Grammar-based code


Grammar-based codes or Grammar-based compression are compression algorithms based on the idea of constructing a context-free grammar for the string to be compressed. Examples include universal lossless data compression algorithms. To compress a data sequence, a grammar-based code transforms into a context-free grammar.
The problem of finding a smallest grammar for an input sequence is known to be NP-hard, so many grammar-transform algorithms are proposed from theoretical and practical viewpoints.
Generally, the produced grammar is further compressed by statistical encoders like arithmetic coding.

Examples and characteristics

The class of grammar-based codes is very broad. It includes block codes, variations of the incremental parsing Lempel-Ziv code, the multilevel pattern matching algorithm, and many other new universal lossless compression algorithms.
Grammar-based codes are universal in the sense that they can achieve asymptotically the entropy rate of any stationary, ergodic source with a finite alphabet.

Practical algorithms

The compression programs of the following are available from external links.