Iterative Threshold Decoding Of High Rates Quasi-Cyclic OSMLD Codes

Majority logic decoding (MLD) codes are very powerful thanks to the simplicity of the decoder. Nevertheless, to find constructive families of these codes has been recognized to be a hard job. Also, the majority of known MLD codes are cyclic which are limited in the range of the rates. In this paper a new adaptation of the Iterative threshold decoding algorithm is considered, for decoding Quasi-Cyclic One Step Majority logic codes (QC-OSMLD) codes of high rates. We present the construction of QC-OSMLD codes based on Singer difference sets of rate 1/2, and codes of high rates based on Steiner triple system which allows to have a large choice of codes with different lengths and rates. The performances of this algorithm for decoding these codes on both Additive White Gaussian Noise (AWGN) channel and Rayleigh fading channel, to check its applicability in wireless environment, is investigated.