While their purpose is also different from ours, as they use this mapping to generate training data for a parsing algorithm based on recursive partitioning using realvalued distances, their encoding could also be applied with our sequence labeling approach.
it has the drawback that it only supports binarized trees, and some of its theoretical properties are worse for our goal, as the way to define the inverse of an arbitrary label sequence can be highly ambiguous: for example, a sequence of n−1 equal labels in this encoding can represent any binary tree with n leaves.