Grammar-based code explained

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. To compress a data sequence

x = x _{1} … x _{n} , a grammar-based code transforms x into a context-free grammar G .The problem of finding a smallest grammar for an input sequence (smallest grammar problem) is known to be NP-hard, so many grammar-transform algorithms are proposed from theoretical and practical viewpoints.Generally, the produced grammar G 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, the multilevel pattern matching (MPM) algorithm, variations of the incremental parsing Lempel-Ziv code, 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.

• Sequitur 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 is a greedy algorithm using the strategy of most-frequent-first substitution. The compressive performance is powerful, although the main memory space requirement is very large.
• GLZA,^[1] which constructs a grammar that may be reducible, i.e., contain repeats, where the entropy-coding cost of "spelling out" the repeats is less than the cost creating and entropy-coding a rule to capture them. (In general, the compression-optimal SLG is not irreducible, and the Smallest Grammar Problem is different from the actual SLG compression problem.)

See also

• Dictionary coder
• Grammar induction
• Straight-line grammar

External links

• GLZA discussion and paper
• 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.

Notes and References

1. Book: Conrad . Kennon J. . Wilson . Paul R. . 2016 Data Compression Conference (DCC) . Grammatical Ziv-Lempel Compression: Achieving PPM-Class Text Compression Ratios with LZ-Class Decompression Speed . 586 . 2016 . 10.1109/DCC.2016.119. 978-1-5090-1853-6 . 3116024 .