Incidence structures from the blown-up plane and LDPC codes

TL;DR

This paper introduces new regular incidence structures derived from conics in a blown-up affine plane, leading to LDPC codes with unique redundancy properties that enhance iterative decoding performance.

Contribution

It presents novel incidence structures from conics in a blown-up plane and explores their LDPC codes, highlighting their redundancy and improved decoding performance.

Findings

Incidence matrices are redundant, with more rows than rank.

Some LDPC codes outperform regular Gallager codes of similar rate.

Codes show promising results under iterative decoding.

Abstract

In this article, new regular incidence structures are presented. They arise from sets of conics in the affine plane blown-up 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.