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Self-synchronizing code

From Wikipedia, the free encyclopedia

Type of code in coding theory

Not to be confused withSelf-clocking signal orSelf-similar process.

Incoding theory, especially intelecommunications, aself-synchronizing code is auniquely decodable code in which thesymbol stream formed by a portion of onecode 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 aprefix code, but not all prefix codes are self-synchronizing.

Other terms for self-synchronizing code aresynchronized code[2] or, ambiguously,comma-free code.[3] A self-synchronizing code permits the properframing of transmitted code words provided that no uncorrected errors occur in thesymbol stream; externalsynchronization is not required. Self-synchronizing codes also allow recovery from uncorrected errors in the stream; with most prefix codes, an uncorrected error in a singlebit may propagate errors further in the stream and make the subsequent datacorrupted.

Importance of self-synchronizing codes is not limited todata transmission. Self-synchronization also facilitates some cases ofdata recovery, for example of adigitally 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 becauseabab containsba.
  • The prefix codeba (using theKleene star) is not self-synchronizing (even though any new code word simply starts aftera) because code wordba contains code worda.

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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