Use of σ-trees as constellations in trellis-coded modulation

Sigma-trees (σ-trees) are a class of geometric structures that include lattices as a constrained special case. These structures allow for signal sets, in spaces of arbitrary dimension, that are more spherical in shape than signal sets based on lattices. In this correspondence, it is shown that σ-trees can be used in the construction of non-lattice trellis-coded modulation schemes (TCM) schemes. A low-complexity σ-tree encoder is presented for multidimensional TCM codes. An optimal TCM decoder that uses the efficient sequential search property of σ-trees is then described. Simulation results based on one- and two-dimensional examples are used to show that the performance of σ-tree-based codes is comparable to that provided by conventional lattice-based codes