JPL sequences or JPL codes consist of two
linear feedback shift register
In computing, a linear-feedback shift register (LFSR) 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 exclusive-or (XOR). Thus, an LFSR is most often a sh ...
s (LFSRs) whose code sequence lengths ''L''
a and ''L''
b must be prime (
relatively prime
In number theory, two integers and are coprime, relatively prime or mutually prime if the only positive integer that is a divisor of both of them is 1. Consequently, any prime number that divides does not divide , and vice versa. This is equiv ...
).
In this case the code sequence length of the generated overall sequence ''L''
c is equal to:
:
It is also possible for more than two LFSRs to be interconnected through multiple
XOR
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 (one ...
s at the output for as long as all code sequence lengths of the individual LFSR are relatively prime to one another.
JPL sequences were originally developed in the
Jet Propulsion Lab
The Jet Propulsion Laboratory (JPL) is a federally funded research and development center (FFRDC) in La Cañada Flintridge, California, Crescenta Valley, United States. Founded in 1936 by California Institute of Technology (Caltech) researche ...
s, from which the name for these code sequences is derived.
Areas of application include distance measurements utilizing
spread spectrum
In telecommunications, especially radio communication, spread spectrum are techniques by which a signal (electrical engineering), signal (e.g., an electrical, electromagnetic, or acoustic) generated with a particular Bandwidth (signal processi ...
signals for satellites and in space technology. They are also utilized in the more precise military
P/Y code used in the
Global Positioning System
The Global Positioning System (GPS) is a satellite-based hyperbolic navigation system owned by the United States Space Force and operated by Mission Delta 31. It is one of the global navigation satellite systems (GNSS) that provide ge ...
(GPS).
However, they are currently replaced by the new M-code.
Due to the relatively long spreading sequences, they can be used to measure relatively long ranges without ambiguities, as required for deep space missions. By having a rough synchronziation between receiver and transmitter, this can be achieved with shorter sequences as well.
Their major advantage is, that they produce relatively long sequences with only two LFSRs, which makes it energy efficient and very hard to detect due to huge spreading factor. The same structure can be used to realize a dither generator, used as an additive noise source to remove a numerical bias in digital computations (due to fixed point arithmetics, that have one more negative than positive number, i.e. the mean value is slightly negative).
See also
*
Gold sequence
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, whi ...
*
Kasami sequence
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 ...
References
External links
* https://www.gps.gov/technical/icwg/
Line codes
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