An approach to Ungerboeck coding for rectangular signal sets (Corresp.)

A method of finding good Ungerboeck codes for large rectangular [quadrature amplitude modulation (QAM)] signal sets is described. Using the concept of Euclidean weights due to Ungerboeck, we prove that a point basic constellation may be employed to determine exactly the free distance for an Ungerboeck-coded rectangular point set, when bits are uncoded and the remaining bits pass through a rate convolutionai encoder. It is shown that rate encoders may be used to achieve most of the theoretically possible coding gain in the proposed scheme where the effect of the error coefficient on the coding gain has been considered.