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

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 G_x representing x in the sense that x is the unique string belonging to the language generated by G_x. Lossless compression of x takes place indirectly via compression of the production rules of the grammar G_x. 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