Error probability for digital transmission over nonlinear channels with application to TCM

The computation of upper and lower bounds to error probability in digital transmission over nonlinear channels with a finite memory is considered. By using orthogonal Volterra series, the authors derive a canonical representation for discrete nonlinear systems, based on a linear convolutional code and a memoryless mapper. This representation shows that finite-memory, discrete nonlinear systems can be analyzed in much the same way as TCM (trellis-coded modulation) schemes. In particular, TCM over nonlinear channels can be analyzed. A technique is derived that expresses an upper bound to error probability based on the computation of the transfer of a state diagram with N branches, and whose branch labels are matrices rather than scalars. Some examples of its application are given. In particular, error bounds are derived for nonlinear TCM schemes and for TCM schemes operating on nonlinear channels