Barker-Code

The Barker code is a term used in telecommunications engineering binary code with minimum autocorrelation, which is used in the field of synchronization and radar technology. It was founded in 1953 by R. Barker developed.

Definition

The code is a sequence of N values ​​of 1 or -1 is, for a j j = 1, ..., N, so that:

Is satisfied for all 1 ≤ v < N. Alternatively, the Barker code may be expressed by the conventional technology in the digital binary values ​​0 and 1. The multiplication must then be replaced by the XOR function. It is believed that the Barker code sequence is greater than 13 do not exist with a length of N. However, there are similar code sequences, such as the Williard code, which in contrast to the Barker codes are not perfect, however, and have a high autocorrelation.

The following table contains all known Barker codes. Barker codes are perfect, with perfect means that the autocorrelation for all shifts in magnitude than 1. In the absence of displacement corresponds to the autocorrelation of the sequence length N. Trivial changes such as negations and inversions are omitted from the table:

Applications

Barker codes, refer to the wireless technology in " Direct Sequence Spread Spectrum" transmission systems and in the field of radar technology in the pulse compression process application because of their low autocorrelation. The consequences in conjunction with matched filters are used to detect the transmitted pulses with very low signal-to - noise ratio.

Applications in the field of synchronization to divide the transmitted binary payload into sections, which are provided with a frame. The recipient of such a framework must be able to reliably detect this. For frame synchronization, the so-called synchronization word is highlighted particularly strongly by using a Barker code, making it easily detectable. In this capacity, the Barker code of length 11 is for frame synchronization in the ISDN, to the Uk0 interface used. Other applications for frame synchronization are in the range of 802.11b Bluetooth or WLAN, IEEE.