Enumerative Coding for Tree Sources

Efficient enumerative coding for tree sources is, in general, surprisingly intricate-a simple uniform encoding of type classes, which is asymptotically optimal in expectation for many classical models such as FSMs, turns out not to be so in this case. We describe an efficiently computable enumerative code that is universal in the class of tree sources in the sense that, for a string emitted by an unknown source supported on a known tree, the expected normalized code length approaches the entropy rate of the source with a convergence rate (K/2)(log n)/n, where K is the number of free parameters of the source. The results extend also to the twice-universal setting, where the tree is unknown.