Efficient decoding algorithm for affine reflection group codes of rank 2

This paper presents an efficient decoding algorithm for group codes based on affine reflection groups of rank 2. The proposed decoding algorithm works exceptionally well for a large number of codewords (or even infinite constellations) which is useful for high data rate transmission. It is derived from the geometry of the groups and is equivalent to the maximum likelihood (ML) criterion. Simulations show signal constellations obtained from affine reflection group A₂ has higher symbol-error rate (SER) performance compared to QAM at the same rate.