The "Art of Trellis Decoding" is NP-Hard

Abstract

Given a linear code C, the fundamental problem of trellis decoding is to find a coordinate permutation of C that yields a code C ′ whose minimal trellis has the least state-complexity among all codes obtainable by permuting the coordinates of C. By reducing from the problem of computing the pathwidth of a graph, we show that the problem of finding such a coordinate permutation is NP-hard, thus settling a long-standing conjecture