LDPC codes generated by conics in the classical projective plane

Authors:
Sean V. Droms;Keith E. Mellinger;Chris Meyer
Affiliations:
Department of Mathematics, University of Mary Washington, Fredericksburg, USA 22401;Department of Mathematics, University of Mary Washington, Fredericksburg, USA 22401;Department of Mathematics, University of Mary Washington, Fredericksburg, USA 22401
Venue:
Designs, Codes and Cryptography
Year:
2006

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Abstract

We construct various classes of low-density parity-check codes using point-line incidence structures in the classical projective plane PG(2,q). Each incidence structure is based on the various classes of points and lines created by the geometry of a conic in the plane. For each class, we prove various properties about dimension and minimum distance. Some arguments involve the geometry of two conics in the plane. As a result, we prove, under mild conditions, the existence of two conics, one entirely internal or external to the other. We conclude with some simulation data to exhibit the effectiveness of our codes.