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 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 LFSR 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) is a set of Gold codes. 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.[4]
See also
- Kasami code
- Zadoff–Chu sequence
- Complementary sequences
- Space Network – a NASA system that uses Gold codes
References
- Inline references
- ↑ George, M.; Hamid, M.; Miller, A. "Gold Code Generators in Virtex Devices" (PDF). Xilinx.com.
- ↑ "Transmitted GPS Signals". The GPS System. kowoma.de.
- ↑ "Robert Gold, BS, MS, Ph.D.". Robert Gold Comm Systems. 2011.
- ↑ Holmes 2007, p. 100
- General references
- Gold, R. (October 1967). "Optimal binary sequences for spread spectrum multiplexing (Corresp.)". IEEE Transactions on Information Theory 13 (4): 619–621. doi:10.1109/TIT.1967.1054048.
- Holmes, Jack K. (30 June 2007). Spread Spectrum Systems for GNSS and Wireless Communications. GNSS Technology and Applications Series 45. Artech House. ISBN 978-1-59693-083-4.
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