Title :
High-rate low-density parity check codes based on anti-Pasch affine geometries
Author_Institution :
Dept. of Electr. & Comput. Eng., Arizona Univ., Tucson, AZ, USA
Abstract :
We introduce a combinatorial construction of regular low-density parity check codes based on balanced incomplete block designs whose bipartite graphs have girth six. Our construction employs a special type of anti-Pasch affine geometry that result in codes having minimum distance of at least six. We are primarily concerned with very high-rate codes and low column weights, but the proposed construction can be used to generate long codes as well as codes of arbitrary column weight.
Keywords :
AWGN channels; geometric codes; graph theory; sparse matrices; AWGN channels; additive white Gaussian noise channels; anti-Pasch affine geometries; bipartite graphs; column weights; combinatorial construction; high-rate codes; long codes; low-density parity check codes; sparse matrices; AWGN; Additive white noise; Belief propagation; Bipartite graph; Computational geometry; Graphical models; Iterative decoding; Message passing; Parity check codes; Sparse matrices;
Conference_Titel :
Communications, 2002. ICC 2002. IEEE International Conference on
Print_ISBN :
0-7803-7400-2
DOI :
10.1109/ICC.2002.997067
