Efficient ring-TCM codes over fading channels

Ring-TCM codes form a class of novel trellis coded modulation schemes in which the operations in the encoder are modulo-q addition and multiplication. To match the encoder to practical multilevel modulation schemes, usually q is selected to be a power of two. These codes can be easily constructed to be rotationally invariant. Consequently, all possible phase rotations due to channel corruption can be removed simply by differentially encoding/decoding. However, as in all classes of TCM codes, R-TCM codes suffer from a rather large number of parallel trellis transitions. We introduce a new class of R-TCM codes, modulo-p to modulo-q (p