Self-synchronization of Huffman codes

All binary prefix codes, including Huffman codes, are "complete", in the sense that the vertices in their decoding trees are either leaves or have two children. An open question has been to characterize which prefix codes and which complete prefix codes have a self-synchronizing string. Various algorithms have been proposed for determining the self-synchronizing string. In this paper, we prove that almost all complete prefix codes have a self-synchronizing string.