Coding for the correction of synchronization errors

Synchronisation is often assumed by the information engineer when working with data. However, diverse systems such as magnetic and optic storage systems, semiconductor devices as well as communication networks are affected by uncertainties in timing. This timing noise introduces or removes spurious symbols in the symbol stream, known as insertion or deletion errors. These errors differ from additive errors and erasure errors in that both the position and value of the error must be determined before correction can take place. In this seminar a brief survey of previous work in synchronization error correction coding is given. We start by introducing definitions for different synchronization errors, followed by definitions for synchronization error correction. The foundation for correcting synchronization errors provided by VI Levenshtein is then discussed. We finally present a general construction of binary algebraic block codes for the correction of multiple random insertion/deletion errors. The talk is concluded with some open problems and possible novel applications of synchronization error correction adjacent to the field of Network Coding. Synchronization error correcting coding is seldom mentioned in literature, due to the lack of understanding of the theory of synchronization channels as well as a lack of adequate mathematical models for this class of errors. This seminar should be of interest to anyone that haven’t come across these codes before and aims to stimulate interest in this research field. Biography Albert Helberg obtained the B.Eng (Cum Laude 1989), M.Eng (Cum Laude 1991) and D.Eng (1993) degrees in electronic engineering from the Rand Afrikaans University, South Africa. After spending time in industry, Albert was appointed at the North-West University in 2001 as professor. Prof. Albert Helberg is currently the research team leader in the TeleNet research group of the Telkom CoE at the North-West University and has filled several management positions in the Faculty, including Director of the School of Electrical, Electronic and Computer Engineering (2002-2006), Director Quality and Teaching (2007-2008) as well as Acting Dean of the Faculty of Engineering (2009). His personal research interests include digital coding techniques for error correction. ** ALL ARE WELCOME ** Host: Professor Raymond W.H.Yeung (Tel: 2609-8375, Email: whyeung@ie.cuhk.edu.hk) Enquiries: Information Engineering Dept., CUHK (Tel.: 2609-8388)

[1]  Lorenzo Calabi,et al.  A family of codes for the correction of substitution and synchronization errors , 1969, IEEE Trans. Inf. Theory.

[2]  J. Luetchford,et al.  Synchronization of a Digital Network , 1980, IEEE Trans. Commun..

[3]  Frederick F. Sellers,et al.  Bit loss and gain correction code , 1962, IRE Trans. Inf. Theory.

[4]  Shimon Even,et al.  On synchronizable and PSK-synchronizable block codes , 1964, IEEE Trans. Inf. Theory.

[5]  W. Lindsey,et al.  Guest Editorial: Special issue on synchronization , 1980, IEEE Trans. Commun..

[6]  Paul H. Siegel,et al.  Recording codes for digital magnetic storage , 1985 .

[7]  Henk D. L. Hollmann,et al.  A relation between Levenshtein-type distances and insertion-and-deletion correcting capabilities of codes , 1993, IEEE Trans. Inf. Theory.

[8]  Stafford E. Tavares,et al.  Matrix approach to synchronization recovery for binary cyclic codes , 1969, IEEE Trans. Inf. Theory.

[9]  O. Antoine,et al.  Theory of Error-correcting Codes , 2022 .

[10]  Eiichi Tanaka,et al.  Synchronization and substitution error-correcting codes for the Levenshtein metric , 1976, IEEE Trans. Inf. Theory.

[11]  R. C. Bose,et al.  Synchronizable Error-Correcting Codes , 1967, Inf. Control..

[12]  Vladimir I. Levenshtein,et al.  Binary codes capable of correcting deletions, insertions, and reversals , 1965 .

[13]  N. J. A. Sloane,et al.  A new table of constant weight codes , 1990, IEEE Trans. Inf. Theory.

[14]  Jack J. Stiffler,et al.  Comma-free error-correcting codes , 1965, IEEE Trans. Inf. Theory.

[15]  Robert A. Scholtz Codes with synchronization capability , 1966, IEEE Trans. Inf. Theory.

[16]  Mario Blaum A (16, 9, 6, 5, 4) error-correcting DC free block code , 1988, IEEE Trans. Inf. Theory.

[17]  Masao Kasahara,et al.  Selfsynchronisable binary Reed-Solomon code , 1991 .

[18]  D. D. Mawhinney Microwave tag identification systems , 1983 .

[19]  Jeffrey D. Ullman,et al.  On the capabilities of codes to correct synchronization errors , 1967, IEEE Trans. Inf. Theory.

[20]  Selmer M. Johnson Improved asymptotic bounds for error-correcting codes , 1963, IEEE Trans. Inf. Theory.

[21]  R.A. Hauslen The promise of automatic vehicle identification , 1977, IEEE Transactions on Vehicular Technology.

[22]  Shu Lin,et al.  Error control coding : fundamentals and applications , 1983 .

[23]  J. LoCicero,et al.  Characteristics of the Hedeman H-1, H-2, and H-3 Codes , 1981, IEEE Transactions on Communications.

[24]  H. C. Ferreira Lower bounds on the minimum hamming distance achievable with runlengh constrained or DC free block codes and the synthesis of a (16,8) D min = 4 DC free block code , 1984 .

[25]  Willard L. Eastman,et al.  On the construction of comma-free codes , 1965, IEEE Trans. Inf. Theory.

[26]  Dalton Soares Arantes,et al.  On Frame Synchronization of PCM Systems , 1980, IEEE Trans. Commun..

[27]  Jae-Kyoon Kim,et al.  A Condition for Stable Minimum-Bandwidth Line Codes , 1985, IEEE Trans. Commun..

[28]  P. Nowosad,et al.  Phase deviations on SDH and SDH/PDH interface , 1993, 1993 IEEE South African Symposium on Communications and Signal Processing.

[29]  Jeffrey D. Ullman,et al.  Near-optimal, single-synchronization-error-correcting code , 1966, IEEE Trans. Inf. Theory.

[30]  T. R. N. Rao,et al.  On the theory of Binary Asymmetric Error Correcting Codes , 1979, Inf. Control..

[31]  Hendrik C. Ferreira,et al.  Constrained codes for the correction of synchronization and additive errors , 1993, 1993 IEEE South African Symposium on Communications and Signal Processing.

[32]  Peter G. Neumann Error-limiting coding using information-lossless sequential machines , 1964, IEEE Trans. Inf. Theory.

[33]  Shih-Yung Tong Correction of synchronization errors with burst-error-correcting cyclic codes , 1969, IEEE Trans. Inf. Theory.

[34]  Robert A. Scholtz,et al.  Frame Synchronization Techniques , 1980, IEEE Trans. Commun..