On the trellis structure of block codes

Abstract

Two main results will be presented: 1. The problem of minimizing the number of states in the trellis for a general (nonlinear) code at a given time index is NP-complete, and thus apparently computationally infeasible for large codes. 2. Minimal linear block code trellises correspond to configurations of non-attacking rooks on a triangular chess board. This correspondence can be used to enumerate the minimal trellises, and also to obtain insight into various bounds on the size of the trellises.<>