Energy efficient information transmission generally requires the transmit symbols to be non-uniformly distributed. This is achieved by probabilistic shaping. Sphere Shaping by Shell Mapping [1][2] is one technique of finding energy-optimal transmission sequences. Recently, an efficient, trellis based coding technique called Enumerative Sphere Shaping [3][4] has been getting more attention.

The student's task is to understand and summarize the Enumerative Sphere Shaping approach and discuss its differences to Shell Mapping and other shaping approaches from the viewpoints of energy efficiency and coding complexity.

[1] Khandani, Kabal 1993 - Shaping multidimensional signal spaces. I. DOI: 10.1109/18.265491
[2] Kschischang, Pasupathy 1994 - Optimal shaping properties of the truncated polydisc. DOI: 10.1109/18.335900
[3] Willems, Wuijts 1993 - A Pragmatic Approach to Shaped Coded Modulation
[4] Gültekin, van Houtum, Keppelaar, Willems 2020 - Enumerative Sphere Shaping for Wireless Communications With Short Packets. DOI: 10.1109/TWC.2019.2951139

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

Probabilistic shaping combines forward error correction and distribution matching. It allows to send encoded information with non-uniform symbol distributions. These non-uniform symbol distributions are required to achieve optimal transmission rates. One way to implement probabilistic shaping is polar coding [1], in particular Honda-Yamamoto coding [2]. For a more practical introduction to polar coding see [3].

The goal is to compare the performances of different encoding and decoding schemes for Honda-Yamamoto codes.

In this Forschungspraxis, the task is to investigate decoder performances for Honda-Yamamoto codes with different, structurally similar, decoders. The student will understand and implement successive-cancellation decoding [1] and successive-cancellation list decoding [4] for polar codes. Using these two decoders, one can directly construct encoders and decoders for Honda-Yamamoto codes for which we compare error correction capability and en-/decoding complexity under probabilistic shaping scenarios.

  [1] https://doi.org/10.1109/TIT.2009.2021379 or https://arxiv.org/abs/0807.3917

  [2] https://doi.org/10.1109/TIT.2013.2282305

  [3] https://tselab.stanford.edu/mirror/ee376a_winter1617/lectures.html

  [4] https://arxiv.org/abs/1206.0050

• Basics in Information Theory (entropy, mutual information, channel capacity)
• Basics in Channel Coding (goal of forward error correction, linear block codes, knowledge about soft decoding algorithms is helpful)