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. 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.
Contents
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 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.
Synchronizing word
A code X over an alphabet A has a synchronizing word (aka "syncword") w in A+ if
x w y ∈ X * ⇒ {x w, w y} ⊆ X * .A prefix code is synchronized if and only if it has a synchronizing word.
Examples
Let's now assume that four letters (two code words) are read. The code 1000 is not a valid code, because 10 is not one of the two code words defined. Similarly, 0001. Even though 00 is a valid word, 01 is not. The only valid way to read two valid words from the example given is by starting at the very beginning, or just after one of the spaces (which have been inserted for clarity only).
Examples
0xxxxxxx and 11xxxxxx are synchronizing words used to mark the beginning of the next valid character