Gold code
A Gold code, also known as Gold sequence, is a type of binary sequence, used in telecommunication (CDMA)[1] and satellite navigation (GPS).[2] Gold codes are named after Robert Gold.[3] Gold codes have bounded small cross-correlations within a set, which is useful when multiple devices are broadcasting in the same range. A set of Gold code sequences consists of 
sequences each one with a period of .
A set of Gold codes can be generated with the following steps. Pick two maximum length sequences of the same length such that their absolute cross-correlation is less than or equal to 
, where 
is the size of the LFSR used to generate the maximum length sequence (Gold '67). The set of the exclusive-ors of the two sequences in their various phases (i.e. translated into all relative positions) is a set of Gold codes. The highest absolute cross-correlation in this set of codes is 
for even and 
for odd .
The exclusive or of two 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.[4]
See also
- Kasami code
- Complementary sequences
- Space Network - a NASA system that uses Gold codes
References
- Inline references
- ^ George, M., Hamid, M., and Miller A. Gold Code Generators in Virtex DevicesPDF (126 KB)
- ^ GPS - explained (Signals)
- ^ Dr. Robert Gold
- ^ Holmes, p.100
- General references
- Gold, R. (1967), Optimal binary sequences for spread spectrum multiplexing (Corresp.), IEEE Transactions on Information Theory, 13 (4), pp. 619–621.
- Holmes, J.K. (2007), Spread Spectrum Systems for GNSS and Wireless Communications, Artech House, Norwood, ISBN 978-1-59693-083-4.
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