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A Gold code, also known as Gold sequence, is a type of binary sequence, used in telecommunications (CDMA)<ref name="George-Hamid-Miller_2008"/> and satellite navigation (GPS).<ref name="GPS_2009"/> Gold codes are named after Robert Gold.<ref name="Gold_2011"/><ref name="Gold_1967"/> 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 balancedTemplate:Spaced ndashthe number of ones and zeros differs by only one.<ref name="Holmes_2007"/>
Gold codes are used in GPS. The GPS C/A ranging codes are Gold codes of period 1,023.
See alsoEdit
- Hadamard code
- JPL code
- Kasami code
- Zadoff–Chu sequence
- Complementary sequences
- Space Network – a NASA system that uses Gold codes
ReferencesEdit
Further readingEdit
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