Sectionalization of the minimal trellis module for convolutional codes

It has been shown by McEliece and Lin that convolutional codes can be represented by a minimal trellis structure in order to reduce the decoding complexity of the Viterbi algorithm. This trellis module has an irregular structure presenting sections with different number of states. In this paper we present the sectionalization of the minimal trellis module which yields a more compact and regular trellis representation (in terms of maximum number of states and total number of sections) with the same decoding complexity and distance spectrum of the minimal trellis module. The decoding complexity measure is strongly related with energy consumption by the receiver. We investigate the effects of the trellis sectionalization over the trellis complexity measure, defined by McEliece and Lin, and over the merge complexity measure. We show that various trellis topologies proposed in the literature are specific cases of the sectionalized minimal trellis.