Coding for multilevel partitioning of integer lattices based on block codes

Large Hamming distance introduces a diversity-like effect and is essential for good codes designed for the Raleigh fading channel. Previous work on multi-dimensional signal constellations (lattices) optimised Euclidean distance; this is usually done by partitioning lattices into cosets using a linear block code. This can provide large Hamming and Euclidean distance between cosets but yields only good Euclidean distance within a coset. In this paper we describe a multilevel partitioning method that attains better Hamming distance within cosets as well as between cosets. The technique provides a Hamming distance gain for the integer Zⁿ lattice or for any lattice Lambda that has a scaled version of Zⁿ as a sub-lattice.