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Not to be confused with Self-clocking signal or Self-similar process.

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

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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

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References

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  1. ^ "Self-synchronizing code – Glossary".
  2. ^ 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.
  3. ^ Berstel, Jean; Perrin, Dominique (1985). Theory of Codes. Pure and Applied Mathematics. Vol. 117. Academic Press. p. 377. Zbl 0587.68066.

Further reading

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📚 Artikel Terkait di Wikipedia

Prefix code

Fibonacci coding uses a 11 to mark the end of every code word. Self-synchronizing codes are prefix codes that allow frame synchronization. A suffix code is a

Comma-free code

codes are also known as self-synchronizing block codes because no synchronization is required to find the beginning of a code word. In the literature, the

Syncword

communications. Prefix codes allow unambiguous identification of synchronization sequences and may serve as self-synchronizing code. In an audio receiver

Code point

from one to four bytes long, forming a self-synchronizing code. See comparison of Unicode encodings for details. Code points are normally assigned to abstract

Self-clocking signal

bits and decide which bit is the first bit of a byte, often a self-synchronizing code is used. Amplitude modulation – modulating a signal M ( t ) {\displaystyle

UTF-16

surrogate code points. (Any scheme that remains a self-synchronizing code would require allocating at least one Basic Multilingual Plane (BMP) code point

Line code

(TS-FO) Physical layer Self-synchronizing code and bit synchronization K. Schouhamer Immink (2022). "Innovation in Constrained Codes". IEEE Communications

Frame synchronization

frequently than every frame. Asynchronous start-stop Phase synchronization Self-synchronizing code Superframe Simpson, William A. (July 1994). PPP in HDLC-like