coding theory Coding theory is the study of the properties of codes and their respective fitness for specific applications. Codes are used for data compression, cryptography, error detection and correction, data transmission and computer data storage, data sto ...

, especially in

telecommunications Telecommunication, often used in its plural form or abbreviated as telecom, is the transmission of information over a distance using electronic means, typically through cables, radio waves, or other communication technologies. These means of ...

, a self-synchronizing code is a uniquely decodable code in which the

symbol A symbol is a mark, Sign (semiotics), sign, or word that indicates, signifies, or is understood as representing an idea, physical object, object, or wikt:relationship, relationship. Symbols allow people to go beyond what is known or seen by cr ...

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. Every self-synchronizing code is a

prefix code A prefix code is a type of code system distinguished by its possession of the prefix property, which requires that there is no whole Code word (communication), code word in the system that is a prefix (computer science), prefix (initial segment) of ...

, but not all prefix codes are self-synchronizing. Other terms for self-synchronizing code are synchronized code or, ambiguously, comma-free code. A self-synchronizing code permits the proper framing of transmitted code words provided that no uncorrected errors occur in the symbol stream; external

synchronization Synchronization is the coordination of events to operate a system in unison. For example, the Conductor (music), conductor of an orchestra keeps the orchestra synchronized or ''in time''. Systems that operate with all parts in synchrony are sa ...

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 Data communication, including data transmission and data reception, is the transfer of data, signal transmission, transmitted and received over a Point-to-point (telecommunications), point-to-point or point-to-multipoint communication chann ...

. Self-synchronization also facilitates some cases of data recovery, for example of a digitally encoded text.

Examples

UTF-8 UTF-8 is a character encoding standard used for electronic communication. Defined by the Unicode Standard, the name is derived from ''Unicode Transformation Format 8-bit''. Almost every webpage is transmitted as UTF-8. UTF-8 supports all 1,112,0 ...

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 is not self-synchronizing; while 0, 1, 01 and 10 are not codes, 00 and 11 are. * The prefix code is not self-synchronizing because ''abab'' contains ''ba''. * The prefix code ''b''^∗a (using the

Kleene star In mathematical logic and theoretical computer science, the Kleene star (or Kleene operator or Kleene closure) is a unary operation on a Set (mathematics), set to generate a set of all finite-length strings that are composed of zero or more repe ...

) is not self-synchronizing (even though any new code word simply starts after ''a'') because code word ''ba'' contains code word ''a''.

Examples

See also

References

Further reading