The "Art of Trellis Decoding" Is NP-Hard

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.

• Type: Conference
• Year: 2007
• Where: AAECC
• Authors: Navin Kashyap
• Keywords: AAECC 2007, Algorithms, Coordinate Permutation, Fundamental Problem, Linear Code C