This repository contains the Quasi Cyclic (QC) representation of classical Generalized Quadrangles (GQ). These have been obtained using the methods described in "Practical Implementation of Geometric Quasi-Cyclic LDPC Codes" by Simeon Ball and Tomàs Ortega. See also PCT/EP2023/062797.
Standard .alist files are provided for LDPC simulations.
Generalized Quadrangles are incidence structures whose main feature is the lack of any triangles (yet they contain many quadrangles). This repository provides a practical Quasi Cyclic representation of their point-line incidence matrix. These matrices can be seen as parity check matrices of error correcting codes, which are particularly useful for LDPC (Low-Density Parity-Check) applications.
All representations are in the representations folder, with subdirectories
-
elliptic_quadrangle - representations for
$Q(5,q)$ and its dual. -
hermitian_quadrangle - representations for
$W(3,q)$ and its dual. -
symplectic_quadrangle - representations for
$H(4,q^2)$ and its dual. -
others - other representations, such as for the projective space
$PG(k-1,q)$ .
All folders contain the raw output from our generation scripts in .txt files, as well as .alist files for LDPC simulations. Files that start with "G_" contain the generator matrix for the corresponding code described by the parity check matrix.
The .alist files provided are ready to use with any standard LDPC BER/FER simulator, such as aff3ct.
The utilities folder contains Python scripts that convert raw outputs to .alist files. The input and output filenames for the conversion have to be edited in the code.
If you find this work helpful, please consider citing
@inproceedings{ball2024QC,
title={Practical Implementation of Geometric Quasi-Cyclic LDPC Codes},
author={Ball, Simeon and Ortega, Tomàs},
booktitle={Discrete Mathematics Days},
year={2024}
}
For questions or inquiries about this repository, feel free to email tomas.ortega@uci.edu.