Task 1: Noisy Channel

In this task I make a simulation of a channel, where transmit a word by a channel and a receptor receive the word and the word could come with some noisy like errors of the word. The program was made in Python making  different methods, simulator() (Simulator make all the logic of the channel), generador() (generator of a letter of the word to send in the channel),  palabra() (gets the word by a large) and transmisor() (It's the transmissor that sends the words by the channel). You can see my code below.

	#Import argv method from sys library
	from sys import argv
	#Import numpy as np
	import numpy as np
	#Random method from random library
	from random import random
	#Time method from time library
	from time import time
	#This is the generator of zeros and ones
	#and this generate the zeros and ones
	# from a frequencie of zeros
	def generador(fz):
	if fz > random():
	return 0
	return 1
	#This generate words and returns it in a tuple,
	#take as a parameter the large of the word and
	#the frequencie of zeros
	def palabra(largo, fz):
	#empty tuple
	palabra = []
	#iterate the large of the word
	# and call generator to get
	# the large word
	for x in xrange(largo):
	palabra.append(generador(fz))
	return palabra
	#This make a transmissions of words
	# take as a parameter the word,
	# probability of zeros turn ones and
	# probability of ones turn zeros
	def transmisor(palabra, pz, pu):
	#empty tuple
	palabra_transmitida = []
	#iterate the word and verify if p is equal to 0 or 1
	#and verify his probability that turn 0 to 1 and 1 to 0
	#and return the transmitted word
	for p in palabra:
	if p == 0 and pz < random():
	palabra_transmitida.append(1)
	elif p == 1 and pu < random():
	palabra_transmitida.append(0)
	else:
	palabra_transmitida.append(p)
	return palabra_transmitida
	#Get the standard desviation
	# taking as a parameter the average, average**2 and the n number
	def desviacion_estandar(s, x2, n):
	return ( ( x2 ) * ( n * x2 ) / ( n - 1.0 ) ) ** (1.0/2.0)
	#This is that make the simulation of the channel taking as parameter
	# the frequencies of zeros, probability of success zeros and ones
	def simulador(freq_zero, probabilidad_de_exito_zero, probabilidad_de_exito_uno):
	#b is the base
	b = 2
	#s is the average
	s = 0
	# x is the square of the average
	x2 = 0
	#the power of the number y number maxium
	n = 10
	#Iterates the numbers of power
	for y in range(n):
	#print b ** y
	#initialize the counter of exitos
	exitos = 0
	#initialize the average
	s = 0
	#initialize the square of average
	x2 = 0
	#take the current time
	t1 = time()
	#make 30 proofs for each large of words
	for x in xrange(30):
	#Get the word from palabra()
	#where sends as parameters the large of the word and the frequency of zeros
	palabra_m = palabra(b ** y, freq_zero)
	#print "Mensaje a enviar: ",palabra_m
	#get the word transmitted using transmisor()
	#taking as parameters the word transmitted, probabilty of zeros
	#probability of ones
	palabra_transmitida = transmisor(palabra_m, probabilidad_de_exito_zero, probabilidad_de_exito_uno)
	#print "Mensaje despues de la transmision: ",palabra_transmitida
	#if the words are the same we'll get an success and add +1
	if palabra_m == palabra_transmitida:
	estado = "Exito"
	exitos += 1
	else:
	estado = "Fracaso"
	#print "Estado: ",estado
	# take the current time
	t2 = time()
	# take the average
	s += ( exitos ) / 30.0
	# take the square of the average
	x2 += ( ( exitos ) / 30.0 ) ** 2
	#desviacion_est = desviacion_estandar(probabilidad, 30, n_exitos_deseados)
	#print "LARGO: ",b**y," PROMEDIO DE EXITOS: ", ( ( exitos ) / 30.0 ) * 100
	#print "EXITOS: ",exitos
	#print "DESVIACION ESTANDAR: ", desviacion_est
	#print "TIEMPO TOTAL: ", ( t2 - t1 ) * 1000.0
	#print s, x2, n
	#print "Desviacion estandar: ", desviacion_estandar( s, x2, n )
	# print the frequency of zeros, probability of success in zeros, probability of success in ones, large of the word, average, and standard desviation
	print freq_zero, probabilidad_de_exito_zero, probabilidad_de_exito_uno, b**y, s,desviacion_estandar( s, x2, n )
	def main():
	#the power of the base of the number selected
	n = 10
	#test all the possible combinations in frecuency of zeros, probabilty of zeros and probability of ones in simulador()
	for fz in xrange(n):
	for pz in xrange(n):
	for pu in xrange(n):
	freq_cero = ( fz * 1.0 ) / ( n * 1.0 )
	prob_cero = ( pz * 1.0 ) / ( n * 1.0)
	prob_uno = ( pu * 1.0 ) / ( n * 1.0)
	simulador( freq_cero, prob_cero, prob_uno)
	main()

