Computation of the minimum Euclidean distance of modulated signals in IIR dispersive channels

We consider the computational problem of finding the minimum Euclidean distance between modulated signals in linear dispersive channels with infinite-duration impulse response. Assuming maximum-likelihood estimation, those channels transform trellis codes to tree codes, and algorithms devised for tree codes, like the branch-and-bound algorithm, must be used. We show that, when the channel response has rational Laplace or z transform, some properties of recursive filters can be explored to reduce the computational effort of the search: upper and lower bounds can more be efficiently calculated via recursive equations, and discrete-time filter theory can be used to find the best way to compute some convolutions. Sample calculations are given for practical examples