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 data storage. Codes are stud ...

, especially in

telecommunication Telecommunication is the transmission of information by various types of technologies over wire, radio, optical, or other electromagnetic systems. It has its origin in the desire of humans for communication over a distance greater than that fe ...

s, a self-synchronizing code is a

uniquely decodable code In coding theory a variable-length code is a code which maps source symbols to a ''variable'' number of bits. Variable-length codes can allow sources to be compressed and decompressed with ''zero'' error (lossless data compression) and still be ...

in which the

symbol A symbol is a mark, sign, or word that indicates, signifies, or is understood as representing an idea, object, or relationship. Symbols allow people to go beyond what is known or seen by creating linkages between otherwise very different conc ...

stream formed by a portion of one

code word In communication, a code word is an element of a standardized code or protocol. Each code word is assembled in accordance with the specific rules of the code and assigned a unique meaning. Code words are typically used for reasons of reliability, ...

, 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 in the system that is a prefix (initial segment) of any other code word in the system. It is trivially t ...

, but not all prefix codes are self-synchronizing. Other terms for self-synchronizing code are synchronized codeBerstel et al (2010) p. 137 or, ambiguously, comma-free code.Berstel & Perrin (1985) p. 377 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 of an orchestra keeps the orchestra synchronized or ''in time''. Systems that operate with all parts in synchrony are said to be synchronou ...

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 The bit is the most basic unit of information in computing and digital communications. The name is a portmanteau of binary digit. The bit represents a logical state with one of two possible values. These values are most commonly represente ...

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 transmission and data reception or, more broadly, data communication or digital communications is the transfer and reception of data in the form of a digital bitstream or a digitized analog signal transmitted over a point-to-point o ...

. Self-synchronization also facilitates some cases of

data recovery In computing, data recovery is a process of retrieving deleted, inaccessible, lost, corrupted, damaged, or formatted data from secondary storage, removable media or files, when the data stored in them cannot be accessed in a usual way. The dat ...

, for example of a digitally encoded text.

Examples

* The prefix code is self-synchronizing because 0, 1, 01 and 10 are not codes. *

UTF-8 UTF-8 is a variable-width encoding, variable-length character encoding used for electronic communication. Defined by the Unicode Standard, the name is derived from ''Unicode'' (or ''Universal Coded Character Set'') ''Transformation Format 8-bit'' ...

is self-synchronizing because its leading (11xxxxxx) and trailing (10xxxxxx) bytes have different bit patterns. *

High-Level Data Link Control High-Level Data Link Control (HDLC) is a bit-oriented code-transparent synchronous data link layer protocol developed by the International Organization for Standardization (ISO). The standard for HDLC is ISO/IEC 13239:2002. HDLC provides both c ...

(HDLC) *

Advanced Data Communication Control Procedures In telecommunication, Advanced Data Communication Control Procedures (or Protocol) (ADCCP) is a bit-oriented data link layer protocol developed by the American National Standards Institute. It is functionally equivalent to the ISO High-Level Data ...

(ADCCP) *

Fibonacci coding In mathematics and computing, Fibonacci coding is a universal code which encodes positive integers into binary code words. It is one example of representations of integers based on Fibonacci numbers. Each code word ends with "11" and contains no ...

Counterexamples: * The prefix code is not self-synchronizing because ''abab'' contains ''ba''. * The prefix code ''b''^∗a (using the

Kleene star In mathematical logic and computer science, the Kleene star (or Kleene operator or Kleene closure) is a unary operation, either on sets of strings or on sets of symbols or characters. In mathematics, it is more commonly known as the free monoid c ...

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

References

* * * Line codes Synchronization {{telecomm-stub

Examples

See also

References