API: Supporting Functions

Supporting Functions for Linear Feedback Shift Register

Primitive Polynomials

get_fpolyList(m=None)
Get the list of primitive polynomials as feedback polynomials for m-bit LFSR. Only half list of primary primitive polynomials are retuned, not the full list (half list), since for each primary primitive polynomial an image polymial can be computed using 'get_Ifpoly' method

get_fpolyList(m=None)

Get the list of primitive polynomials as feedback polynomials for m-bit LFSR. Only half list of primary primitive polynomials are retuned, not the full list (half list), since for each primary primitive polynomial an image polymial can be computed using ‘get_Ifpoly’ method

Parameters:

m: 1<int<32, if None, list of feedback polynomials for 1 < m < 32 is return as a dictionary

Returns:

fpoly_list: list of polynomial if m is not None else a dictionary

Example:

import pylfsr as PYL
#returns a dictionary of polynomial
polylist = PYL.get_fpolyList(m=None)

#returns list of polynomial for m-bit LFSR
polylist = PYL.get_fpolyList(m=5)

print(polylist)
[[5, 2], [5, 4, 2, 1], [5, 4, 3, 2]]

Image Replica of a polynomial

get_Ifpoly(fpoly)
Get image replica of feebback polynomial

get_Ifpoly(fpoly)

Parameters:

fpoly: polynomial as list e.g. [5,2] for x^5 + x^2 + 1

: should be a valid primitive polynomial

Returns:

ifpoly: polynomial as list e.g. [5,3] for x^5 + x^3 + 1

Example

import pylfsr as PYL

#returns image polynomial of given polynomial
ipoly = PYL.get_Ifpoly([5, 4, 2, 1])

print(ipoly)
[5, 4, 3, 1]

Display LFSR

dispLFSR(state, fpoly, conf='fibonacci', seq='', out_bit_index=-1, ob=None, fb=None, fs=25, ax=None, show_labels=False, title='', title_loc='left', box_color='lightblue', alpha=0.5, output_arrow_color='C0', output_arrow_style='h')

Display LFSR for given state, fpoly and conf.

Parameters:

state: current state of LFSR fpoly: feedback polynomial of LFSR seq: str, output sequence ob: output bit fb: feedback bit ax: axis to plot, if None, new axis will be created, (default None) show: if True, plt.show() will be excecuted, (default True) fs: fontsize (default 25) show_label: if true, will display names title: str, title of figure, default ‘’, title_loc, alignment of title, ‘left’, ‘right’, ‘center’, (default ‘left’) box_color: color of register box, default=’lightblue’

Example:

import pylfsr as PYL

PYL.dispLFSR(state=[1,1,1,1,0], fpoly=[5,3], conf='fibonacci', seq='111', title='R1')

Lempel-Ziv Complexity

lempel_ziv_complexity(seq)

lempel_ziv_complexity(seq):

Lempel-Ziv Complexity.

It is defined as the number of different patterns exists in a given stream.

As an example: s = ‘1001111011000010’ patterns ==> 1, 0, 01, 11, 10, 110, 00, 010 #patterns = 8

Parameters:

seq: as string of sequence, could be binary or any other

Returns:

lc: number of different patterns in LZ dictionary

Example:

import pylfsr as PYL
from pylfsr import LFSR

L = LFSR()
L.runKCycle(100)
seq = L.getSeq()
lc = PYL.lempel_ziv_complexity(seq)
print(lc)

29

–

lempel_ziv_patterns(seq)

lempel_ziv_patterns(seq):

Lempel-Ziv patterns.

It is defined as a set of different patterns exists in a given sequence.

As an example: s = ‘1001111011000010’ patterns ==> 1, 0, 01, 11, 10, 110, 00, 010

Parameters:

seq: as string of sequence, could be binary or any other

Returns:

dictionary of all the LZ patterns in given sequence

Example:

import pylfsr as PYL
from pylfsr import LFSR

L = LFSR()
L.runKCycle(100)
seq = L.getSeq()
pdict = PYL.lempel_ziv_patterns(seq)
print(pdict)

{'0',
 '00',
 '000',
 '0001',
 '00010',
 '001',
 '0011',
 '01',
 '010',
 '0100',
 '0101',
 '011',
 '0111',
 '1',
 '10',
 '100',
 '1000',
 '101',
 '1011',
 '10110',
 '101100',
 '11',
 '110',
 '1100',
 '1101',
 '11010',
 '11011',
 '111',
 '1111'}