Grammar-based code
Grammar-based codes or Grammar-based compression are compression algorithms based on the idea of constructing a context-free grammar (CFG) 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 transforms 
into a context-free grammar 
.
The problem to find a smallest grammar for an input sequence is known to be NP-hard,[2] 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,[3] the multilevel pattern matching (MPM) algorithm,[4] 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 following are available from external links.
- Sequitur[5] is a classical grammar compression algorithm that sequentially translates an input text into a CFG, and then the produced CFG is encoded by an arithmetic coder.
- Re-Pair[6] is a greedy algorithm by the strategy of most-frequent-first substitution. The compressive performance is powerful, although the main memory space is very large.
See also
References
- ↑ Kieffer, J. C.; Yang, E.-H. (2000), "Grammar-based codes: A new class of universal lossless source codes", IEEE Trans. Inform. Theory 46 (3): 737–754, doi:10.1109/18.841160
- ↑ Charikar, M.; Lehman, E.; Liu, D.; Panigrahy, R.; Prabharakan, M.; Sahai, A.; Shelat, A. (2005), "The Smallest Grammar Problem", IEEE Trans. Inform. Theory 51 (7): 2554–2576, doi:10.1109/tit.2005.850116
- ↑ Kieffer, J. C.; Yang, E.-H.; Nelson, G.; Cosman, P. (2000), "Universal lossless compression via multilevel pattern matching", IEEE Trans. Inform. Theory 46 (4): 1227–1245, doi:10.1109/18.850665
- ↑ Ziv, J.; Lempel, A. (1978), "Compression of individual sequences via variable rate coding", IEEE Trans. Inform. Theory 24 (5): 530–536, doi:10.1109/TIT.1978.1055934
- ↑ Nevill-Manning, C. G.; Witten, I. H. (1997), "Identifying Hierarchical Structure in Sequences: A linear-time algorithm", Journal of Artificial Intelligence Research 7 (4): 67–82, hdl:10289/1186
- ↑ Larsson, N. J.; Moffat, A. (2000), "Offline Dictionary-Based Compression", IEEE 88 (11): 1722–1732, doi:10.1109/5.892708
External links
- Description of grammar-based codes with example
- Sequitur codes
- Re-Pair codes
- Re-Pair codes a version of Gonzalo Navarro.
- GrammarViz 2.0 - implementation of Sequitur, Re-Pair, and parallel Re-Pair in Java.