A pseudorandom binary sequence (PRBS), pseudorandom binary code or pseudorandom bitstream is a binary sequence that, while generated with a deterministic algorithm, is difficult to predict[1] and exhibits statistical behavior similar to a truly random sequence.
PRBS generators are used in telecommunication, such as in analog-to-information conversion,[2] but also in encryption, simulation, correlation technique and time-of-flight spectroscopy.
The most common example is the maximum length sequence generated by a (maximal) linear feedback shift register (LFSR).
In telecommunications, pseudorandom binary sequences are known as pseudorandom noise codes (PN or PRN codes) due to their application as pseudorandom noise.
A BS is a pseudorandom binary sequence (PRBS) if[3] its autocorrelation function, given by has only two values: where is called the duty cycle of the PRBS, similar to the duty cycle of a continuous time signal.
A PRBS is 'pseudorandom', because, although it is in fact deterministic, it seems to be random in a sense that the value of an
A PRBS can be stretched to infinity by repeating it after
In contrast, truly random sequence sources, such as sequences generated by radioactive decay or by white noise, are infinite (no pre-determined end or cycle-period).
[4] Pseudorandom binary sequences can be generated using linear-feedback shift registers.
[5] Some common[6][7][8][9][10] sequence generating monic polynomials are An example of generating a "PRBS-7" sequence can be expressed in C as In this particular case, "PRBS-7" has a repetition period of 127 values.
The PRBSk or PRBS-k notation (such as "PRBS7" or "PRBS-7") gives an indication of the size of the sequence.
is the maximum number[4]: §3 of bits that are in the sequence.
The k indicates the size of a unique word of data in the sequence.
possible non-zero 3-bit binary words, not in numeric order.