Foto von Constantin Runge

M.Sc. Constantin Runge

Technische Universität München

Lehrstuhl für Nachrichtentechnik (Prof. Kramer)


Theresienstr. 90
80333 München


  • Wissenschaftlicher Mitarbeiter am Lehrstuhl für Nachrichtentechnik der TUM seit Oktober 2021
  • M.Sc. in Elektro- und Informationstechnik an der TUM, 2019 - 2021
  • B.Sc. in Elektro- und Informationstechnik an der TUM, 2015 - 2019


  • Distribution Matching and Probabilistic Shaping
  • Coding for Multi-user Scenarios
  • Coded Modulation
  • Theory of Modern Channel Coding


  • Advanced Topics in Communications Engineering: Lossless Source Coding (SS22)
  • Multi-user Information Theory (SS23)


Angebotene Abschlussarbeiten

Lattice coding for AWGN channels


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


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


Laufende Abschlussarbeiten

Enumerative Sphere Shaping for General Target Distributions

probabilistic shaping, trellis, sphere shaping


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.



Constantin Runge - Prof. Frans Willems (TU/e)



  • Runge, C.: Channel Polarization, Probabilistic Shaping, and Binning. Munich Doctoral Seminar on Communications, 2022 mehr…
  • Runge, C.; Wiegart, T.; Lentner, D.; Prinz, T.: Multilevel Binary Polar-Coded Modulation Achieving the Capacity of Asymmetric Channels. IEEE International Symposium on Information Theory (ISIT), 2022Espoo, Finland mehr… Volltext ( DOI )


  • Runge, C.: Higher-Order Polar-Coded Modulation for Asymmetric Channels. 2021 mehr… Volltext (mediaTUM)
  • Runge, C.: Higher-Order Polar Coded Modulation with Arbitrary Probabilistic Shaping. Ferienakademie 2021: Advanced Topics in Information Theory and Communications, 2021Sarentino, Italy mehr…