Low-Density Cover-Metric Codes
Coding, Error Correction
Probabilistic error correction in the cover metric
A common assumption for the construction of error correcting codes is that errors occur independently.
However, in many applications errors are actually highly correlated.
Coding in the cover-metric considers correlated errors which occur as 2-dimensional burst errors.
Such errors can be corrected using rank-metric codes.
Originally Gabidulin codes were proposed for this.
In , low-rank parity check (LRPC) codes are introduced, which utilize a probabilistic decoding procedure.
The goal of the master thesis is to
- apply LRPC codes to the cover-metric
- derive expressions on the success probability of the decoding by modifying the existing results for the rank metric
- check these results using simulations
Depending on personal preference, this basic idea will be extended into different directions:
- consider interleaved scenario as in 
- consider a modified construction, which utilizes the additional structure of cover-metric errors compared to rank-metric errors (cf. )
If you are interested, please write an email, then we'll discuss the details.
 Aragon, Gaborit, Hauteville, Ruatta, Zemor, "Low Rank Parity Check Codes: New Decoding Algorithms and Applications to Cryptography", https://arxiv.org/abs/1904.00357
 Renner, Jerkovits, Bartz, "Efficient Decoding of Interleaved Low-Rank Parity-Check Codes", https://arxiv.org/abs/1908.10839
 Bitzer, Renner, Wachter-Zeh, Weger, "Generic Decoding in the Cover Metric", https://arxiv.org/abs/2205.12738