Pseudorandom binary sequence
Encyclopedia
A binary sequence
(BS) is a sequence of
bits,
for 
,
i.e.
ones and 
zeros. A BS is pseudo-random
(PRBS) if its autocorrelation function:
has only two values:
where
is called the duty cycle of the PRBS.
A PRBS is random in a sense that the value of an
element is independent of the values of any of the other elements, similar to real random sequences.
It is 'pseudo' because it is deterministic and after
elements it starts to repeat itself, unlike real random sequences, such as sequences generated by radioactive decay
or by white noise. The PRBS is more general than the n-sequence, which is a special pseudo-random binary sequence of n bits generated as the output of a linear shift register. An n-sequence always has a 1/2 duty cycle and its number of elements
. PRBS's are used in telecommunication
, encryption
, simulation
, correlation
technique and time-of-flight spectroscopy
.
s.
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...
(BS) is a sequence of
bits, for ,i.e.
ones and zeros. A BS is pseudo-randomPseudorandomness
A pseudorandom process is a process that appears to be random but is not. Pseudorandom sequences typically exhibit statistical randomness while being generated by an entirely deterministic causal process...
(PRBS) if its autocorrelation function:
has only two values:
where
is called the duty cycle of the PRBS.
A PRBS is random in a sense that the value of an
element is independent of the values of any of the other elements, similar to real random sequences.It is 'pseudo' because it is deterministic and after
elements it starts to repeat itself, unlike real random sequences, such as sequences generated by radioactive decayRadioactive decay
Radioactive decay is the process by which an atomic nucleus of an unstable atom loses energy by emitting ionizing particles . The emission is spontaneous, in that the atom decays without any physical interaction with another particle from outside the atom...
or by white noise. The PRBS is more general than the n-sequence, which is a special pseudo-random binary sequence of n bits generated as the output of a linear shift register. An n-sequence always has a 1/2 duty cycle and its number of elements
. PRBS's are used in telecommunicationTelecommunication
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...
, encryption
Encryption
In cryptography, encryption is the process of transforming information using an algorithm to make it unreadable to anyone except those possessing special knowledge, usually referred to as a key. The result of the process is encrypted information...
, simulation
Simulation
Simulation is the imitation of some real thing available, state of affairs, or process. The act of simulating something generally entails representing certain key characteristics or behaviours of a selected physical or abstract system....
, correlation
Correlation
In statistics, dependence refers to any statistical relationship between two random variables or two sets of data. Correlation refers to any of a broad class of statistical relationships involving dependence....
technique and time-of-flight spectroscopy
Spectroscopy
Spectroscopy is the study of the interaction between matter and radiated energy. Historically, spectroscopy originated through the study of visible light dispersed according to its wavelength, e.g., by a prism. Later the concept was expanded greatly to comprise any interaction with radiative...
.
Practical implementation
Pseudorandom binary sequences can be generated using linear feedback shift registerLinear 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...
s.
See also
- Pseudorandom number generatorPseudorandom number generatorA pseudorandom number generator , also known as a deterministic random bit generator , is an algorithm for generating a sequence of numbers that approximates the properties of random numbers...
- Gold codeGold codeA Gold code, also known as Gold sequence, is a type of binary sequence, used in telecommunication and satellite navigation . 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...
- 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...
- Bit Error Rate Test