The structure of DMC [dynamic Markov compression]

The popular dynamic Markov compression algorithm (DMC) offers 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 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 finite-context characterization exists, which was proved in using a finiteness argument. This paper presents and proves the first finite-context characterization of the states of DMC´s data model Our analysis reveals that the DMC model, with or without its counterproductive portions, offers abstract structural features not found in other models. Ironically, the space-hungry DMC algorithm actually has a greater capacity for economical model representation than its counterparts have. Once identified, DMC´s distinguishing features combine easily with the best features from other techniques. These combinations have the potential for achieving very competitive compression/memory tradeoffs