Self-synchronizing code

Not to be confused with self-clocking signal.

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. 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.

Synonym for self-synchronizing code are synchronized code or comma-free code. However, sometimes the term comma-free code is used in the meaning of prefix code. The latter is a broader concept: every self-synchronizing code is a prefix code, but not all prefix codes are self-synchronizing.

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 unreadable.

Synchronizing word

A code X over an alphabet A has a synchronizing word w in A⁺ if

$xwy\in X^{*}\Rightarrow xw,wy\in X^{*}\ .$

A prefix code is synchronized if and only if it has a synchronizing word.

Examples

• The prefix code {ab,ba} has abba as a synchronizing word.
• The prefix code b^∗a has a as a synchronizing word.

Examples

• High-Level Data Link Control (HDLC)
• Advanced Data Communication Control Procedures (ADCCP)
• UTF-8

See also

• Bit slip
• Self-clocking signal

References

• 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. Archived from the original on 2022-01-22. (in support of MIL-STD-188).