LDPC codes generated by conics in the classical projective plane |
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Authors: | Sean V Droms Keith E Mellinger Chris Meyer |
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Institution: | (1) Department of Mathematics, University of Mary Washington, 1301 College Avenue, Trinkle Hall, Fredericksburg, VA 22401, USA |
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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. |
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Keywords: | LDPC code Projective plane Conic |
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