Given a linear code \({\mathcal C}\), the fundamental problem of trellis decoding is to find a coordinate permutation of \({\mathcal C}\) that yields a code \({\mathcal C}'\) whose minimal trellis has the least state-complexity among all codes obtainable by permuting the coordinates of \({\mathcal C}\). 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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Navin Kashyap
    • 1
  1. 1.Dept. Mathematics and Statistics, Queen’s University, Kingston, ON, K7L 3N6Canada

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