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][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.

This article is about binary codes used in telecommunications (CDMA) and GPS. For the authentication codes used to command a launch of nuclear weapons, see Gold Codes.

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.[5]

Gold codes are used in GPS. The GPS C/A ranging codes are Gold codes of period 1,023.

See also

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

References

1. George, M.; Hamid, M.; Miller, A. "Gold Code Generators in Virtex Devices" (PDF). Xilinx.com. Archived from the original (PDF) on July 5, 2008.
2. "Transmitted GPS Signals". The GPS System. kowoma.de. Archived from the original on 2012-08-04.
3. "Robert Gold, BS, MS, Ph.D." Robert Gold Comm Systems. 2011.
4. 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.
5. Holmes 2007, p. 100

Further reading

• 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.CS1 maint: ref=harv (link)