Lossless data compression algorithms based on substitution tables

This paper presents a class of new lossless data compression algorithms. Each algorithm in this class first transforms the original data to be compressed into an irreducible table representation and then uses an arithmetic code to compress the irreducible table representation. From the irreducible table representation, one can fully reconstruct the original data by performing multistage parallel substitution. A set of rules is described on how to perform hierarchical transformations from the original data to irreducible table representations. Theoretically, it is proved that all these algorithms outperform any finite state sequential compression algorithm and hence achieve the ultimate compression rate for any stationary and ergodic source. Furthermore, experiments on several standard images show that even a simple algorithm in this class, the so-called multi-level pattern matching algorithm, outperforms the Lempel-Ziv algorithms and arithmetic codes.