Low density parity check codes based on finite geometries: a rediscovery

Abstract

LDPC codes with iterative decoding based on belief propagation have been shown to achieve astonishing error performance. But no algebraic or geometric method has been found for constructing these codes. Codes that have been found are largely computer generated, especially long codes. In this paper, we present two classes of high rate LDPC codes whose constructions are based on the lines of two-dimensional finite Euclidean and projective geometries, respectively.