Input-constrained Gaussian waveform channels are considered in [1]. The waveform channel consists of a linear filter and Gaussian noise with constant power spectral density is added on the receiver side.

The transmitter outputs a continuous-time waveform x(t). While no bandwidth limit is imposed on the transmit waveform, 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 the capacity for both constraints is equal. Input-constrained channels with a value constraint are of great importance for applications such as magnetic storage media.

[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

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].

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