Computation of the active distances for trellis coded modulation

Recently, the concept of active distances, originally introduced for binary convolutional codes, was extended to the case of nonlinear trellis coded modulation. These distance measures allow an improved evaluation of the error correcting capability for trellis codes. Typically, the larger the slope of the active distances the better the performance of the trellis code for low . Moreover, these distance measures are of particular interest for the design of concatenated coding schemes, with respect to the choice of the inner trellis code as well as the interleaver. In this paper we present a matrix based method to compute the active distances for trellis codes in Euclidean space, encoded by an -state finite state machine. The computation is based on a simplified version of the distance generating matrix, which is well known from the calculation of the distance spectrum of trellis codes. In general the distance generating matrix is of size . We show that for trellis codes, encoded by an -state FSM, the distance generating matrix can always be reduced to fiffflffi !"ff. Finally, simulation results are presented that confirm the importance of the active distances.