Entropy coding with variable-length rewriting systems

This paper describes a family of codes for entropy coding of memoryless sources. These codes are defined by sets of production rules of the form a (l) over bar -> (b) over bar, where a is a source symbol, and (l) over bar, (b) over bar are sequences of bits. The coding process can be modeled as a finite-state machine (FSM). A method to construct codes which preserve the lexicographic order in the binary-coded representation is described. For a given constraint on the number of states for the coding process, this method allows the construction of codes. with a better compression efficiency than the Hu-Tucker codes. A second method is proposed to construct codes such that the marginal bit probability of the compressed bitstream converges to 0.5 as the sequence length increases. This property is achieved even if the probability distribution function is not known by the encoder.