A Gold code, also known as Gold sequence, is a type of binary
sequence
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called ''elements'', or ''terms''). The number of elements (possibly infinite) is cal ...
, used in
telecommunications
Telecommunication, often used in its plural form or abbreviated as telecom, is the transmission of information over a distance using electronic means, typically through cables, radio waves, or other communication technologies. These means of ...
(
CDMA
Code-division multiple access (CDMA) is a channel access method used by various radio communication technologies. CDMA is an example of multiple access, where several transmitters can send information simultaneously over a single communicatio ...
)
and satellite navigation (
GPS).
Gold codes are named after Robert Gold.
Gold codes have bounded small
cross-correlation
In signal processing, cross-correlation is a measure of similarity of two series as a function of the displacement of one relative to the other. This is also known as a ''sliding dot product'' or ''sliding inner-product''. It is commonly used f ...
s 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
In signal processing, cross-correlation is a measure of similarity of two series as a function of the displacement of one relative to the other. This is also known as a ''sliding dot product'' or ''sliding inner-product''. It is commonly used f ...
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
Exclusive or, exclusive disjunction, exclusive alternation, logical non-equivalence, or logical inequality is a logical operator whose negation is the logical biconditional. With two inputs, XOR is true if and only if the inputs differ (on ...
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.
See also
*
Hadamard code
The Hadamard code is an error-correcting code named after the French mathematician Jacques Hadamard that is used for error detection and correction when transmitting messages over very noisy or unreliable channels. In 1971, the code was used ...
*
JPL code
*
Kasami code
Kasami sequences are binary sequences of length where is an even integer. Kasami sequences have good cross-correlation values approaching the Welch lower bound. There are two classes of Kasami sequences—the small set and the large set.
Kasami ...
*
Zadoff–Chu sequence
A Zadoff–Chu (ZC) sequence is a complex-valued mathematical sequence which, when applied to a signal, gives rise to a new signal of constant amplitude. When cyclically shifted versions of a Zadoff–Chu sequence are imposed upon a signal the r ...
*
Complementary sequences
: ''For complementary sequences in biology, see complementarity (molecular biology). For integer sequences with complementary sets of members see Lambek–Moser theorem.''
In applied mathematics, complementary sequences (CS) are pairs of sequences ...
*
Space Network
Space Network (SN) is a NASA program that combines space and ground elements to support spacecraft communications in Earth vicinity. The SN Project Office at Goddard Space Flight Center (GSFC) manages the SN, which consists of:
* The geosynchr ...
– a NASA system that uses Gold codes
References
Further reading
*
* (xii+201+1 pages)
* (xiv+225 pages)
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