## Neural Networks (NNs) for Direct Detection

#### Description

In [1] we consider a short-reach fiber-optic link with a single photodiode at the receiver, which is a so-called direct detector (DD). The DD outputs a signal, propotional to the squared **magnitude** of its input. At first glance, this makes phase modulation challgenging. In [1] we showed that inter-symbol intereference (ISI) can be used to retrieve the phase. A suboptimal symbol-wise MAP detector was then proposed for phase retrieval. However, the detector exhibits a large complexity, which grows exponentially in the amount of ISI.

The task of the student is to efficiently approximate the MAP detector using a NN. An appropriate NN type/structure needs to be selected. Finally, lower bounds on the achievable rates are computed to evaluate the performance of the NN and compare it to the MAP detector [1].

[1] D. Plabst *et al*., "Achievable Rates for Short-Reach Fiber-Optic Channels With Direct Detection," in *Journal of Lightwave Technology*, vol. 40, no. 12, pp. 3602-3613, 15 June15, 2022, doi: 10.1109/JLT.2022.3149574.

#### Prerequisites

Machine Learning

Statistical Signal Processing

#### Supervisor:

## 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 in 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