Seminar Topics

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

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

You need to apply for available topics of your interest by 14.04.2023. Please apply for more than one, but not more than 4. Directly write an E-Mail with subject "[Seminar Topic Application]" to the supervisors of your selected topics and put the main organizer (bensu.baran@tum.de) on CC.

It is not mandatory to attach a CV and/or transcript of records.

A brief schedule of this course:

  • Kick-off Meeting
  • Lecture 1: Technical Presentations
  • Lecture 2: Reading Technical Papers 
  • Lecture 3: Writing Technical Papers

*Parcipation of exercises is voluntary, but highly recommended.

You can find the open topics below.

--- Open Topics will be published on 03.04.2023 ---

 

Seminar on Coding and Cryptography

Seminars

Random Walks for Decentralized Learning

Description

Fully decentralized schemes do not require a central entity and have been studied in [1, 2]. These works aim to reach consensus on a desirable machine learning model among all clients. We can mainly distinguish between i) gossip algorithms [3] where clients share their result with all neighbors, naturally leading to high communication complexities, and ii) random walk approaches like [4, 5] where the model is communicated only to a specific neighbor until matching certain convergence criteria. Such random walk approaches are used in federated learning to reduce the communication load in the network and at the clients’ side.

The main task of the student is to study the work in [5], which additionally accounts for the heterogeneity of the clients’ data. Further, drawbacks and limitations of the proposed approach should be determined.

[1] J. B. Predd, S. B. Kulkarni, and H. V. Poor, “Distributed learning in wireless sensor networks,” IEEE Signal Process. Mag., vol. 23, no. 4, pp. 56–69, 2006.

[2] S. Boyd, N. Parikh, E. Chu, B. Peleato, J. Eckstein et al., “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Found. Trends Mach. Learn., vol. 3, no. 1, pp. 1–122, 2011.

[3] S. S. Ram, A. Nedi ?c, and V. V. Veeravalli, “Asynchronous gossip algorithms for stochastic optimization,” in IEEE Conf. Decis. Control. IEEE, 2009, pp. 3581–3586.

[4] D. Needell, R. Ward, and N. Srebro, “Stochastic gradient descent, weighted sampling, and the randomized kaczmarz algorithm,” Adv. Neural Inf. Process. Syst., vol. 27, 2014.

[5] G. Ayache, V. Dassari, and S. E. Rouayheb, “Walk for learning: A random walk approach for federated learning from heterogeneous data,” arXiv preprint arXiv:2206.00737, 2022.

Prerequisites

- Machine Learning and Statistics
- Information Theory

Supervisor:

Hard Problems in Coding Theory

Description

For many applications, including post-quantum cryptography, it is of interest to know which problems are difficult to solve.

The task of the student would be to familiarize themselves with the various difficult problems that appear in coding theory such as the syndrome decoding problem, code equivalence problem, etc. and their variations. They would then summarise what is known about them in terms of the difficulty of solving them e.g. best known complexity, whether they are known to be NP-hard, etc.

References:
- Barg, Alexander. "Complexity issues in coding theory." Algebraic Coding (1998).
- Berlekamp, Elwyn, Robert McEliece, and Henk Van Tilborg. "On the inherent intractability of certain coding problems (corresp.)." IEEE Transactions on Information Theory 24.3 (1978): 384-386.

Prerequisites

  • Channel Coding
  • Complexity Theory

Supervisor:

Anmoal Porwal

Post-Quantum Cyptography based on Codes: Ternary Syndrome Decoding

Keywords:
code-based cryptography, ternary syndrome decoding with large weight, decoding attack

Description

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 [2].

Recently, different variants of the classical syndrome decoding problem (SDP) in the Hamming metric have been proposed [1,3].
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 ternary syndrome decoding with large weight, in which the error has few or no zero-entries [1].

The goal of this topic is understanding the properties of the decoding problem and analyzing the cost of existing solvers such as Sterns algorithm [2].

 

Main Paper:

[1] Bricout, R., Chailloux, A., Debris-Alazard, T., & Lequesne, M. (2020). Ternary syndrome decoding with large weight. In Selected Areas in Cryptography–SAC 2019: 26th International Conference, Waterloo, ON, Canada, August 12–16, 2019, Revised Selected Papers 26 (pp. 437-466). Springer International Publishing.

can be found here: https://arxiv.org/pdf/1903.07464.pdf

 

References:

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

[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.

Prerequisites

Security in Communications and Storage

 

 

 

Supervisor:

Rank-Metric Codes and Their Applications

Description

Rank-matric codes are codes that live in a vector space that is endowed with a different metric than the Hamming metric: in the rank-metric the distance between two codewords, represented as matrices over a smaller field, is defined as the rank of their difference.

