A binary sequence (BS) is a sequence of N bits,

a_j for j=0,1,...,N-1,

i.e. m ones and N-m zeros. A BS is pseudo-random (PRBS) if its

autocorrelation function

C(v)=\sum_{j=0}^{N-1} a_ja_{j+v}

has only two values:

C(v)= \begin{cases} m, \mbox{ if } v\equiv 0\;\; (\mbox{mod}N)\\ mc, \mbox{ otherwise } \end{cases}

where

c=\frac{m-1}{N-1}

is called the duty cycle of the PRBS.

A PRBS is random in a sense that the value of an a_j 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 N 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 N = 2^k-1. PRBS's are used in telecommunication, encryption, simulation, correlation technique and time-of-flight spectroscopy.

Practical implementation

Pseudorandom binary sequences can be generated using linear feedback shift registers. ^[1]

References

See also

• Gold code
• Complementary sequences
• Bit Error Rate Test

External links

• http://www.scriptwell.net/correlation.htm
• Free sample RTL code for PRBS 9 - PRBS 31

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