Partial-prefix synchronizable codes

A new class of codes for frame synchronization is proposed. Commonly, the beginning of every fixed or variable-length frame is identified by a given contiguous sequence called a prefix. To avoid the occurrence of the prefix elsewhere in the frame, a prefix synchronizable code (PS-code) is used. PS-codes have the property that the prefix does not occur in any codeword or in any concatenation of codewords in any position other than the first position. The new codes, termed partial-prefix synchronizable codes (PPS-codes), use a fixed sequence of symbols that is interspersed with symbols that carry information. The contiguous sequence from the first fixed symbol to the last fixed symbol is called a "partial-prefix." Consequently, not one but a set of possible prefixes is used, and none of these prefixes is allowed to occur at any other than the first position of a codeword. The cardinality of PPS-codes is determined, and coding algorithms are proposed which have a computational complexity proportional to the length of the codewords. It is demonstrated that in comparison with PS-codes, PPS-codes have similar coding and prefix detection complexity, but they have a larger code size and have better error control capabilities.