Optimization of Eight-Fold Discrete Modulation Constellations by Rational Choice of the Space Bijection Method

When transmitting digital signals over communication channels, modern modems use multiple methods of discrete modulation, called constellations, formed according to certain rules. In this case, signal transformations occur that can be considered as successive bijections of different spaces, which most often correspond to the Euclidean space and the Hamming space. These transformations do not meet the isomorphism condition, which must be taken into account when searching for optimal or close to optimal methods for constructing signal-code constellations, taking into account the models of existing interference and the resulting errors of different multiplicity.