Non-binary Euclidean Geometry codes: Majority Logic Decoding

Non-binary One Step Majority Logic decodable (OSMLD) codes have several advantages over their binary counterparts but unfortunately their decoding complexity is significantly challenging. In this paper, we propose two contributions. Our first contribution is to use the Majority-Logic Decoding (MLGD) algorithm for non-binary cyclic OSMLD codes, since it involves only finite field addition and multiplication, in addition to a majority vote, and hence has significantly lower complexity than other decoding algorithms, which seems to be an attractive choice. The second contribution is to use finite geometry codes, even those of prime fields, because they have a large number of orthogonal equations which makes them good candidates for the MLGD algorithm, so we can benefit from its low complexity. We also investigate the power correction of this algorithm and the results are quite satisfying. © 2016 IEEE.