Gold code

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 Gold code, also known as Gold sequence, is a type of binary sequence, used in telecommunication (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 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 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.

See also

• Kasami code
• Complementary sequences
• Space Network - a NASA system that uses Gold codes

References

Inline references

General references

• Gold, R. (1967), Optimal binary sequences for spread spectrum multiplexing (Corresp.), IEEE Transactions on Information Theory, 13 (4), pp. 619–621.
• Holmes, J.K. (2007), Spread Spectrum Systems for GNSS and Wireless Communications, Artech House, Norwood, ISBN 978-1-59693-083-4.