A GEOMETRIC CONSTRUCTION PROCEDURE FOR GEOMETRICALLY UNIFORM TRELLIS CODES

The problem of maximizing the minimum free squared Euclidean distance of a trellis code is developed from a geometric point of view. This ap proach provides a new may of constructing constellations for trellis c oding. A decomposition of the trellis topology leads to a systematic c onstruction of signal sets and generators for geometrically uniform tr ellis codes. An algorithm is proposed to construct geometrically unifo rm trellis codes, and examples show how to obtain large free distance trellis codes. This approach unifies the construction of convolutional codes over the binary field and trellis codes over the real field.