Input-constrained Gaussian waveform channels are considered in [1]. The channel consists of a linear filter and Gaussian noise is added at the receiver.

The transmitter generates a waveform x(t). While x(t) has no bandwidth limit, the authors compare the channel capacity under

1. a value constraint on x(t) such that x(t) can take only two values,
2. and a peak-power constraint.

The paper shows that capacity under both constraints is equal.

Input-constrained channels with a value constraint are of great importance for applications such as magnetic storage media.

The student should understand and be able to interpret why capacity is equal under constraints 1. and 2., and how according lower bounds are obtained.

[1] L. H. Ozarow, A. D. Wyner and J. Ziv, "Achievable rates for a constrained Gaussian channel," in IEEE Transactions on Information Theory, vol. 34, no. 3, pp. 365-370, May 1988, doi: 10.1109/18.6018.

• Information theory.
• Linear Systems Theory.

During the internship, the student will be researching the application of Neural Network-based signal predistortion to mitigate the effects of fiber chromatic dispersion in direct detection systems.

• basic Python skills beneficial

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We are interested in computing upper bounds (on capacity) for bandlimited 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].

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.

Information Theory

Linear System Theory