Grammar-based code

Grammar-based codes 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 ^[1] and SEQUITUR, among others. To compress a data sequence $x=x_{1}\cdots x_{n}$ , a grammar-based code first transforms $x$ into a context-free grammar $G$ , and then uses an arithmetic coding algorithm to compress the grammar $G$ .

Examples and Characteristics

The class of grammar-based codes is very broad. It includes block codes, variations of the incremental parsing Lempel-Ziv code ^[2], the multilevel pattern matching (MPM) algorithm^[3], 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.

References

^ Kieffer, J. C.; Yang, E.-H. (2000), "Grammar-based codes: A new class of universal lossless source codes", IEEE Trans. Inform. Theory, 46: 737–754
^ Kieffer, J. C.; Yang, E.-H.; Nelson, G.; Cosman, P. (2000), "Universal lossless compression via multilevel pattern matching", IEEE Trans. Inform. Theory, 46: 1227–1245
^ Ziv, J.; Lempel, A. (1978), "Compression of individual sequences via variable rate coding", IEEE Trans. Inform. Theory, 24: 530–536

External Links

Description of grammar-based codes with example

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[1] Kieffer, J. C.; Yang, E.-H. (2000), "Grammar-based codes: A new class of universal lossless source codes", IEEE Trans. Inform. Theory, 46: 737–754

[2] Kieffer, J. C.; Yang, E.-H.; Nelson, G.; Cosman, P. (2000), "Universal lossless compression via multilevel pattern matching", IEEE Trans. Inform. Theory, 46: 1227–1245

[3] Ziv, J.; Lempel, A. (1978), "Compression of individual sequences via variable rate coding", IEEE Trans. Inform. Theory, 24: 530–536

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