Bounds on the performance of maximum-likelihood and reduced-state decoding of trellis codes on channels with intersymbol interference

A method is presented for computing a bound on the probability of error for maximum-likelihood decoding of trellis codes on channels with intersymbol interference. In general, computing such bounds requires the solution of a system of 2^2(v+kL) equations, where v is the constraint-length of a rate k/n trellis code and L is the length of the channel impulse response. Direct solution of this set of equations is unreasonable for many cases of interest, and therefore an alternative method for computing a bound is presented. A bound on the probability of error for reduced-state decoding under the assumption of no error propagation is presented. This reduced-state bound can be formulated as the solution of a system of 2^2(v+kL) equations, and this bound can be computed using the same method given for the maximum-likelihood bound