Self-synchronizing code

Not to be confused with self-clocking signal.

In coding theory, especially in telecommunications, a self-synchronizing code is a uniquely decodable code in which the symbol stream formed by a portion of one code word, or by the overlapped portion of any two adjacent code words, is not a valid code word.^[1] Put another way, a set of strings (called "code words") over an alphabet is called a self-synchronizing code if for each string obtained by concatenating two code words, the substring starting at the second symbol and ending at the second-last symbol does not contain any code word as substring. Every self-synchronizing code is a prefix code, but not all prefix codes are self-synchronizing.

Other terms for self-synchronizing code are synchronized code^[2] or, ambiguously, comma-free code.^[3] A self-synchronizing code permits the proper framing of transmitted code words provided that no uncorrected errors occur in the symbol stream; external synchronization is not required. Self-synchronizing codes also allow recovery from uncorrected errors in the stream; with most prefix codes, an uncorrected error in a single bit may propagate errors further in the stream and make the subsequent data corrupted.

Importance of self-synchronizing codes is not limited to data transmission. Self-synchronization also facilitates some cases of data recovery, for example of a digitally encoded text.

Examples

• The prefix code {00, 11} is self-synchronizing because 0, 1, 01 and 10 are not codes.
• UTF-8 is self-synchronizing because its leading (11xxxxxx) and trailing (10xxxxxx) bytes have different bit patterns.
• High-Level Data Link Control (HDLC)
• Advanced Data Communication Control Procedures (ADCCP)
• Fibonacci coding

Counterexamples:

• The prefix code {ab,ba} is not self-synchronizing because abab contains ba.
• The prefix code b^∗a (using the Kleene star) is not self-synchronizing (even though any new code word simply starts after a) because code word ba contains code word a.

See also

• Bit slip
• Comma code
• Self-clocking signal
• Consistent Overhead Byte Stuffing

References

1. "Self-synchronizing code – Glossary".
2. Berstel et al (2010) p. 137
3. Berstel & Perrin (1985) p. 377

• Berstel, Jean; Perrin, Dominique (1985), Theory of Codes, Pure and Applied Mathematics, vol. 117, Academic Press, Zbl 0587.68066
• Berstel, Jean; Perrin, Dominique; Reutenauer, Christophe (2010). Codes and automata. Encyclopedia of Mathematics and its Applications. Vol. 129. Cambridge: Cambridge University Press. ISBN 978-0-521-88831-8. Zbl 1187.94001.
•   This article incorporates public domain material from Federal Standard 1037C. General Services Administration. (in support of MIL-STD-188).