C-grammars and tree-codifications

摘要

The paper introduces two new concepts, namely C-grammar and tree-codification, based on the theory of formal languages, by means of which we try to exhibit a new aspect of general coding theory. Both linear algebraic coding and convolutional coding are presented here as a particular case of tree-codification. The main result of the paper gathers the two new concepts mentioned above. Thus, Theorem 10 establishes that to each tree-codification corresponds a C-grammar in which that tree-codification can be achieved, and vice versa. Some examples are given justifying both the concepts and the assertion that any algebraic coding (linear or convolutional) can be looked upon as a tree-codification.