Optimization of Trellis Codes with Multilevel Amplitude Modulation with Respect to an Error Probability Criterion

An easily computed upper bound on the error probability of a data communications system with combined trellis coding and multilevel/phase modulation is derived, assuming an additive white Gaussian noise channel and maximum-likelihood decoding. This bound is used to search for codes obtained by set-partitioning that minimize the bound for a fixed number of trellis states. Only amplitude modulated signals typically used in voiceband modem applications are considered. The signal levels that minimize the error probability bound subject to an average power constraint are presented for some specific codes.