Reconstruction of constellation labeling with convolutional coded data

We propose here an algorithm for reconstructing an unknown constellation labeling. Our method assumes that the underlying error correcting code is a convolutional code. We define the notions of linear and affine equivalence among labelings. Those notions will help us to reduce the cost of the search. We show that the search is intractable with our method as the constellation size grows. In that case we restrict the search to Gray labelings. Our algorithm adapts very well to that constraint and allows an easy reconstruction up to a constellation of 256 points.