Set partitioning of Gaussian integer constellations and its application to two-dimensional interleaving

Codes over Gaussian integers have been proposed for coding over two-dimensional (2D) signal spaces, for example, using quadrature amplitude modulation. Here, it is demonstrated that the concept of set partitioning can be applied to Gaussian integer constellations that are isomorphic to 2D modules over rings of integers modulo p. This enables multilevel code constructions over Gaussian integers. The authors derive upper bounds on the achievable minimum distance in the subsets and present a construction for the set partitioning. This construction achieves optimal or close to optimal minimum distances. Furthermore, it is demonstrated that this set partitioning can be applied to an interleaving technique for correcting 2D cyclic clusters of errors. The authors propose a novel combination of generalised concatenated codes with 2D interleaving to correct 2D error clusters and independent errors.