Barker code

In telecommunication technology, a Barker code or Barker sequence is a finite sequence of digital values with the ideal autocorrelation property. It is used as a synchronising pattern between the sender and receiver of a stream of bits. Apart from the trivial sequence of length 1, the known Barker sequences have lengths 2, 3, 4, 5, 7, 11 and 13. It is conjectured that no longer sequence exists; this is proved for odd lengths, while the possible existence of an even Barker sequence longer than 4 remains open. A stream of binary digits carries no timing information by itself: the receiver cannot tell where one group of digits ends and the next begins. Transmitting a pre-arranged pattern of digits resolves this, provided the receiver can recognise that pattern reliably. In simple terms it is equivalent to attaching a label to one digit, after which the positions of the remaining digits follow by counting. Such a pattern is useful only if it is unlikely to be imitated by the surrounding data or by noise, and if a partial overlap between the received signal and the stored pattern gives a much weaker response than exact alignment. The relevant measure is the pattern's autocorrelation: the correlation of the pattern with a shifted copy of itself should be large at zero shift and small at every other shift, so that a correlator or matched filter in the receiver produces a sharp, unambiguous indication of the correct position. Barker sequences are the binary patterns for which these off-peak values are as small as possible; they are named after Ronald Hugh Barker, who set out this requirement for group synchronisation in 1953.