# MT Generate Bits (Fibonacci, Primitive Polynomial) (G Dataflow)

Generates Fibonacci pseudonoise (PN) bit sequences. The node repeats the selected pattern until it generates the number of total bits that you specify. Use this node to specify the primitive polynomial that determines the connection structure of the linear feedback shift register (LFSR).

## total bits

Total number of pseudorandom bits to be generated.

Default: 128

## specify primitive polynomial

The primitive polynomial for the PN bit sequence to be generated. The degree of the primitive polynomial determines the PN order.

The primitive polynomial is specified by an 8-bit signed integer array. If the degree of the primitive polynomial is N, for example, p(x) =a0 + a1x + a2x 2 +……+ a N a N , the array contains (N + 1) elements. The first element is a0, and the last element is aN. Ensure that the polynomial you provide is a primitive polynomial. For example, if the primitive polynomial is p(x) = 1 + x 14 + x 15 , then N = 15, and the array contains N + 1=16 elements.

## seed in

Initial state of the PN generator shift register. If no seed is specified, the default seed is used.

Default: 169

## error in

Error conditions that occur before this node runs. The node responds to this input according to standard error behavior.

Default: no error

## 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: TRUE

## output bit stream

The generated pseudorandom data bits.

## seed out

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

## error out

Error information. The node produces this output according to 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 $L={2}^{m}-1$ 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.

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: $1+{X}^{14}+{X}^{15}$

Initial seed: 000000010101001

The following figure shows the circuitry:

Seed Output
000000010101001 0+0=0
000000101010010 0+0=0
000001010100100 0+0=0
000010101001000 0+0=0
000101010010000 0+0=0
001010100100000 0+0=0
010101001000000 0+1=1
101010010000001 1+0=1
2. The second example depicts the Galois implementation. Inputs are specified as follows:

Primitive polynomial: $1+{X}^{14}+{X}^{15}$

Initial seed: 000000010101001

The circuitry is shown in the following figure:

Seed Output
000000010101001 0
000000101010010 0
000001010100100 0
000010101001000 0
000101010010000 0
001010100100000 0
010101001000000 0
101010010000000 1
110100100000001 1
001001000000011 0
010010000000110 0
100100000001100 1
101000000011001 1
110000000110011 1
000000001100111 0
000000011001110 0

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported