Barker code
The Barker code is a binary code used in communications technology with minimal autocorrelation , which is used in the field of synchronization and radar technology . It was developed by RH Barker in 1953.
definition
The code represents a sequence of N values a j = ± 1 with j = 1, ..., N , whose autocorrelation with the sequence shifted by v for all 1 ≤ v < N results in the inequality
Fulfills. Alternatively, the Barker code can also be expressed using the binary values 0 and 1 that are common in digital technology . The multiplication must then be replaced by the XOR function and the calculation of the autocorrelation adapted accordingly.
It is assumed that Barker code sequences with a length N greater than 13 do not exist. However, there are similar code sequences, e.g. B. the Williard code , which, in contrast to the Barker codes, are not perfect and have a higher autocorrelation.
The following table contains all known Barker codes. Barker codes are perfect, where perfect means that the autocorrelation is a maximum of 1 for all shifts. If there is no shift, the autocorrelation corresponds to the length N of the sequence. Trivial adjustments such as negations and inversions are left out in the table:
| length | Code sequence | Side lobe [dB] |
|
|---|---|---|---|
| 2 | +1 −1 | +1 +1 | −6 |
| 3 | +1 +1 −1 | −9.5 | |
| 4th | +1 −1 +1 +1 | +1 −1 −1 −1 | −12 |
| 5 | +1 +1 +1 −1 +1 | −14 | |
| 7th | +1 +1 +1 −1 −1 +1 −1 | −16.9 | |
| 11 | +1 +1 +1 −1 −1 −1 +1 −1 −1 +1 −1 | −20.8 | |
| 13 | +1 +1 +1 +1 +1 −1 −1 +1 +1 −1 +1 −1 +1 | −22.3 | |
Applications
Because of their low autocorrelation, Barker codes are used in radio technology for “ Direct Sequence Spread Spectrum ” transmission systems and in the field of radar technology for pulse compression . In connection with optimal filters , the sequences are used to detect transmission pulses with a very low signal-to-noise ratio .
Applications in the field of synchronization subdivide the binary user data to be transmitted into sections which are provided with a frame. The recipient of such a frame must be able to reliably recognize it. For frame synchronization, the so-called synchronization word is emphasized particularly strongly by using a Barker code and is therefore easy to detect. In this capacity, the Barker code of length 11 is used for frame synchronization in the ISDN on the UK0 interface . Further applications for frame synchronization are in the area of Bluetooth or WLAN according to IEEE 802.11b.
Individual evidence
- ^ RH Barker: Group Synchronizing of Binary Digital Sequences . Communication Theory, London 1953, pp. 273 to 287 .
- ^ D. Zwillinger: CRC Standard Mathematical Tables and Formulas . CRC Press, 1995, pp. 223 .
- ↑ Talal Darwich: Amplitude Shifting for Sidelobes Cancellation pulse compression. (No longer available online.) Center for Advanced Computer Studies University of Louisiana at Lafayette, 2006, archived from the original on September 23, 2015 ; Retrieved June 24, 2014 . Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice.
literature
- Hans Dieter Lüke : Correlation signals . Springer, Berlin 1992, ISBN 3-540-54579-4 .
Web links
- Barker code at Mathworld