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 s ...
s (LFSRs) whose code sequence lengths ''L''
a and ''L''
b must be prime (
relatively prime
In mathematics, 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 equival ...
).
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 or exclusive disjunction is a logical operation that is true if and only if its arguments differ (one is true, the other is false).
It is symbolized by the prefix operator J and by the infix operators XOR ( or ), EOR, EXOR, , , ...
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 Labs, from which the name for these code sequences is derived.
Areas of application include distance measurements utilizing
spread spectrum
In telecommunication and radio communication, spread-spectrum techniques are methods by which a signal (e.g., an electrical, electromagnetic, or acoustic signal) generated with a particular bandwidth is deliberately spread in the frequency dom ...
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 (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
*
Kasami sequence
References
External links
* https://www.gps.gov/technical/icwg/
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Line codes