Linear time universal coding of tree sources via FSM closure

Abstract

Applying generalized trees and their finite state machine closures, a two-pass version of context, a twice-universal lossless coding scheme for tree models, can be implemented in linear encoding/decoding time. As it turns out, an optimal selection rule and the corresponding transitions are computationally not more expensive than the various steps involved in the implementation of the Burrows-Wheeler transform (BWT) and use, in fact, similar tools. Also the paper presents a reversible transform that displays the same context deinterleaving feature as the BWT but is naturally based on an optimal tree. This transform offers insight into the workings of the BWT and the nature of its suboptimality for twice-universal coding of tree models.