Assignment 1: Noisy channel

For this homework we need to do a simulation of a noisy channel where we have a binary input alphabet with probabilities that can handle the success or fail to pass a word that we would like to transmit.


For do this experiment I use a combination between:

• Python that took for parameters:
• Size of the word
• frequency of succeed
• Probability for one that can transmit
• Probability for zero that can transmit  
• Times that we want to do an experiment.

• In a Bash do:
• Change the frequency of succeed
• Change Probability for one and zero
• Call to the python script to change those variables

• In AWK I can:
• Obtain a mean and also an standard deviation.

Then we use gnuplot to interpret the data that we obtain, so in the following plot I will explain about who a noisy channel works and how all the data that we use in the experiment are connected each other and made that a channel fail or success in transmit binary data.

This is a graphic that I generated for demonstrate that, when I augmented the size of the binary word, the success for transmit is  almost nothing, both if we have a word for example 2**0, the test only send 1 bit, so we have a many chances that this bit can transmit.

Also, this is another graphic that we can see that, when we have a large word we have a 0 probability to send the word correctly, so we can view the circle in black express the standard deviation that we can compute in the AWK script.

This are the same graphics but separated between the probability success 1 and 0.

We can notice that, when we have more frequency of zeros and more probability of success of 1, the probability of zeros is poor, so the standard deviation is going to down, that is because the word transmit more 1 than 0.

Code.

Python

	import random
	import numpy
	import sys
	def genera_bin(tam, prob):
	palabra = ""
	for i in xrange(tam):
	x = random.random()
	if (prob < x):
	palabra = palabra + str(0)
	else:
	palabra = palabra + str(1)
	return palabra
	def transmite(palabra, Q):
	"""
	"""
	palabra_trans = ''
	for i in xrange(len(palabra)):
	bit = palabra[i]
	x = random.random()
	if (x < Q[int(bit)]):
	palabra_trans = palabra_trans + str(bit)
	else:
	if bit == "0":
	palabra_trans = palabra_trans + str(1)
	else:
	palabra_trans = palabra_trans + str(0)
	return palabra_trans
	def repeticiones(num, palabra, Q):
	mal = 0
	bien = 0
	for i in xrange(num):
	transmitida = transmite(palabra, Q)
	if transmitida != palabra:
	mal = mal + 1
	else:
	bien = bien + 1
	return (bien, mal)
	def main():
	tam = int(sys.argv[1])
	frecuencia = float(sys.argv[2])
	Q0 = float(sys.argv[3])
	Q1 = float(sys.argv[4])
	rep = int(sys.argv[5])
	palabra = genera_bin(tam, frecuencia)
	Q = [Q0, Q1]
	(bien, mal) = repeticiones(rep, palabra, Q)
	print float(bien * 100)/float(rep)
	main()

view raw tarea_1.py hosted with ❤ by GitHub

Bash

	#!/bin/bash
	tam=1
	frec=0.5
	rep=30
	init=1
	count=0
	res=1
	lim=100
	pot=0
	palabras=30
	q0=0
	q1=0
	touch datos.dat
	touch tmp.dat
	rm datos.dat
	rm tmp.dat
	echo $tam
	while [[ tam -le lim ]]
	do
	for frec in 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
	do
	for q0 in 0.1 0.5 0.9
	do
	for q1 in 0.1 0.5 0.9
	do
	touch tmp.dat
	rm tmp.dat
	touch tmp.dat
	conta=1
	while [[ conta -le palabras ]]
	do
	res=`python tarea_1.py $tam $frec $q0 $q1 $rep`
	echo $conta $tam $frec $res $q0 $q1 >> tmp.dat
	conta=$((1+$conta))
	done
	resu=`./experimento.awk -v tam=$tam -v frec=$frec tmp.dat`
	echo $pot $frec $resu $q0 $q1 >> datos.dat
	rm tmp.dat
	done
	done
	done
	pot=$((1+$pot))
	tam=$((2*$tam))
	echo $tam
	done

view raw experimento.sh hosted with ❤ by GitHub

GNUPLOT

	set grid layerdefault
	set term png
	set title 'Probability success 1'
	set ylabel 'Frequency'
	set xlabel 'Word size, power of two'
	set label ""
	set output "grafica_4.png"
	set key off
	plot "datos.dat" using 1:6:4 with points palette pt 11 ps 3
	set grid layerdefault
	set term png
	set title 'Probability success 0'
	set ylabel 'Frequency'
	set xlabel 'Word size, power of two'
	set label ""
	set output "grafica_3.png"
	set key off
	plot "datos.dat" using 1:5:4 with points palette pt 13 ps 3
	set grid layerdefault
	set term png
	set title 'Word size vs Success Transmit'
	set ylabel 'Frequency'
	set xlabel 'Word size, power of two'
	set label ""
	set output "grafica_2.png"
	set key off
	plot "datos.dat" using 1:2:4 with points palette pt 7 ps 3
	set grid layerdefault
	set term png
	set title 'Word with Success Transmit'
	set xlabel 'Power of 2'
	set ylabel 'Probability of success to Transmit'
	set label ""
	set arrow from 0,0 to 6,0
	set output "grafica_1.png"
	set key off
	plot "datos.dat" using 1:2:3 with yerrorbars pt 7 ps 3

view raw graficas.gnu hosted with ❤ by GitHub

AWK

	#!/usr/bin/awk -f
	{
	if($2 == tam && $3 == frec){
	suma+=$4
	conta+=1
	}
	}
	END{
	promedio = suma/conta
	print promedio
	}
	{
	if($2 == tam && $3 == frec){
	dato = $4
	x = promedio - dato
	suma_cuadrado+=x^2
	}
	}END {
	varianza = suma_cuadrado/(conta-1)
	desviacion = sqrt(varianza)
	print desviacion
	}

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