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Grammar based code

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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 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.

Contents

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 (MPM) 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.

  • 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.

    • References

    Grammar-based code Wikipedia
    (Text) CC BY-SA


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