Self-synchronizing code
In today's world, Self-synchronizing code has become a relevant topic of great interest to a wide audience. The impact of Self-synchronizing code has been felt in different areas of society, from politics to culture, economics and technology. Its influence has no limits and its presence becomes increasingly evident in everyday life. In this article, we will thoroughly explore the phenomenon of Self-synchronizing code and analyze its implications in today's society.
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
- 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 {00, 11} is not self-synchronizing; while 0, 1, 01 and 10 are not codes, 00 and 11 are.
- 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
- Consistent overhead byte stuffing
- Dynkin sequence
- Kraus principle
- Kruskal's principle
- Overlapping instructions
- Pollard's lambda method
- Self-clocking signal
- Self-synchronizing block code
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