The "Art of trellis decoding" is NP-hard

Authors:
Navin Kashyap
Affiliations:
Dept. Mathematics and Statistics, Queen's University, Kingston, ON, Canada
Venue:
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
Year:
2007

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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.