In large-scale distributed storage systems, data is stored on multiple servers. Erasure codes (mostly linear MDS codes) are used to protect the data against disk and server failures. Since the failure rates can change over time, it is beneficial to convert the code parameters (code length and code dimension) at a later point in time. This is called the code conversion problem.

Recent work has studied the access cost of the code conversion problem [1-3], which is the number of servers that needs to be accessed to perform the code conversion. The papers derive fundamental limits of the access cost and propose an achievable encoding scheme. The problem is first studied for the "merge regime" [1,2], and then generalized to other parameter regimes [3].

The goal of the seminar is to understand the code conversion problem, the fundamental limits on access cost, and how to construct suitable codes for different parameter regimes. The findings shall be presented in a written report and a scientific presentation.

[1] Maturana, Francisco, and K. V. Rashmi. "Convertible codes: new class of codes for efficient conversion of coded data in distributed storage." 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Schloss Dagstuhl-Leibniz-Zentrum für Informatik, 2020.

[2] F. Maturana and K. V. Rashmi, "Convertible Codes: Enabling Efficient Conversion of Coded Data in Distributed Storage," in IEEE Transactions on Information Theory, vol. 68, no. 7, pp. 4392-4407, July 2022, doi: 10.1109/TIT.2022.3155972.

[3] F. Maturana, V. S. C. Mukka and K. V. Rashmi, "Access-optimal Linear MDS Convertible Codes for All Parameters," 2020 IEEE International Symposium on Information Theory (ISIT), Los Angeles, CA, USA, 2020, pp. 577-582, doi: 10.1109/ISIT44484.2020.9173947.

• Coding theory (Channel coding course recommended)
• Linear algebra

Novel use cases for mobile communication networks include the aggregation of large amounts of data, which is stored in a distributed manner across network users. For instance, Federated Learning requires the aggregation of machine learning model updates from contributing users.

Over-the-Air (OtA) computation is an approach with the potential to drastically reduce the communication overhead of wireless distributed data-processing systems (e.g. Federated Learning). It exploits the multiple-access property and linearity of the wireless channel to compute sums of pre-processed data by the channel. This important property at the same time opens great opportunities for eavesdroppers to learn about the transmitted signal. If the legitimate receiver shall have exclusive access to the computation result, it is crucial to employ additional security measures.

Artificial noise can be employed to secure the communication. This noise is either generated by dedicated users jamming the communication [3], or by jointly designing the noise contribution of each user, [1][2]. The latter approach makes it possible to minimize the distortion at the legitimate receiver, but requires a centrally coordinated noise design. Therefore, an open problem is how to allow for the distributed design of artifical noise.

[1] Maßny, Luis, and Antonia Wachter-Zeh. "Secure Over-the-Air Computation using Zero-Forced Artificial Noise." arXiv preprint arXiv:2212.04288 (2022).
[2] Liao, Jialing, Zheng Chen, and Erik G. Larsson. "Over-the-Air Federated Learning with Privacy Protection via Correlated Additive Perturbations." arXiv preprint arXiv:2210.02235 (2022).
[3] Yan, Na, et al. "Toward Secure and Private Over-the-Air Federated Learning." arXiv preprint arXiv:2210.07669 (2022).

- basic knowledge in statistics and estimation theory
- basic knowledge about linear wireless channels