Pseudorandom binary sequence


Pseudorandom binary sequence

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)=egin{cases}m, mbox{ if } vequiv 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. [Paul H. Bardell, William H. McAnney, and Jacob Savir, "Built-In Test for VLSI: Pseudorandom Techniques", John Wiley & Sons, New York, 1987.]

References

See also

* Gold code
* Complementary sequences
* Bit Error Rate Test

External links

* http://www.scriptwell.net/correlation.htm


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