Insertion/Deletion Detecting Codes and the Boundary Problem

• Published in: IEEE transactions on information theory Vol. 59; no. 9; pp. 5935 - 5943
• Main Authors: Paluncic, Filip, Abdel-Ghaffar, Khaled A. S., Ferreira, Hendrik C.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.09.2013; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Codes; Codeword boundary; Coding theory; Decoding; Delays; Exact sciences and technology; Indexes; Information theory; Information, signal and communications theory; insertion/deletion detection; Number theory; Receivers; Synchronization; systematic codes; Systematics; Telecommunications and information theory; Vectors; insertion/deletion detection; Codeword boundary; Error correction; systematic codes; Number theory
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2013.2264825

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.