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Data compression

compressionvideo compressioncompressed
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.
Grammar-based codes like this can compress highly repetitive input extremely effectively, for instance, a biological data collection of the same or closely related species, a huge versioned document collection, internet archival, etc. The basic task of grammar-based codes is constructing a context-free grammar deriving a single string.

Straight-line grammar

Algorithms for context-free grammar generation
Straight-line grammar
Grammar-based code

Context-free grammar

context-free grammarscontext-freecontext free grammar
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.

Lossless compression

losslesslossless data compressioncompression
Examples include universal lossless data compression algorithms.

Arithmetic coding

arithmetic coderarithmetic encodingarithmetic code
Generally, the produced grammar G is further compressed by statistical encoders like arithmetic coding.

Block code

linear block codedistanceblock encoding
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.

LZ77 and LZ78

LZ77Lempel-ZivLempel-Ziv compression
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.

Entropy rate

ratesource information rate
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.

Ergodicity

ergodicnon-ergodicergodic measure
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.

Sequitur algorithm

Sequitur
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.

Heavy path decomposition

Subsequent applications of heavy path decomposition have included solving the level ancestor problem, computing the edit distance between trees, graph drawing and greedy embedding, finding a path near all nodes of a given graph, fault diagnosis in fiber-optic communication networks, and decoding grammar-based codes, among others.