Abstract
In this paper, new regular incidence structures are presented. They arise from sets of conics in the affine plane blownup at its rational points. The LDPC codes given by these incidence matrices are studied. These sparse incidence matrices turn out to be redundant, which means that their number of rows exceeds their rank. Such a feature is absent from random LDPC codes and is in general interesting for the efficiency of iterative decoding. The performance of some codes under iterative decoding is tested. Some of them turn out to perform better than regular Gallager codes having similar rate and row weight.
| Original language | English |
|---|---|
| Article number | 5895059 |
| Pages (from-to) | 4401-4416 |
| Number of pages | 16 |
| Journal | IEEE Transactions on Information Theory |
| Volume | 57 |
| Issue number | 7 |
| DOIs | |
| Publication status | Published - 1 Jan 2011 |
Keywords
- Algebraic geometry
- LDPC codes
- blowing up
- conics
- finite geometry
- incidence structures
- linear systems of curves