An algorithm for computing the distance spectrum of trellis codes

A class of quasiregular codes is defined for which the distance spectrum can be calculated from the codeword corresponding to the all-zero information sequence. Convolutional codes and regular codes are both quasiregular, as well as most of the best known trellis codes. An algorithm to compute the distance spectrum of linear, regular, and quasiregular trellis codes is presented. In particular, it can calculate the weight spectrum of convolutional (linear trellis) codes and the distance spectrum of most of the best known trellis codes. The codes do not have to be linear or regular, and the signals do not have to be used with equal probabilities. The algorithm is derived from a bidirectional stack algorithm, although it could also be based on the Viterbi algorithm. The algorithm is used to calculate the beginning of the distance spectrum of some of the best known trellis codes and to compute tight estimates on the first-event-error probability and on the bit-error probability.