On groups of complex integers used as QAM signals

Abstract

Recently, the multiplicative group of units in the Gaussian quotient ring Z[i]/(2 2 + 2 n i) was used to obtain a quadrature amplitude modulation (QAM) signal space of 2 2 n points and to design one error correcting codes. In this paper it is shown that the multiplicative group of units in the quotient ring Z[i]/(2 n ) can also be used to obtain a QAM signal space of 2 2 n−1 points and to design one error correcting codes. The required modulo operation in this paper is simpler and block codes constructed in this paper are able to correct one error with more values.