# 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:

:$C(v)=egin\{cases\}m,\; mbox\{\; if\; \}\; vequiv\; 0;;\; (mbox\{mod\}N)\backslash \; mc,\; mbox\{\; otherwise\; \}end\{cases\}$

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 then-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 intelecommunication ,encryption ,simulation ,correlation technique and time-of-flightspectroscopy .**Practical implementation**Pseudorandom binary sequences can be generated using

linear feedback shift register s. [*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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