Performance evaluation of coded modulation schemes based on binary lattices

Computational techniques for the evaluation of error probability of schemes based on binary lattices and multilevel coding stem from the representation of a binary lattice in the form of a trellis whose structure depends on the block codes on which the lattice is based. Multilevel coded-modulation schemes can also be described through a trellis; by combining with this the trellis structure of the lattice constellation, the authors obtain a single trellis that can be used for maximum-likelihood decoding using the Viterbi algorithm and for computing the error probability. A union upper bound is obtained from the transfer function of the trellis with suitable labels, and is applicable to both maximum-likelihood and staged decoding