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 the leading byte (
11xxxxxx) and subsequent bytes (10xxxxxx) of a multi-byte code point 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
References
- ↑ "Self-synchronizing code – Glossary".
- ↑ Berstel, Jean; Perrin, Dominique; Reutenauer, Christophe (2010). Codes and automata. Encyclopedia of Mathematics and its Applications. Vol. 129. Cambridge, UK: Cambridge University Press. p. 137. ISBN 978-0-521-88831-8. Zbl 1187.94001.
- ↑ Berstel, Jean; Perrin, Dominique (1985). Theory of Codes. Pure and Applied Mathematics. Vol. 117. Academic Press. p. 377. Zbl 0587.68066.
Further reading
- "self-synchronizing code". Federal Standard 1037C: Telecommunications: Glossary of Telecommunication Terms. General Services Administration. 1996-08-06. Archived from the original on 2022-01-22.
- MIL-STD-188