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Gold code

Binary codes used in telecommunications

Binary codes used in telecommunications

Note

binary codes used in radiocommunications

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 balancedthe 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

References

  1. (2001-01-10). "Gold Code Generators in Virtex Devices". [[Xilinx]].
  2. (2009-04-19). "Transmitted GPS Signals". kowoma GPS.
  3. (2011). "Robert Gold, BS, MS, Ph.D.". Robert Gold Comm Systems.
  4. (October 1967). "Optimal binary sequences for spread spectrum multiplexing". [[IEEE Transactions on Information Theory]].
  5. Holmes, Jack K.. (2007-06-30). "Spread Spectrum Systems for GNSS and Wireless Communications". Artech House.
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