels,
Kurzbeschreibung:
An introduction into the quantum identification will be presented. In particular, the quantum version of Ahlswede and Dueck theory of identification will be comprehended.

Beschreibung

Understanding of the following and present them

  1. Quantum and classical channel (similarities and differences)
  2. Classical message identification
  3. Quantum message identification

 

Student should study and touch the following paper:
 

  1. Winter, A., 2004. Quantum and Classical Message Identification via Quantum Channels. arXiv preprint quant-ph/0401060

  2. Winter, A., 2013. Identification via Quantum Channels. In Information Theory, Combinatorics, and Search Theory (pp. 217-233). Springer, Berlin, Heidelberg

In particular, non-classic features like superposition and entanglement are understood.

 

Voraussetzungen

Basics of

  1. Information Theory
  2. Identification Theory
  3. Quantum Theory

Betreuer:

Mohammad Salariseddigh

Generalized Shannon Capacity (Intro.)

Stichworte:
Sperner Theorem, Zero-Undetected-Error capacity, Zero-Error Capacity

Beschreibung

The student will study the fundamental result introduced for the Sperner capacity.

S/he start with understanding the Sperner Theorem.

The connection to Zero-Undetected-Error capacity will be investigated and it would be understood why and in which sense the Sperner capacity is called generalized zero error capaciy.

A conjecture of Ahlswede and its proof by other authors will be reviewed.

As well, the relation to r-cover families will be also considered.

Voraussetzungen

Interested students as first step should contact me directly and send me a CV as well as the academic transcripts and relevant courses that they have attended.

Also the Basics of below are required to be known:

  1. Graph Theory
  2. Zero Error Capacity
  3. r-Cover Familiy

 

Betreuer:

Mohammad Salariseddigh

Polarization-adjusted convolutional codes

Beschreibung

The student's task is to understand a recently introduced coding scheme, namely polarization-adjusted convolutional (PAC) codes [1]. 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 [4], which is closely related to the good performance of not only concatenated polar codes but also PAC codes.

Voraussetzungen

Information Theory

Channel Coding

Channel Codes for Iterative Decoding

Kontakt

mustafa.coskun@tum.de

Betreuer:

Mustafa Coskun

[quantum] Results from QIP or TQC conferences

Stichworte:
quantum

Beschreibung

The QIP (Quantum Information Processing) and TQC (Theory of Quantum Computation, Communication and Cryptography) conferences are two of the most important conference in quantum theory. The student will have the freedom of choosing one article from the latest conferences and will then have to understand and report on the article.

The schedule and the list of talks and abstracts can be found at:
https://www.mcqst.de/qip2021/program/conference-program/
https://tqc2021.lu.lv/program/schedule/

Betreuer:

Graph Capacity (Intro.)

Stichworte:
Shannon Capacity of A Graph, Confusability Graph, Graph Powers.
Kurzbeschreibung:
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.

Beschreibung

Specifically the following topics will be touched:

  1. Shannon Capacity of A Graph
  2. Zero-Error Capacity
  3. Zero-Error Applications (Perfect Hash Function, Superimposed Codes)
  4. Sperner Capacity
  5. Lovasz Number
  6. Haemers Bound
  7. Confusability Graph
  8. Hyper-graph Capacity
  9. Graph Alphabets:
  • Independenc Number
  • Chromatic Number
  • Graph Entropy
  • Graph Powers

Voraussetzungen

Interested students as first step should contact me directly and send me a CV as well as the academic transcripts and relevant courses that they have attended.

Also the Basics of below are required to be known:

  1. Information Theory
  2. Graph Theory
  3. Coding Theory
  4. Channel Coding

Kontakt

References:

  1. Alon, N. "The Shannon Capacity of a Union." Combinatorica 18, 301-310, 1998.
  2. Haemers, W. "An Upper Bound for the Shannon Capacity of a Graph." In Algebraic Methods in Graph Theory. Szeged, Hungary: pp. 267-272, 1978.
  3. Lovász, L. "On the Shannon Capacity of a Graph." IEEE Trans. Inform. Th. IT-25, 1-7, 1979.
  4. Shannon, C. E. "The Zero-Error Capacity of a Noisy Channel." IRE Trans. Inform. Th. 2, 8-19, 1956.
  5. Cohen, G., Körner, J. and Simonyi, G., 1990. "Zero-error capacities and very different sequences." In Sequences (pp. 144-155). Springer, New York, NY.
  6. Korner, Janos, and Alon Orlitsky. "Zero-error information theory." IEEE Trans. Inform. Th. IT-25, no. 6 (1998): 2207-2229.

 

Betreuer:

Mohammad Salariseddigh

Seminar on Optical Communications

Seminare

Modeling Bent Waveguide Characteristics

Beschreibung

For many optical integrated components, bent waveguides are the key building blocks. There are various schemes on how to model characteristics of a bent waveguide. 

The task of the student is to compare and describe the scheme of at least two approaches.

 

[1] Andrea Melloni et al., "Determination of Bend Mode Characteristics in Dielectric Waveguides" 

[2] Wayne W. Lui et al., "Full-Vectorial Wave Propagation in Semiconductor Optical Bending Waveguides and Euivalent Straight Waveguide Approximations"

[3] Jiangtao Huangfu et al., "Application of Coordinate Transformation in Bent Waveguides"

[4] Mordehai Heiblum et al., "Analysis of Curved Optical Waveguides by Conformal Transformation"

[5] Sangin Kim et al., "Vector Analysis of Optical Dielectric Waveguide Bends Using Finite-Difference Method"

Voraussetzungen

- good understanding of Maxwell's equations

- lecture: Optical Communication Systems 

Betreuer:

Computing Discrete Eigenvalues by Contour Integrals in the Nonlinear Fourier Domain

Beschreibung

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 [3] and an overview on existing methods from [4]. Subsequently, by studying references [1-2] (mostly [1]) 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 [1]), identify benefits and drawbacks compared to other existing methods and also discussing the simulation results for the test cases presented in the paper.

[1] Vasylchenkova, Anastasiia, Prilepsky, Jaroslaw . "Contour integrals for numerical computation of discrete eigenvalues in the Zakharov-Shabat problem"

[2] Delves, L. M., Lyness, J. N. "A numerical method for locating the zeros of an analytic function"

[3] Yousefi, Mansoor I., and Frank R. Kschischang. "Information transmission using the nonlinear Fourier transform, Part I: Mathematical tools."

[4] Yousefi, Mansoor I., and Frank R. Kschischang. "Information transmission using the nonlinear Fourier transform, Part II: Numerical methods."

Voraussetzungen

Optical Communication Systems, Nonlinear Optics (both are not stricly necessary but highly beneficial for this topic)

Betreuer: