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

Abstract

This work demonstrates that the concept of set partitioning can be applied to Gaussian integer constellations that are isomorphic to two-dimensional modules over rings of integers modulo p. We 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, we demonstrate that this set partitioning can be applied to an interleaving technique for correcting two-dimensional cyclic clusters of errors.