Performance evaluation of coded modulation schemes based on binary lattices

We describe computational techniques for the evaluation of error probability of modulation schemes based on binary lattices and multilevel coding. These techniques stem from the representation of a binary lattice in the form of a trellis whose structure depends on the block codes on which the binary 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 we obtain a single trellis that can be used for maximum-likelihood decoding using the Viterbi algorithm and for computing the error probability. An upper bound to error probability can be obtained from the transfer function of the trellis with suitable labels, and is applicable to both maximum-likelihood and staged decoding.<>