Insertion/Deletion Detecting Codes and the Boundary Problem

Abstract

Insertion/deletion detecting codes were introduced by Konstantinidis In this paper we define insertion/deletion detecting codes in a slightly different manner, and based on this definition, we introduce multiple deletion and multiple insertion detecting codes. It is shown that these codes, which are systematic, are optimal in the sense that there exists no other systematic multiple deletion (insertion) detecting codes with a better rate. One of the limitations of number-theoretic code constructions intended to correct insertion/deletion errors, e.g., the Levenshtein code, is that they require received codeword boundaries to be known in order to successfully decode. In literature, a number of schemes have been proposed to deal with this problem. We show how insertion/deletion detecting codes as presented in this paper can be used to improve and/or extend some of these schemes.