# 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

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

has only two values:

:

where

:$c=frac\left\{m-1\right\}\left\{N-1\right\}$

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

* Gold code
* Complementary sequences
* Bit Error Rate Test

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

Wikimedia Foundation. 2010.

### Look at other dictionaries:

• Pseudorandom number sequence — A Pseudorandom number sequence is a sequence of numbers that has been computed by some defined arithmetic process but is effectively a random number sequence for the purpose for which it is required. Although a pseudorandom number sequence in… …   Wikipedia

• Pseudorandom number generator — A pseudorandom number generator (PRNG), also known as a deterministic random bit generator (DRBG),[1] is an algorithm for generating a sequence of numbers that approximates the properties of random numbers. The sequence is not truly random in… …   Wikipedia

• Pseudorandom noise — In cryptography, pseudorandom noise (PRN[1][2]) is a signal similar to noise which satisfies one or more of the standard tests for statistical randomness. Although it seems to lack any definite pattern, pseudorandom noise consists of a… …   Wikipedia

• Maximum length sequence — A maximum length sequence (MLS) is a type of pseudorandom binary sequence. They are bit sequences generated using maximal linear feedback shift registers and are so called because they are periodic and reproduce every binary sequence that can be… …   Wikipedia

• Maximum length sequence — Une maximum length sequence (MLS) est une pseudorandom binary sequence (en) (PRBS) c est à dire une suite périodique de valeurs produite par un linear feedback shift register (LFSR) qui explore toutes les valeurs pouvant être produites par… …   Wikipédia en Français

• M-sequence — An M sequence may refer to: *Regular sequence, which is an important topic in commutative algebra. *A maximum length sequence, which is a type of pseudorandom binary sequence …   Wikipedia

• Cryptographically secure pseudorandom number generator — A cryptographically secure pseudo random number generator (CSPRNG) is a pseudo random number generator (PRNG) with properties that make it suitable for use in cryptography. Many aspects of cryptography require random numbers, for example: Key… …   Wikipedia

• PRBS — pseudorandom binary sequence …   Military dictionary

• PRBS — pseudorandom binary sequence …   Medical dictionary

• PRBS — • pseudorandom binary sequence …   Dictionary of medical acronyms & abbreviations