Grammar-based code

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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, 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.

[edit] 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.

[edit] References

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 

[edit] External links

• Description of grammar-based codes with example