A Characterization of the Dynamic Markov Compression FSM with Finite Conditioning Contexts

The popular Dynamic Markov Compression Algorithm (DMC) [8] is a member of the family of data compression algorithms that combine an on-line stochastic data model with an arithmetic coder. DMC's distinguishing feature is an elegant but ad hoc modeling technique that provides state-of-the-art compression performance and matchless conceptual simplicity. In practice, however, the cost of DMC's simplicity and performance is often outrageous memory consumption. Several known attempts at reducing DMC's unwieldy model growth (e.g., [15, 19]) have rendered DMC's compression performance uncompetitive. One reason why DMC's model growth problem has resisted solution is that the algorithm is poorly understood. DMC is the only published stochastic data model for which a characterization of its states, in terms of conditioning contexts, is unknown. Up until now, all that was certain about DMC was that a nite-context characterization exists, which was proved in [3] using a niteness argument.