A tutorial on hierarchical lossless data compression

Abstract

Hierarchical lossless data compression is a compression technique that has been shown to effectively compress data in the face of uncertainty concerning a proper probabilistic model for the data. In this technique, one represents a data sequence x using one of three kinds of structures: (1) a tree called a pointer tree, which generates x via a procedure called “subtree copying”; (2) a data flow graph which generates x via a flow of data sequences along its edges; or (3) a contextfree grammar which generates x via parallel substitutions accomplished with the production rules of the grammar. The data sequence is then compressed indirectly via compression of the structure which represents it. This article is a survey of recent advances in the rapidly growing field of hierarchical lossless data compression. In the article, we illustrate how the three distinct structures for representing a data sequence are equivalent, outline a simple method for designing compact structures for representing a data sequence, and indicate the level of compression performance that can be obtained by compression of the structure representing a data sequence.