Moderate Density Parity-Check Codes from Projective Bundles
Abstract
A new construction for moderate density parity-check (MDPC) codes using finite geometry is proposed. We design a parity-check matrix for this family of binary codes as the concatenation of two matrices: the incidence matrix between points and lines of the Desarguesian projective plane and the incidence matrix between points and ovals of a projective bundle. A projective bundle is a special collection of ovals which pairwise meet in a unique point. We determine minimum distance and dimension of these codes, showing that they have a natural quasi-cyclic structure. In addition, we analyze the error-correction performance within one round of a modification of Gallager's bit-flipping decoding algorithm. In this setting, our codes have the best possible error-correction performance for this range of parameters.
Cite
@article{arxiv.2103.09722,
title = {Moderate Density Parity-Check Codes from Projective Bundles},
author = {Jessica Bariffi and Sam Mattheus and Alessandro Neri and Joachim Rosenthal},
journal= {arXiv preprint arXiv:2103.09722},
year = {2021}
}
Comments
19 pages