USE OF SIGMA-TREES AS CONSTELLATIONS IN TRELLIS-CODED MODULATION

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