MT Generate Bits (Fibonacci, PN Order)

Generates Fibonacci pseudonoise (PN) bit sequences. The node repeats the selected pattern until it generates the number of bits that you specify. Use this node to specify a PN sequence order based on which the node selects a primitive polynomial that returns a maximal length shift register sequence, or m-sequence.

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Inputs/Outputs

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total bits

Total number of pseudorandom bits to be generated.

Default value: 128

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PN sequence order

Order of the PN bit sequence to be generated. Valid values are 5 to 31, inclusive.

Default value: 9

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seed in

Initial state of the PN generator shift register.

Default value: 169

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error in

Error conditions that occur before this node runs.

The node responds to this input according to standard error behavior.

Standard Error Behavior

Default value: No error

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reset?

A Boolean that determines whether to continue generating bits using the previous iteration states.

TRUE The PN generator has been initiated with a new PN seed.
FALSE The PN sequence generator has resumed from where it had stopped during the previous iteration.

Default value: TRUE

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output bit stream

The generated pseudorandom data bits.

If the PN sequence order is N, the output data is periodic with period T = 2N-1. For example, if N = 7, the output sequence repeats after every T = 127 bits.

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seed out

A seed for use in the seed in parameter during the next call to this node when reset? is set to FALSE.

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error out

Error information.

The node produces this output according to standard error behavior.

Standard Error Behavior

Definition of Pseudorandom Sequences

Though deterministic in nature, seudorandom or pseudonoise (PN) sequences satisfy many properties of random numbers, such as autocorrelation, crosscorrelation, and so on. PN sequences are used in many applications and standards such as 802.11a and DVB. Some examples of PN sequences are maximal length shift register sequences, or m-sequences, Gold sequences, and Kasami sequences. An m-sequence generates a periodic sequence of length

L=2m1
bits and is generated by linear feedback shift registers (LFSRs). Two well known implementations of m-sequences are the Fibonacci implementation and the Galois implementation.

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The preceding figure shows the Fibonacci and Galois implementations of m-sequences. As can be seen in these figures, m-sequences contain m shift registers. The shift register set is filled with an m-bit initial seed that can be any value except 0. If the m bits in the m shift registers are all zero, then it is a degenerate case and the output of the generator is 0.

Examples of Fibonacci and Galois Implementation of Pseudorandom Sequences

The following examples demonstrate bit generation:

  1. The first example depicts the Fibonacci implementation. This structure is used in different standards, including DVB. Inputs are specified as follows:

    Primitive polynomial:

    1+X14+X15

    Initial seed: 000000010101001

    The following figure shows the circuitry:

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    Seed Output
    0000000101010010+0=0
    0000001010100100+0=0
    0000010101001000+0=0
    0000101010010000+0=0
    0001010100100000+0=0
    0010101001000000+0=0
    0101010010000000+1=1
    1010100100000011+0=1
  2. The second example depicts the Galois implementation. Inputs are specified as follows:

    Primitive polynomial:

    1+X14+X15

    Initial seed: 000000010101001

    The circuitry is shown in the following figure:

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    Seed Output
    0000000101010010
    0000001010100100
    0000010101001000
    0000101010010000
    0001010100100000
    0010101001000000
    0101010010000000
    1010100100000001
    1101001000000011
    0010010000000110
    0100100000001100
    1001000000011001
    1010000000110011
    1100000001100111
    0000000011001110
    0000000110011100