view raw simulador.py hosted with ❤ by GitHub

And with the help of a batch, awk and gnuplot I made a graphic of the output of the program.

	#!/bin/bash
	#iterate in power of 2
	# sends to a program in awk to get the info
	#and create different files for differents outputs
	for i in 1 2 4 8 16 32 64 128 256 512
	do
	./separa.awk -v seleccionado=$i < experimento.dat > largo$i.dat

view raw gistfile1.bat hosted with ❤ by GitHub

	#!/usr/bin/awk -f
	{
	if ($4 == seleccionado) {
	print $0
	}
	}

view raw gistfile1.bat hosted with ❤ by GitHub

	set ytics 0.1, 0.2
	set xtics 0.1, 0.2
	set ztics 0.1, 0.2
	#unset surf
	#set style line 1 lt 4 lw .5
	#set pm3d #at s hidden3d 1
	set origin 0, 4
	set label 1 "Largo 1" offset 0, 8 font "Helvetica Bold"
	splot "largo1.dat" using 1:2:3:($5+1):6 with points pt 9 ps variable palette #lc variable
	unset label 1
	set origin 1, 4
	set label 1 "Largo 2" offset 0, 8 font "Helvetica Bold"
	splot "largo2.dat" using 1:2:3:($5+1):6 with points pt 9 ps variable palette #lc variable
	unset label 1
	set origin 0, 3
	set label 1 "Largo 4" offset 0, 8 font "Helvetica Bold"
	splot "largo4.dat" using 1:2:3:($5+1):6 with points pt 9 ps variable palette #lc variable
	unset label 1
	set origin 1, 3
	set label 1 "Largo 8" offset 0, 8 font "Helvetica Bold"
	splot "largo8.dat" using 1:2:3:($5+1):6 with points pt 9 ps variable palette #lc variable
	unset label 1
	set origin 0, 2
	set label 1 "Largo 16" offset 0, 8 font "Helvetica Bold"
	splot "largo16.dat" using 1:2:3:($5+1):6 with points pt 9 ps variable palette #lc variable
	unset label 1
	set origin 1, 2
	set label 1 "Largo 32" offset 0, 8 font "Helvetica Bold"
	splot "largo32.dat" using 1:2:3:($5+1):6 with points pt 9 ps variable palette #lc variable
	unset label 1
	set origin 0, 1
	set label 1 "Largo 64" offset 0, 8 font "Helvetica Bold"
	splot "largo64.dat" using 1:2:3:($5+1):6 with points pt 9 ps variable palette #lc variable
	unset label 1
	set origin 1, 1
	set label 1 "Largo 128" offset 0, 8 font "Helvetica Bold"
	splot "largo128.dat" using 1:2:3:($5+1):6 with points pt 9 ps variable palette #lc variable
	unset label 1
	set origin 0, 0
	set label 1 "Largo 256" offset 0, 8 font "Helvetica Bold"
	splot "largo256.dat" using 1:2:3:($5+1):6 with points pt 9 ps variable palette #lc variable
	unset label 1
	set origin 1, 0
	set label 1 "Largo 512" offset 0, 8 font "Helvetica Bold"
	splot "largo512.dat" using 1:2:3:($5+1):6 with points pt 9 ps variable palette #lc variable
	unset label 1
	unset multiplot

view raw gistfile1.py hosted with ❤ by GitHub

This is the graphic where the axis x is the frequency of zero, axis y is the probability of ones, axis z is the probability of zero. The heat map represent the probability of success.