Field of Research

The nonlinear Schrödinger equation (NLSE) describes the propagation of the optical field complex envelope in a single-mode optical fiber. As it is not solvable in closed-form, iterative approaches, e.g., the split-step Fourier method, must be used to calculate the channel output from the channel input.

Vannucci et al. introduced a new method based on regular perturbation and improved the accuracy with the so-called enhanced regular perturbation [1]. The logarithmic perturbation model [2] concludes the class of perturbation-based solutions of the NLSE widely used today. See [3] for a comparison of the methods.

Content of the Seminar Paper

There are two options regarding the content of the seminar paper:

1. Understand regular perturbation and be able to explain it and how to use it to model optical communication systems. See [4, Sec. 2] for an easy introduction on how to use it and [5] for a discussion on drawbacks, particularly in terms of accuracy, and how to overcome them.
2. Understand regular perturbation, enhanced regular perturbation, and logarithmic perturbation. Explain all three and point out similarities and differences.

Organization of the Supervision

• After you successfully apply for the topic, we will have a kick-off meeting to discuss everything necessary for the upcoming work. After that, the responsibility for the seminar paper is all on you. You can always contact me, ask questions, and ask for meetings, and I am happy to assist you along the way, but I need you to be proactive.
• I can comment on your work (e.g., the paper's outline and some paragraphs you have already written) anytime you need it and guide you as you prepare your paper and presentation. Regarding final drafts, I comment on one complete version of your paper. Ideally, this would mean that you do some work (literature research, the paper's outline, the body, the introduction, and the conclusion), and we discuss your results after every step. Ultimately, you give me one draft, and I comment on it. This method is more successful and instructive than writing a paper a few days before the deadline.
• Beware that when I comment on your work, this is not the same as a correction. My comments are suggestions on improving the quality of the work, but I cannot spend the time searching for and fixing every mistake there is or could be (this would also not fit the seminar's purpose).
• I expect solid research. There should be two significant references. Those are papers you know in detail and which majorly impact your work. Of course, they are always accompanied by supporting references.

[1] A. Vannucci, P. Serena and A. Bononi, "The RP method: a new tool for the iterative solution of the nonlinear Schrödinger equation," 2002, doi: 10.1109/JLT.2002.800376.

[2] E. Forestieri and M. Secondini, "Solving the nonlinear Schrödinger equation," in "Optical Communication Theory and Techniques," E. Forestieri, ed. 2005, doi:10.1007/0-387-23136-6_1.

[3] M. Secondini and E. Forestieri, "A Comparative Analysis of Different Perturbation Models for the Nonlinear Fiber Channel," 2015, doi: 10.1364/ACPC.2015.AM3D.1.

[4] R. Dar, M. Feder, A. Mecozzi, and M. Shtaif, "Properties of nonlinear noise in long, dispersion-uncompensated fiber links," 2013, doi: 10.1364/OE.21.025685.

[5] A. Barreiro, G. Liga and A. Alvarado, "Data-Driven Enhancement of the Time-Domain First-Order Regular Perturbation Model," 2023, doi: 10.1109/JLT.2023.3237041.

Voraussetzungen

Turbo equalization is an iterative approach to achieve a gain in terms of AIR compared to memoryless receivers for channels with memory. The student should read into the topic of Turbo equalization using, e.g., [1-2] or similar references and then search for applications for either optical channels, e.g., [3] or phase noise channels with memory, e.g. [4]

[1] https://ieeexplore.ieee.org/document/1267050

[2] https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1006557

[3] https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6595045

[4] https://ieeexplore.ieee.org/document/1504908

The capacity-achieving input distribution of many channels, e.g., memoryless AWGN channels, is non-uniform. This motivates investigating constellations with arbitrary probability mass functions for data transmission. To map sequences of uniformly distributed bits to sequences of non-uniformly distributed symbols, distribution matchers (DM) are used. In particular, constant composition distribution matchers (CCDM) [1] enable fixed blocklength to fixed blocklength (f2f) mapping.

The seminar paper should provide a good overview of CCDM. This includes but is not limited to a comprehensible motivation for DM, a description of how DM embed into communication systems, a high-level overview of how CCDM works, and considerations regarding practical implementations, e.g., [1, Sec. IV].  

The successful student will develop a profound understanding of DM and CCDM; see [2, Sec. 9.2], [3, Sec. 4.3], and references therein. Good literature research is an essential part of the task. The student is rewarded with a good understanding of an emerging research field in communications and a review of the foundations of modern communication systems.

The seminar paper may be extended to a research internship or master thesis afterward.



[1] P. Schulte and G. Böcherer, "Constant Composition Distribution Matching," in IEEE Transactions on Information Theory, vol. 62, no. 1, pp. 430-434, Jan. 2016.
[2] G. Böcherer, “Principles of Coded Modulation,” Habilitation thesis, Tech. Univ. Munich, Munich, Germany, 2018.
[3] P. Schulte, “Algorithms for distribution matching,” Ph.D. dissertation, Technische Universität München, May 2020.

Voraussetzungen