The duality principle is a powerful concept extensively used in various scientific disciplines, such as Lagrangian duality in optimization theory. In information theory, however, there are many different types of 'duality', which vary in formality. Starting with Shannon's observations on a source-channel duality [1], other notions of duality were later introduced, including functional duality [2] and operational duality [3]. The duality of Gaussian broadcast channels and Gaussian multiple-access channels [4] helped to compute the dirty-paper achievable rate region efficiently for the Gaussian multiple-input multiple-output broadchast channel [5]. The student will review and compare different fomulations of duality in the literature on information theory. Two case studies shall demonstrate how duality was applied to solve a new problem. Students interested in this topic should have a strong background in information theory and multi-user information theory.

[1] C. E. Shannon, “Coding theorems for a discrete source with a fidelity criterion,” IRE Int. Conv. Rec, pp. 142–163, Mar. 1959.
[2] S. Pradhan, J. Chou, and K. Ramchandran, “Duality between source coding and channel coding and its extension to the
side information case,” IEEE Trans. Inf. Theory, vol. 49, no. 5, pp. 1181–1203, May 2003. DOI: 10.1109/TIT.2003.810622.
[3] A. Gupta and S. Verdu, “Operational duality between lossy compression and channel coding,” IEEE Trans. Inf. Theory, vol. 57, no. 6, pp. 3171–3179, Jun. 2011. DOI: 10.1109/TIT.2011.2136910.
[4] N. Jindal, S. Vishwanath, and A. Goldsmith, “On the duality of gaussian multiple-access and broadcast channels,” IEEE Trans. Inf. Theory, vol. 50, no. 5, pp. 768–783, May 2004. DOI: 10.1109/TIT.2004.826646.
[5] S. Vishwanath, N. Jindal, and A. Goldsmith, “Duality, achievable rates, and sum-rate capacity of Gaussian MIMO broadcast channels,” IEEE Transactions on Information Theory, vol. 49, no. 10, pp. 2658–2668, Oct. 2003, doi: 10.1109/TIT.2003.817421.

Prerequisites

I regularly offer theses in the fields of probabilistic shaping, coding for high-throuput applications, and algorithms for communication. Please reach out if you are interested in a thesis in any of my research fields. A good background in information theory and channel coding are preferable, but the requirements generally depend on your interests.

Please include a description of your interests and corresponding academic background in your application. If you have a thesis idea, I am happy to discuss your suggestions. Also, I am available to supervise external theses as long as they are in my field of expertise.

We analyze the edge cases of polar codes for coding with side-information and construct tailored codes for these.

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In this internship, we investigate rate matching techniques for future 6G radio access networks.