Grammar-based codes: a new class of universal lossless source codes

  • Authors:
  • J. C. Kieffer;En-Hui Yang

  • Affiliations:
  • Dept. of Electr. & Comput. Eng., Minnesota Univ., Minneapolis, MN;-

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2006

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Abstract

We investigate a type of lossless source code called a grammar-based code, which, in response to any input data string x over a fixed finite alphabet, selects a context-free grammar Gx representing x in the sense that x is the unique string belonging to the language generated by Gx. Lossless compression of x takes place indirectly via compression of the production rules of the grammar Gx. It is shown that, subject to some mild restrictions, a grammar-based code is a universal code with respect to the family of finite-state information sources over the finite alphabet. Redundancy bounds for grammar-based codes are established. Reduction rules for designing grammar-based codes are presented