We investigate an extension of [1] to complex-valued constellations, as well as a general optimization of constellations, which work with [1].

[1] M. Secondini and E. Forestieri, “Direct detection of bipolar pulse amplitude modulation,” J. Lightw. Technol., vol. 38, no. 21, pp. 5981– 5990, 2020.

Two work is two-fold:

• Physically consistent modelling of space division multiplexing (SDM) over a short-reach multimode fiber, including direct detection (DD) per mode.
• a) Analysis of achievable rates, simple upper and lower bounds on capacity for SDM with DD.
• b) (MIMO) Equalization for SDM with DD.

The topic deals with maximizing the generalized mutual information (GMI) for short-reach fiber-optic links. In particular, we are interested in jointly optimizing transmit and receive filters.

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)

The students task is to understand and summarize [1], which is about a new method of calculating matrix-vector products in a fast way using coding theory.

[1] https://arxiv.org/pdf/2102.00398.pdf

Channel Coding, Information Theory