Variable-Length Codes Independent or Closed with respect to Edit Relations
This work addresses a theoretical problem in coding theory for domains like information transmission and storage, but it appears incremental as it extends existing concepts of independent and closed sets to variable-length codes.
The paper tackles the problem of inferring variable-length codes for applications like noisy information transmission and information retrieval-storage, where constant-length codes are traditionally used, by characterizing maximal codes in families of τ-independent or τ-closed codes based on edit relations involving deletion, insertion, or substitution.
We investigate inference of variable-length codes in other domains of computer science, such as noisy information transmission or information retrieval-storage: in such topics, traditionally mostly constant-length codewords act. The study is relied upon the two concepts of independent and closed sets. We focus to those word relations whose images are computed by applying some peculiar combinations of deletion, insertion, or substitution. In particular, characterizations of variable-length codes that are maximal in the families of $τ$-independent or $τ$-closed codes are provided.