Abstract
Sigma-trees (/spl sigma/-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 /spl sigma/-trees can be used in the construction of non-lattice trellis-coded modulation schemes (TCM) schemes. A low-complexity /spl sigma/-tree encoder is presented for multidimensional TCM codes. An optimal TCM decoder that uses the efficient sequential search property of /spl sigma/-trees is then described. Simulation results based on one- and two-dimensional examples are used to show that the performance of /spl sigma/-tree-based codes is comparable to that provided by conventional lattice-based codes.
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