Low complexity trellis representations of convolutional codes via sectionalization of the minimal trellis

Abstract

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. We investigate the effects of the trellis sectionalization over the trellis and merge complexity measures. A set of rules are constructed to govern these effects. A list of the most compact sectionalized trellis modules with the same complexities than the minimal module is shown for codes of several rates. We show that various trellis topologies proposed in the literature are specific cases of the sectionalized minimal trellis.