Gold code

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 2 n + 1 sequences each one with a period of 2 n − 1. A set of Gold codes can be generated with the following steps. Pick two maximum-length sequences of the same length 2 n − 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 2 n − 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 2 n + 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. Gold codes are used in GPS. The GPS C/A ranging codes are Gold codes of period 1,023.

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 2 n + 1 sequences each one with a period of 2 n − 1. A set of Gold codes can be generated with the following steps. Pick two maximum-length sequences of the same length 2 n − 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 2 n − 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 2 n + 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. Gold codes are used in GPS. The GPS C/A ranging codes are Gold codes of period 1,023. ==See also== Hadamard code Hamming code JPL code Kasami code Zadoff–Chu sequence Complementary sequences Space Network – a NASA system that uses Gold codes ==References== ==Further reading== (xii+201+1 pages) (xiv+225 pages) de:Linear rückgekoppeltes Schieberegister#Gold-Folgen

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