Multiplicative groups used for coding QAM signals

Recently, some multiplicative groups of algebraic integers wereused to obtain quadrature amplitude modulation (QAM) signalspaces and to design error-correcting codes. This paper showsthat one subgroup of the multiplicative group of units in thealgebraic integer ring of each quadratic number field with uniquefactorization property Q(m), modulo the ideal (2ⁿ), can be usedto obtain a QAM signal space of 2^2n–2 points with goodgeometrical properties, where n 3, m 1 (mod 8) and m is asquare-free rational integer. These QAM signals can be codedsuch that a differentially coherent method can be applied todemodulate the QAM signals. The multiplicative subgroups canalso be used to construct block codes over Gaussian integerswhich are able to correct some error patterns.