The theory of rank-metric codes has interesting connections to many topics in discrete mathematics and promissing applications to code-based cryptography and network coding.

In this seminar work, the student will study properties and constructions of rank-metric codes and one or more applications. The goal is to understand and summarize parts of the following papers:

[1] H. Bartz, L. Holzbaur, H. Liu, S. Puchinger, J. Renner, A. Wachter-Zeh (2022). “Rank-Metric Codes and Their Applications”. arXiv: 2203.12384  https://arxiv.org/pdf/2203.12384.pdf 

[2] K. Marshall, (2016). “A study of cryptographic systems based on Rank metric codes”, Dissertation, University of Zurich  https://www.zora.uzh.ch/id/eprint/127105/1/Diss%20Kyle.pdf

[3] T. Randrianarisoa, (2018). “Rank metric codes, codes using linear complexity and applications to public key cryptosystems”, Dissertation, University of Zurich  https://www.zora.uzh.ch/id/eprint/153545/1/153545.pdf

[4] E. Gorla (2019). “Rank-metric codes”. arXiv: 1902.02650  https://arxiv.org/pdf/1902.02650.pdf

[5] E. Gorla and A. Ravagnani. (2018). “Codes endowed with the rank metric”. In: Network Coding and Subspace Designs. Springer. 3–23.  https://link.springer.com/content/pdf/10.1007/978-3-319-70293-3.pdf 

Supervisor:

Decoding Schemes beyond Unique Decoding Radius

Keywords:
unique decoding radius, Reed-Solomon codes, Homogeneous interleaved codes, array codes
Short Description:
Error-correcting codes beyond the designed decoding radius with high probability are interesting in storage applications.

Description

In the literature on coding theory, there are two classes of codes: scaler codes and array codes. In the array codes, a codeword of a linear code over a finite field $\mathbb{F}_p$, for some prime number $p$ represents a row of the array codeword over $\mathbb{F}_{p^m}$, where $m > 1$ is referred to as the subpacketization. This class of codes is promising in storage applications. For example, a flash memory unit commonly stores any of the $2^m$ values as a binary column representation such that each bit located on a different page belongs to a particular $2^m$-ary memory cell and holds either $0$ or $1$. The remarkable property of array codes is that they are seen as codes over an extension field with the same parameters, then $m > 1$ is referred to as the extension degree. Homogeneous interleaved codes [1] [2], types of array codes, have a significant feature which is increasing the decoding radius beyond $\lfloor\frac{d-1}{2}\rfloor$, i.e., they decode up to $d-2$ errors with high probability.

The student's tasks are differentiating these classes of codes, understanding their applications, and focusing on array codes. Then the student summarizes the algorithms/schemes that correct errors beyond the unique decoding radius, i.e., beyond $\lfloor\frac{d-1}{2}\rfloor$ suggested by [1] and [2].

 

[1] V. Y. Krachkovsky and Yuan Xing Lee, "Decoding for iterative Reed-Solomon coding schemes," in IEEE Transactions on Magnetics, vol. 33, no. 5, pp. 2740-2742, Sept. 1997, doi: 10.1109/20.617715.

[2] J. J. Metzner and E. J. Kapturowski, "A general decoding technique applicable to replicated file disagreement location and concatenated code decoding," in IEEE Transactions on Information Theory, vol. 36, no. 4, pp. 911-917, July 1990, doi: 10.1109/18.53757.

Prerequisites

  • Basics of Channel Coding 
  • Finite field theory
  • Linear Algebra

Supervisor:

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

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

Description

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.

Supervisor:

Anisha Banerjee

Seminar on Digital Communications

Seminars

Neural Network-Based Compensation Techniques for Nonlinear Distortions in Fibre-Optic Links

Description

Optical signals experience nonlinear distortions - so called Kerr nonlinearities - when propagating through a fiber. This makes signal processing more complicated than in linear systems. Multiple ways to cope with this have been proposed in the past, including, e.g., digital backpropagation (DBP), Volterra equalizers or phase conjugation (see [1] for a good overview of conventional methods). Unfortunately, these methods are often unfeasible.

Due to their inherent nonlinear characteristics, neural networks might be a suitable solution for compensating Kerr nonlinearities. They might be used, e.g, as a demapper [2] or as a more efficient alternative to DBP [3]. A good overview of usage of neural networks for nonlinearity compensation is given in [4, Sec. Vb] . This paper also provides a good introduction to machine learning techniques relevant for optical communications.

In this seminar, the student is expected to research neural network based compensation techniques for fibre nonlinearities (e.g., one of the ones briefly described in [4, Sec. Vb]) and present either one in detail or multiple ones as an overview.

Prerequisites

Basic knowledge of optical communications (Optical Communication Systems EI5075, Digital Signal Processing for Optical Communication Systems EI71067 or comparable) is required. Some experience with machine learning is helpful, but papers like [4] can alternatively provide a good introduction to machine learning, as well.

