Groups of complex integers used as QAM signals

Block codes which allow error correction in a two-dimensional QAM signal space are given. The properties of these codes are used to demodulate QAM signals in a differentially coherent detection scheme on a noisy channel. The block codes presented are not group codes; however, their components belong to a group G_n or G´_n which is constructed starting from the Gaussian integers G=Z[i] modulo a nonprime ideal (2ⁿ+2ⁿi) and taking on it the multiplicative group of units. The authors classify and factor these multiplicative groups and use them to construct the block codes which become optimal and efficient from the point of view of transmission rate and decoding