Abstract
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.
This work was supported in part by a research grant from the Natural Sciences and Engineering Research Council (NSERC) of Canada.
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Kashyap, N. (2007). The “Art of Trellis Decoding” Is NP-Hard. In: Boztaş, S., Lu, HF.(. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 2007. Lecture Notes in Computer Science, vol 4851. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77224-8_24
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DOI: https://doi.org/10.1007/978-3-540-77224-8_24
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