Variable-length codes independent or closed with respect to edit relations

We investigate inference of variable-length codes in other domains computer science, such as noisy information transmission or retrieval-storage: topics, traditionally mostly constant-length codewords act. The study is relied upon the two concepts independent and closed sets: given an alphabet A a binary relation τ⊆A⁎×A⁎, set X⊆A⁎ τ-independent if τ(X)∩X=∅; X τ-closed τ(X)⊆X. focus to those word relations whose images are computed by applying some peculiar combinations deletion, insertion, substitution. In particular, characterizations that maximal families provided.