Journal Article

Multiplicative groups used for coding QAM signals

Xue‐dong Dong, Cheong Boon Soh and Erry Gunawan

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 19, issue 3, pages 229-243
Published in print September 2002 | ISSN: 0265-0754
Published online September 2002 | e-ISSN: 1471-6887 | DOI:
Multiplicative groups used for coding QAM signals

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Recently, some multiplicative groups of algebraic integers were used to obtain quadrature amplitude modulation (QAM) signal spaces and to design error‐correcting codes. This paper shows that one subgroup of the multiplicative group of units in the algebraic integer ring of each quadratic number field with unique factorization property Q(√m), modulo the ideal (2n), can be used to obtain a QAM signal space of 22n–2 points with good geometrical properties, where n ≥ 3, m ≢ 1 (mod 8) and m is a square‐free rational integer. These QAM signals can be coded such that a differentially coherent method can be applied to demodulate the QAM signals. The multiplicative subgroups can also be used to construct block codes over Gaussian integers which are able to correct some error patterns.

Keywords: multiplicative group of units; block code; QAM signal space

Journal Article.  0 words. 

Subjects: Mathematics

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