A new method of multilevel coding based on multidimensional signal constellations and corresponding decoding algorithm is presented in this paper. The method solves the problem that the decoding complexity grows approximately exponentally with the increase of coding gains in previously known trellis-coded modulation systems. As examples

Some coding systems based on the four dimensional lattice D4 and the eight dimensional lattice E8 are given. The results show that the required normalized （each two dimensional） decoding complexity of the new coding scheme grows almost linearly with the increase of coding gains.