Gold code

{{About|binary codes used in radiocommunications|the authentication codes used to command a launch of nuclear weapons|Gold Codes}}

A Gold code, also known as Gold sequence, is a type of binary sequence, used in telecommunications (CDMA) and satellite navigation (GPS). Gold codes are named after Robert Gold. 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. 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{{spaced ndash}}the number of ones and zeros differs by only one.

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

References

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{{cite web |last1=George |first1=Maria |last2=Hamid |first2=Mujtaba |last3=Miller |first3=Andy |title=Gold Code Generators in Virtex Devices |type=Application note |publisher=Xilinx |id=XAPP217 |version=1.1 |work=Virtex Series, Virtex-II Series, and Spartan-II family |date=2001-01-10 |url=http://www.xilinx.com/support/documentation/application_notes/xapp217.pdf |url-status=dead |archive-url=https://web.archive.org/web/20080705134550/http://www.xilinx.com/support/documentation/application_notes/xapp217.pdf |archive-date=2008-07-05}} (9 pages)

{{cite web |title=Transmitted GPS Signals |date=2009-04-19 |work=The GPS System |publisher=kowoma GPS |url=http://www.kowoma.de/en/gps/signals.htm |archive-url=https://archive.today/20120804185510/http://www.kowoma.de/en/gps/signals.htm |url-status=dead |archive-date=2012-08-04}}

{{cite web |title=Robert Gold, BS, MS, Ph.D. |date=2011 |publisher=Robert Gold Comm Systems |url=http://www.rgcsystems.com/ppl1_gold.htm |access-date=2008-07-18 |archive-date=2017-06-24 |archive-url=https://web.archive.org/web/20170624101852/http://www.rgcsystems.com/ppl1_gold.htm |url-status=dead }}

{{cite journal |author-last=Gold |author-first=Robert |title=Optimal binary sequences for spread spectrum multiplexing |type=Correspondence |journal=IEEE Transactions on Information Theory |volume=IT-13 |issue=4 |pages=619–621 |date=October 1967 |doi=10.1109/TIT.1967.1054048}}

{{cite book |first=Jack K. |last=Holmes |title=Spread Spectrum Systems for GNSS and Wireless Communications |url=https://books.google.com/books?id=-AUfAQAAIAAJ |date=2007-06-30 |publisher=Artech House |isbn=978-1-59693-083-4 |volume=45 |series=GNSS Technology and Applications Series |page=100}}

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Gold code

See also

References

Further reading