The author designs multilevel trellis codes based on lattices and cosets that provide greater immunity to Gaussian noise and/or greater resistance to impulse noise than previous approaches. He shows how to calculate minimum-squared distance and path multiplicity in terms of the norms and multiplicities of the different cosets. The multilevel structure allows the redundancy in the coset selection procedure to be allocated efficiently among the different levels. The proposed codes admit a staged decoding procedure that requires very few trellis states and has performance/complexity advantages over maximum-likelihood decoding.