Low-density parity-check codes based on finite geometries: A rediscovery and new results

@article{Kou2001LowdensityPC,
  title={Low-density parity-check codes based on finite geometries: A rediscovery and new results},
  author={Yu Kou and Shu Lin and Marc P. C. Fossorier},
  journal={IEEE Trans. Inf. Theory},
  year={2001},
  volume={47},
  pages={2711-2736}
}
This paper presents a geometric approach to the construction of low-density parity-check (LDPC) codes. Four classes of LDPC codes are constructed based on the lines and points of Euclidean and projective geometries over finite fields. Codes of these four classes have good minimum distances and their Tanner (1981) graphs have girth 6. Finite-geometry LDPC codes can be decoded in various ways, ranging from low to high decoding complexity and from reasonably good to very good performance. They… 
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