Gold code
Encyclopedia
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
sequences each one with a period of 
.
A set of Gold codes can be generated with the following steps. Pick two maximum length sequence
s of the same length
such that their absolute cross-correlation
is less than or equal to
, where 
is the size of the LFSR
used to generate the maximum length sequence (Gold '67). The set of the
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 
for even 
and 
for odd 
.
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.
Sequence
In mathematics, a sequence is an ordered list of objects . Like a set, it contains members , and the number of terms is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence...
, used in telecommunication
Telecommunication
Telecommunication is the transmission of information over significant distances to communicate. In earlier times, telecommunications involved the use of visual signals, such as beacons, smoke signals, semaphore telegraphs, signal flags, and optical heliographs, or audio messages via coded...
(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
sequences each one with a period of .A set of Gold codes can be generated with the following steps. Pick two maximum length sequence
Maximum length sequence
A maximum length sequence is a type of pseudorandom binary sequence.They are bit sequences generated using maximal linear feedback shift registers and are so called because they are periodic and reproduce every binary sequence that can be reproduced by the shift registers...
s of the same length
such that their absolute cross-correlationCross-correlation
In signal processing, cross-correlation is a measure of similarity of two waveforms as a function of a time-lag applied to one of them. This is also known as a sliding dot product or sliding inner-product. It is commonly used for searching a long-duration signal for a shorter, known feature...
is less than or equal to
, where is the size of the LFSRLinear feedback shift register
A linear feedback shift register is a shift register whose input bit is a linear function of its previous state.The most commonly used linear function of single bits is XOR...
used to generate the maximum length sequence (Gold '67). The set of the
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 for even and for odd .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 codeKasami codeKasami sequences are binary sequences of length 2N-1 where N 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....
- Complementary sequencesComplementary sequencesIn applied mathematics, complementary sequences are pairs of sequences with the useful property that their out-of-phase aperiodic autocorrelation coefficients sum to zero. Binary complementary sequences were first introduced by Marcel J. E. Golay in 1949...
- Space NetworkSpace NetworkSpace Network 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 manages the SN, which consists of:...
- a NASA system that uses Gold codes