Gold code
A Gold code, also known as Gold sequence, is a type of binary sequence, used in telecommunications (CDMA)[1] and satellite navigation (GPS).[2] Gold codes are named after Robert Gold.[3][4] 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.[4] 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.[5]
Gold codes are used in GPS. The GPS C/A ranging codes are Gold codes of period 1,023.
See also
[edit | edit source]- Hadamard code
- JPL code
- Kasami code
- Zadoff–Chu sequence
- Complementary sequences
- Space Network – a NASA system that uses Gold codes
References
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Further reading
[edit | edit source]- Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value).
- Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value). (xii+201+1 pages)
- Lua error in Module:Citation/CS1/Configuration at line 2172: attempt to index field '?' (a nil value). (xiv+225 pages)