Pseudorandom binary sequence
A binary sequence (BS) is a sequence of N bits, i.e. m ones and N-m zeros. A BS is pseudo-random (PRBS) if its autocorrelation function has only two values:
C(v) = m if v=0 (mod N)
C(v) = h = mc if v≠0 (mod N)
where c=(m-1)/(N-1) is called the duty cycle of the PRBS.
A PRBS defined above is random in a sense that the value of an element is independent of the values of any of the other elements. It is pseudo because it is deterministic and after N elements it starts to repeat itself. PRBS is more general than the n-sequence, which is a pseudorandom binary sequence of n bits that is the output of a linear shift register. An N-sequence always has a 1/2 duty cycle and its number of elements N = 2k -1. PRBS's are used in telecommunication, encryption, simulation, time-of-flight spectroscopy.