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Pseudorandom binary sequence

Seemingly random, difficult to predict bit stream created by a deterministic algorithm

  • 4 min read
  • 3 chapters

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In telecommunications, pseudorandom binary sequences are known as pseudorandom noise codes (PN or PRN codes) due to their application as pseudorandom noise.

Details

A binary sequence (BS) is a sequence a0,…,aN−1 of N bits, i.e.

aj∈{0,1} for j=0,1,...,N−1.

A BS consists of m=∑aj ones and N−m zeros.

A BS is a pseudorandom binary sequence (PRBS) if its autocorrelation function, given by

C(v)=∑j=0N−1ajaj+v

has only two values:

C(v)={m, if v≡0(modN)mc, otherwise 

where

c=m−1N−1

is called the duty cycle of the PRBS, similar to the duty cycle of a continuous time signal. For a maximum length sequence, where N=2k−1, the duty cycle is 1/2.

A PRBS is 'pseudorandom', because, although it is in fact deterministic, it seems to be random in a sense that the value of an aj element is independent of the values of any of the other elements, similar to real random sequences.

A PRBS can be stretched to infinity by repeating it after N elements, but it will then be cyclical and thus non-random. 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). However, as a result of this predictability, PRBS signals can be used as reproducible patterns (for example, signals used in testing telecommunications signal paths).

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