2020 IEEE International Symposium
on Information Theory
21-26 June 2020 • Los Angeles, California, USA
| Paper ID | A.1.4 | ||
| Paper Title | Low-Rank Parity-Check Codes over the Ring of Integers Modulo a Prime Power | ||
| Authors | Julian Renner, Technical University of Munich, Germany; Sven Puchinger, Technical University of Denmark, Denmark; Antonia Wachter-Zeh, Technical University of Munich, Germany; Camilla Hollanti, Ragnar Freij-Hollanti, Aalto University, Finland | ||
| Session | A.1: Algebraic Coding Theory I | ||
| Presentation | Lecture | ||
| Track | Algebraic and Combinatorial Coding Theory | ||
| Manuscript | Click here to download the manuscript | ||
| Virtual Presentation | Click here to watch in the Virtual Symposium | ||
| Abstract | We define and analyze low-rank parity-check (LRPC) codes over extension rings of the finite chain ring $\ZZ_{p^r}$, where $p$ is a prime and $r$ is a positive integer. LRPC codes have originally been proposed by Gaborit et al. (2013) over finite fields for cryptographic applications. The adaption to finite rings is inspired by a recent paper by Kamche et al. (2019), which constructed Gabidulin codes over finite principle ideal rings with applications to space-time codes and network coding. We give a decoding algorithm based on simple linear-algebraic operations. Further, we derive an upper bound on the failure probability of the decoder. The upper bound is valid for errors whose rank is equal to the free rank. | ||
Plan Ahead
2021 IEEE International Symposium on Information Theory
11-16 July 2021 | Melbourne, Victoria, Australia
