Cryptocurrencies like Bitcoin and Ethereum use a decentralized ledger called Blockchain to track transactions. Whenever a new block is added to the Blockchain, the change is spread through the network using a gossip-like protocol. This process is known as block propagation.

To increase scalability, the efficiency of block propagation is crucial. This thesis aims to explore the information theoretic limits of block propagation, derive realistic models based on real data, and investigate innovative and efficient techniques for block propagation.

The thesis will be conducted at the Institute of Communications and Navigation at DLR (German Aerospace Center) in Oberpfaffenhofen.

Required qualifications are

• basic knowledge of information theory
• programming experience in Matlab, C, or python.
• Interest in cryptocurrencies.

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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

Gallager [1] studied the capacity regions of energy limited channels as in wideband and multi-access communication. He showed that reliable communication over such channels is fundamentally limited by a normalized rate, the capacity per unit energy. Verdu's capacity per unit cost [2] generalizes this concept to channels with arbitrary per-symbol cost functions. Since then, capacity per unit cost has been used to analyze a variety of communication scenarios in research literature.

The student will understand the concept and motivation of capacity per unit cost, and will be able to discuss the differences to Shannon's capacity result. The student will identify and review scenarios in literature where capacity per unit cost has been applied. Finally, the student will choose one of these applications and discuss in more detail how capacity per unit cost relates to this problem and how it helped in solving it.

References:

[1] R. G. Gallager, “Energy limited channels: Coding, multiaccess, and spread spectrum,” Tech. Rep. LIDS-P-1714, Nov. 1987.

[2] S. Verdú, “On channel capacity per unit cost,” IEEE Trans. Inf. Theory, vol. 36, no. 5, pp. 1019–1030, Sep. 1990.

1. Information Theory.
2. (Optional but helpful) One of the following courses:

• Mobile communications.
• Wireless Communications.
• Multi-User Information Theory.
• MIMO Systems.