We are interested in computing upper bounds (on capacity) for frequency-selective channels with a memoryless nonlineary at the transmitter/receiver.

One application for these bounds are short-reach fiber-optic communication systems with a single photodiode at the receiver. The photodiode is a memoryless nonlinearity, as it produces an output that is proportional to the squared magnitude of the input signal.

A simple upper bound for the above model is given in [Sec. III D, 2].

Information Theory

Linear System Theory

Capacity and capacity-achieving distributions are available for some memoryless channels. For the average-power constrained memoryless channel with additive white Gaussian noise, Shannon provided a closed form description of capacity. Closed form solutions for capacity also exist for some simple discrete memoryless channels (DMCs). In addition, numerical algorithms for calculating the capacity (and capacity-achieving discrete distributions) of general DMCs are available through the works of Arimoto and Blahut.

However, often wireless or fiber-optic channels of practical interest contain intersymbol interference (ISI), and the memory due to ISI can no longer be neglected. When considering discrete channel inputs, one may be interested in determining the capacity and capacity-achieving distribution for these ISI channels. In fact, discrete stationary Markov processes asymptotically achieve the capacity of finite-state ISI channels as the order of the Markov process goes to infinity.

An algorithm [1] for optimizing discrete Markov processes of a certain order M is presented to maximize the information rate between channel input and output. As the order of the Markov process increases, tighter lower bounds on capacity are obtained.

[1] A. Kavcic, "On the capacity of Markov sources over noisy channels," GLOBECOM'01. IEEE Global Telecommunications Conference (Cat. No.01CH37270), 2001, pp. 2997-3001 vol.5, doi: 10.1109/GLOCOM.2001.965977.

Further reading (if required):

[2] P. O. Vontobel, A. Kavcic, D. M. Arnold and H. -A. Loeliger, "A Generalization of the Blahut–Arimoto Algorithm to Finite-State Channels," in IEEE Transactions on Information Theory, vol. 54, no. 5, pp. 1887-1918, May 2008, doi: 10.1109/TIT.2008.920243.

[3] T. Lang, A. Mezghani and J. A. Nossek, "Channel-matched trellis codes for finite-state intersymbol-interference channels," 2010 IEEE 11th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC), 2010, pp. 1-5, doi: 10.1109/SPAWC.2010.5670890.

Information Theory

Distributed Acoustic Sensing (DAS) employs advanced signal processing to enhance the performance for strain and vibrations sensing. However, the algorithms exhibit high complexity as well as inaccuracy due to nonlinear effects.

The task of the student is to replace this conventional signal processing blocks by a neural network (NN). An appropriate NN type/architecture needs to be selected. Finally, the performance of the NN has to be evaluated and compared to conventional algorithms.

[1] Karapanagiotis, Christos, Konstantin Hicke, and Katerina Krebber. "A collection of machine learning assisted distributed fiber optic sensors for infrastructure monitoring.", 2023.