Name
Abstract | ||
|---|---|---|
Recently, Fuchsian codes have been proposed in Blanco-Chacón et al. (2014) [2] for communication over channels subject to additive white Gaussian noise (AWGN). The two main advantages of Fuchsian codes are their ability to compress information, i.e., high code rate, and their logarithmic decoding complexity. In this paper, we improve the first property further by constructing Fuchsian codes with arbitrarily high code rates while maintaining logarithmic decoding complexity. Namely, in the case of Fuchsian groups derived from quaternion algebras over totally real fields we obtain a code rate that is proportional to the degree of the base field. In particular, we consider arithmetic Fuchsian groups of signature (1;e) to construct explicit codes having code rate six, meaning that we can transmit six independent integers during one channel use. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1016/j.jpaa.2015.06.005 | Journal of Pure and Applied Algebra |
Field | DocType | Volume |
Discrete mathematics,Topology,Concatenated error correction code,Group code,Code rate,Algebra,Block code,Linear code,Decoding methods,Additive white Gaussian noise,Code (cryptography),Mathematics | Journal | 220 |
Issue | ISSN | Citations |
1 | 0022-4049 | 0 |
PageRank | References | Authors |
0.34 | 9 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Iván Blanco-Chacón | 1 | 4 | 1.90 |
| Camilla Hollanti | 2 | 308 | 40.21 |
| Montserrat Alsina | 3 | 4 | 1.22 |
| Dionís Remón | 4 | 6 | 1.62 |