• Source: Gold code

A Gold code, also known as Gold sequence, is a type of binary sequence, used in telecommunications (CDMA) and satellite navigation (GPS). Gold codes are named after Robert Gold. Gold codes have bounded small cross-correlations within a set, which is useful when multiple devices are broadcasting in the same frequency range. A set of Gold code sequences consists of 2n + 1 sequences each one with a period of 2n − 1.
A set of Gold codes can be generated with the following steps. Pick two maximum length sequences of the same length 2n − 1 such that their absolute cross-correlation is less than or equal to 2(n+2)/2, where n is the size of the linear-feedback shift register used to generate the maximum length sequence (Gold '67). The set of the 2n − 1 exclusive-ors of the two sequences in their various phases (i.e. translated into all relative positions) together with the two maximum length sequences form a set of 2n + 1 Gold code sequences. The highest absolute cross-correlation in this set of codes is 2(n+2)/2 + 1 for even n and 2(n+1)/2 + 1 for odd n.
The exclusive or of two different Gold codes from the same set is another Gold code in some phase.
Within a set of Gold codes about half of the codes are balanced – the number of ones and zeros differs by only one.
Gold codes are used in GPS. The GPS C/A ranging codes are Gold codes of period 1,023.




See also


Hadamard code
JPL code
Kasami code
Zadoff–Chu sequence
Complementary sequences
Space Network – a NASA system that uses Gold codes




References






Further reading


Goiser, Alois M. J. (1998). "4.3.2. Gold-Folgen" [Gold sequences]. Handbuch der Spread-Spectrum Technik [Handbook of the spread-spectrum technique] (in German) (1 ed.). Vienna, Austria: Springer Verlag. ISBN 3-211-83080-4.
Skaug, Reidar; Hjelmstad, Jens F. (1985). "Coding for bandwidth spreading". In Flood, J. E.; Hughes, C. J. (eds.). Spread Spectrum in Communication. IEE Telecommunications Series. Vol. 12 (1 ed.). London, UK: Peter Peregrinus Ltd. / The Institution of Electrical Engineers. pp. 82–. ISBN 0-86341-034-0. (xii+201+1 pages)
Rudolph, Dietmar; Rudolph, Matthias (2011-04-12). "46.3.1 Gold-Codes". Modulationsverfahren (PDF) (in German). Cottbus, Germany: Brandenburg University of Technology (BTU). pp. 212–214. Archived (PDF) from the original on 2021-06-16. Retrieved 2021-06-14. (xiv+225 pages)

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