Low-density parity-check codes based on Galois fields
Fedor I. Ivanov, Victor Zyablov, В. Г. Потапов · Journal of Communications Technology and Electronics · 2012
Methods for constructing a mapping of the elements of a multiplicative group of a Galois field onto a symmetric group of permutation matrices are proposed. A technique minimizing the order of the symmetric group is suggested. The results are used for constructing an ensemble of low-density parity-check codes. The obtained code constructions are tested on an iterative belief propagation (sum-product) decoding algorithm on transmission of a code word through a binary channel with an additive Gaussian white noise.