Te "art of trellis decoding" is computationally hard-for large fields

The problem of minimizing the trellis complexity of a code by coordinate permutation is studied. Three measures of trellis complexity are considered: the total number of states, the total number of edges, and the maximum state complexity of the trellis. The problem is proven NP-hard for all three measures, provided the field over which the code is specified is not fixed. We leave open the problem of dealing with the case of a fixed field, in particular GF(2).