If you are interested, feel free to just contact me via email. We can then discuss the details and fit the topic to your interests.


-----------------------------------------------------------------------------------------------------------------------------------------------


[1] A. Amari, O. A. Dobre, R. Venkatesan, O. S. S. Kumar, P. Ciblat and Y. Jaouën, "A Survey on Fiber Nonlinearity Compensation for 400 Gb/s and Beyond Optical Communication Systems," in IEEE Communications Surveys & Tutorials, vol. 19, no. 4, pp. 3097-3113, Fourthquarter 2017, doi: 10.1109/COMST.2017.2719958.

[2] M. Schaedler, S. Calabrò, F. Pittalà, C. Bluemm, M. Kuschnerov and S. Pachnicke, "Neural Network-Based Soft-Demapping for Nonlinear Channels," 2020 Optical Fiber Communications Conference and Exhibition (OFC), San Diego, CA, USA, 2020, pp. 1-3.

[3] C. Häger and H. D. Pfister, "Nonlinear Interference Mitigation via Deep Neural Networks," 2018 Optical Fiber Communications Conference and Exposition (OFC), San Diego, CA, USA, 2018, pp. 1-3.

[4] F. N. Khan, Q. Fan, C. Lu and A. P. T. Lau, "An Optical Communication's Perspective on Machine Learning and Its Applications," in Journal of Lightwave Technology, vol. 37, no. 2, pp. 493-516, 15 Jan.15, 2019, doi: 10.1109/JLT.2019.2897313.

Supervisor:

Alex Jäger

Factor Graphs and the Sum-Product Algorithm

Description

 

This paper [1] introduces factor graphs and describes the sum-product algorithm, which is a generic message-passing algorithm operating on factor graphs. The algorithm computes various marginal functions associated with the global function.  

This algorithm is very powerful, in fact, a surprisingly wide variety of algorithms developed in the artificial intelligence, signal processing, and digital communications communities can be seen as specific instances of the sum-product algorithm, operating in an appropriately chosen factor graph. Some examples are the forward/backward algorithm, the Viterbi algorithm, Pearl’s belief propagation algorithm, the iterative turbo decoding algorithm, the Kalman filter, and even certain FFT algorithms.

The task of the student is to learn and understand factor graphs and the sum-product algorithm. The student can then relate and analyze other known algorithm under the framework of the sum-product algorithm.

[1] https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=910572

Prerequisites

Information Theory

Supervisor:

Lattice coding for AWGN channels

Description

For rate-optimal transmission over the AWGN channel Shannon showed that a Gaussian distributed channel input is required. This poses problems for digital implementations, where symbols are necessarily quantized. One solution to this is coded modulation via lattice coding. Lattice coding creates code code books by quantizing continuous space into periodic regions.

The student's task is to understand lattice transmission schemes (see e.g. [1], [2], [3]) and in particular the schemes from [4], summarize the important concepts of lattice coding, and give an explanation of coding schemes achieving capacity over the AWGN channel.

[1] Conway, Sloane 1982 - Voronoi regions of lattices, second moments of polytopes, and quantization. DOI: 10.1109/TIT.1982.1056483
[2] Conway, Sloane 1983 - A fast encoding method for lattice codes and quantizers. DOI: 10.1109/TIT.1983.1056761
[3] Forney 1989 - Multidimensional constellations. 2. Voronoi constellations. DOI: 10.1109/49.29616
[4] Erez, Zamir 2004 - Achieving 0.5log(1+SNR) on the AWGN Channel With Lattice Encoding and Decoding. DOI: 10.1109/TIT.2004.834787

Prerequisites

  • Information Theory
  • Introduction to Channel Coding
  • Introduction to Coded Modulation helpful but not required

Supervisor:

Anticode (Intro.)

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

Description

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.

Prerequisites

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.

Contact

Interested students please contact me directly and send me a cv and transcripts of Bsc and Msc both.

Supervisor:

Mohammad Salariseddigh

Quantum Identification (Intro.)

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

Description

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.

 

Prerequisites

Basics of

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

Contact

Interested students please contact me directly and send me a cv and transcripts of Bsc and Msc both.

Supervisor:

Mohammad Salariseddigh

Generalized Shannon Capacity (Intro.)

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

Description

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.

Prerequisites

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

 

Contact

Interested students please contact me directly and send me a cv and transcripts of Bsc and Msc both.

Supervisor:

Mohammad Salariseddigh

Capacity per Unit Cost

Description

Gallager [1] studied the capacity regions of energy limited channels as in wideband and multi-access communication. He showed that reliable communication over such channels is fundamentally limited by a normalized rate, the capacity per unit energy. Verdu's capacity per unit cost [2] generalizes this concept to channels with arbitrary per-symbol cost functions. Since then, capacity per unit cost has been used to analyze a variety of communication scenarios in research literature.

