On trellis complexity of block codes: lower bounds
A. Lafourcade-Jumenbo, Alexander Vardy · 2002
We present a new lower bound on the state-complexity of linear codes, which includes all the existing bounds as special cases. For a large number of codes this results in a considerable improvement upon the DLP bound. Moreover, we generalize the new bound to nonlinear codes, and introduce several alternative techniques for lower bounding the trellis complexity, based on the distance spectrum and other combinatorial properties of the code. We also show how our techniques may be employed to lower bound the maximum and the total number of branches in the trellis. The asymptotic behavior of the new bound is investigated and shown to improve upon the known asymptotic estimates of trellis complexity.