Evaluating distance spectra and performance bounds of trellis codes on channels with intersymbol interference

A general class of trellis codes whose generating trellis can be labeled by a set of linear labels is defined. It is shown that for these codes there exist conditions on the signal mapping that make it possible to calculate the distance spectrum with respect to a distance measure (e.g., Euclidean distance) assuming an arbitrary correct sequence. This class of new codes contains most known trellis codes. It is then shown that this approach can be extended to calculate the distance spectra of certain trellis codes on intersymbol interference channels, e.g., Ungerboeck 8-PSK trellis codes. Examples of the distance spectra and union bounds on the bit-error probability for channels with and without intersymbol interference are evaluated. A comparison to simulation results is used to demonstrate the tightness of the bounds.