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

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2 Author(s)
J. C. Kieffer ; Dept. of Electr. & Comput. Eng., Minnesota Univ., Minneapolis, MN, USA ; En-Hui Yang

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

Published in:

IEEE Transactions on Information Theory  (Volume:46 ,  Issue: 3 )