The student will understand the concept and motivation of capacity per unit cost, and will be able to discuss the differences to Shannon's capacity result. The student will identify and review scenarios in literature where capacity per unit cost has been applied. Finally, the student will choose one of these applications and discuss in more detail how capacity per unit cost relates to this problem and how it helped in solving it.

References:

[1] R. G. Gallager, “Energy limited channels: Coding, multiaccess, and spread spectrum,” Tech. Rep. LIDS-P-1714, Nov. 1987.

[2] S. Verdú, “On channel capacity per unit cost,” IEEE Trans. Inf. Theory, vol. 36, no. 5, pp. 1019–1030, Sep. 1990.

Prerequisites

  1. Strong background in Information Theory.
  2. At least one of the following courses:
  • Mobile communications.
  • Multi-User Information Theory.
  • MIMO Systems.

Supervisor:

[quantum] Results from QIP or TQC conferences

Keywords:
quantum

Description

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.

Supervisor:

Graph Capacity (Intro.)

Keywords:
Shannon Capacity of A Graph, Confusability Graph, Graph Powers.
Short Description:
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.

Description

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

Prerequisites

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

Contact

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.

 

Interested students please contact me directly and send me a cv and transcripts of Bsc and Msc both.

Supervisor:

Mohammad Salariseddigh

Seminar on Optical Communications

Seminars

Hollow Core Fibers for Optical Communication Systems

Keywords:
Optical Communications, Fibers

Description

In order to increase the capacity of the current optical networks, new transmission architectures are under investigation. Hollow-core fibers are a new technology, which promise, among the others, to have reduced losses and extremely low nonlinear effects. New propagation impairments, which are still under study, would arise compared to the well-known single-mode fibers (SMFs). Yet, their employment in the field of optical communications seems likely to bring about a breakthrough over the current SMF-based solutions.

The student is required to provide an overview on the design and modeling of hollow-core fibers, emphasizing their advantages and disadvantages against wideband frequency-division multiplexing (FDM) systems based on SMFs, starting from the provided references. 

 

REFERENCES:

[1] E. N. Fokua et al., ``Loss in hollow-core optical fibers: mechanisms, scaling rules, and limits'', 2023

[2] P. Poggiolini, F. Poletti, ``Opportunities and Challenges for Long-Distance Transmission in Hollow-Core Fibres'', 2022

Prerequisites

Bases in optical communication systems and, possibly, in guided mode propagation.

Supervisor:

Introduction to Photonic Crystal Fibers

Description

Photonic crystal fibers (PCFs) have emerged as a promising platform for a wide range of applications due to their unique properties and design flexibility. These fibers consist of a periodic array of microstructured air holes that run along the length of the fiber, which enables precise control over the propagation of light. Of particular interest are hollow core fibers, which are characterized by a central void that enables light to be confined within the hollow core. As research and development in this field continue to advance, photonic crystal fibers are poised to play a pivotal role in the next generation of optical communication and sensing systems.

The students task is to provide a comprehensive overview of PCFs with a focus on characterizing their distinctive linear and nonlinear properties. 

 

Possible literature:

  • Philip St.J. Russell, "Photonic-Crystal Fibers," J. Lightwave Technol. 24, 4729-4749 (2006)
  • Benabid, F., and P. J. Roberts. "Linear and nonlinear optical properties of hollow core photonic crystal fiber." Journal of Modern Optics 58.2 (2011): 87-124.

Prerequisites

  • lecture: Optical Communication Systems

Supervisor:

Digital Coherent Optical Receivers: Algorithms and Subsystems

Description

Digital coherent optical receivers have revolutionized optical transmission system design through the integration of advanced subsystems and algorithms. This paper presents a comprehensive analysis of these components, including the optical front end, analog-to-digital converter (ADC), and digital signal processing (DSP) algorithms that contribute to the performance of the system. The paper delves into the methods used to compensate for transmission impairments, both static and dynamic, with a particular focus on dynamic-channel equalization.

 

 

[1] S. J. Savory, "Digital Coherent Optical Receivers: Algorithms and Subsystems," in IEEE Journal of Selected Topics in Quantum Electronics, vol. 16, no. 5, pp. 1164-1179, Sept.-Oct. 2010.

Prerequisites

Recommended Courses:

   - Digital Signal Processing for Optical Communication Systems

   - Optical Communication Systems

Contact

utku.akin@tum.de

Supervisor:

Computing Discrete Eigenvalues by Contour Integrals in the Nonlinear Fourier Domain

Description

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."

Prerequisites

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

Supervisor: