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We investigate code construction algorithms for SC list decoding of polar codes [1] based on methods like [2].

• [1] https://doi.org/10.1109/TIT.2015.2410251
• [2] https://doi.org/10.1109/TCOMM.2021.3120274

We apply information-theoretic perspectives from rate-distortion theory to optimize wildfire notifications from earth observation satellites.

For rate-optimal transmission over the AWGN channel Shannon showed that a Gaussian distributed channel input is required. This poses problems for digital implementations, where symbols are necessarily quantized. One solution to this is coded modulation via lattice coding. Lattice coding creates code code books by quantizing continuous space into periodic regions.

The student's task is to understand lattice transmission schemes (c.f. [1], [2], [3], [4]) and in particular the schemes from [5], summarize the important concepts of lattice coding, and give an explanation of how these coding schemes achieve capacity over the AWGN channel.

These types of communication schemes are also important in certain information theoretic security scenarios, in particular on the so-called wiretap channel, on which the student is free to focus instead.

[1] Conway, Sloane 1982 - Voronoi regions of lattices, second moments of polytopes, and quantization. DOI: 10.1109/TIT.1982.1056483
[2] Conway, Sloane 1983 - A fast encoding method for lattice codes and quantizers. DOI: 10.1109/TIT.1983.1056761
[3] Forney 1989 - Multidimensional constellations. 2. Voronoi constellations. DOI: 10.1109/49.29616
[4] Calderbank, Ozarow 1990 - Nonequiprobable Signaling on the Gaussian Channel. DOI: 10.1109/18.53734
[5] Erez, Zamir 2004 - Achieving 0.5log(1+SNR) on the AWGN Channel With Lattice Encoding and Decoding. DOI: 10.1109/TIT.2004.834787

• Information Theory
• Introduction to Channel Coding
• Introduction to Coded Modulation helpful but not required