AGold code,also known asGold sequence,is a type of binarysequence,used intelecommunications(CDMA)[1]and satellite navigation (GPS).[2]Gold codes are named after Robert Gold.[3][4]Gold codes have bounded smallcross-correlationswithin 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 twomaximum length sequencesof the same length 2n− 1 such that their absolutecross-correlationis less than or equal to 2(n+2)/2,wherenis the size of thelinear-feedback shift registerused to generate the maximum length sequence (Gold '67). The set of the 2n− 1exclusive-orsof 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 evennand 2(n+1)/2+ 1 for oddn.
Theexclusive orof 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 inGPS.TheGPS C/Aranging codes are Gold codes of period 1,023.
See also
edit- Hadamard code
- JPL code
- Kasami code
- Zadoff–Chu sequence
- Complementary sequences
- Space Network– a NASA system that uses Gold codes
References
edit- ^George, Maria; Hamid, Mujtaba; Miller, Andy (2001-01-10)."Gold Code Generators in Virtex Devices"(PDF).Virtex Series, Virtex-II Series, and Spartan-II family(Application note). 1.1.Xilinx.XAPP217. Archived fromthe original(PDF)on 2008-07-05.(9 pages)
- ^"Transmitted GPS Signals".The GPS System.kowoma GPS. 2009-04-19. Archived fromthe originalon 2012-08-04.
- ^"Robert Gold, BS, MS, Ph.D."Robert Gold Comm Systems. 2011. Archived fromthe originalon 2017-06-24.Retrieved2008-07-18.
- ^Gold, Robert (October 1967). "Optimal binary sequences for spread spectrum multiplexing".IEEE Transactions on Information Theory(Correspondence). IT-13 (4): 619–621.doi:10.1109/TIT.1967.1054048.
- ^Holmes, Jack K. (2007-06-30).Spread Spectrum Systems for GNSS and Wireless Communications.GNSS Technology and Applications Series. Vol. 45. Artech House. p. 100.ISBN978-1-59693-083-4.
Further reading
edit- Goiser, Alois M. J. (1998). "4.3.2. Gold-Folgen" [Gold sequences].Handbuch der Spread-Spectrum Technik[Handbook of the spread-spectrum technique] (in German) (1 ed.). Vienna, Austria:Springer Verlag.ISBN3-211-83080-4.
- Skaug, Reidar; Hjelmstad, Jens F. (1985). "Coding for bandwidth spreading". In Flood, J. E.; Hughes, C. J. (eds.).Spread Spectrum in Communication.IEE Telecommunications Series. Vol. 12 (1 ed.). London, UK: Peter Peregrinus Ltd. /The Institution of Electrical Engineers.pp. 82–.ISBN0-86341-034-0.(xii+201+1 pages)
- Rudolph, Dietmar; Rudolph, Matthias (2011-04-12). "46.3.1 Gold-Codes".Modulationsverfahren(PDF)(in German). Cottbus, Germany:Brandenburg University of Technology(BTU). pp. 212–214.Archived(PDF)from the original on 2021-06-16.Retrieved2021-06-14.(xiv+225 pages)
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