Noisy channel

Python creates certain number words that come as a parameter, then sends the same word many times to see the probability of success or failure
Python:

	#!/usr/bin/python
	import random
	from numpy import *
	import sys
	def generador_palabra(largo_palabra, frecuencia):
	"""genera palabras binarias pseudoaleatoriamente
	usando frecuencias definidas como parametros para los
	ceros y unos
	"""
	palabra = ""
	for i in range(largo_palabra):
	x = random.random()
	if(x < frecuencia):
	palabra = palabra + str(0)
	else:
	palabra = palabra + str(1)
	return palabra
	def repetir(num_rep,largo_palabra, frecuencia, Q):
	"""repite el experimento
	"""
	exito = 0
	palabra = generador_palabra(largo_palabra, frecuencia)
	for i in range(num_rep):
	transmitida = transmite(palabra, Q)
	if transmitida == palabra:
	exito = exito + 1
	porcentaje = (exito * 100.0)/num_rep
	return porcentaje
	def transmite(palabra, prob):
	"""toma como parametro una palabra binaria y simula su
	transmision por un canal cuyas probabilidades de transicion
	estan dadas como parametros de 2x2
	"""
	transmitida = ""
	for i in palabra:
	bit = i
	x = random.random()
	if x < prob[int(i)]:
	transmitida = transmitida + i
	else:
	if i == "0":
	transmitida= transmitida + "1"
	else:
	transmitida = transmitida + "0"
	return transmitida
	largo_palabra = int(sys.argv[1])
	frecuencia = float(sys.argv[2])
	q_0 = float(sys.argv[3])
	q_1 = float(sys.argv[4])
	repeticiones = int(sys.argv[5])
	porcentaje = repetir(repeticiones,largo_palabra, frecuencia, [q_0,q_1])
	print porcentaje

view raw gistfile1.py hosted with ❤ by GitHub

In the shell script I do repetitions of words of a certain length, also i change the length of the word and the probability of 0 and 1, then in an awk script I can get the standard deviation and the averange, and send this data to the final file and process the data.

Shell script

	#!/bin/bash
	pot=0
	tam=1
	fr=0.5
	rep=30
	lim=100
	init=1
	count=0
	res=1
	palabras=30
	touch datos.dat
	touch tmp.dat
	rm datos.dat
	rm tmp.dat
	#se comienzan a crear las palabras con diferentes tamanos
	while [[ tam -le lim ]]
	do
	for fr in 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
	#diferentes frecuencias
	do
	for q0 in 0.1 0.3 0.5 0.7
	#probabilidades de obtener 0
	do
	for q1 in 0.1 0.3 0.5 0.7
	#probabilidades de obtener 1
	do
	touch temp.dat
	rm temp.dat
	touch temp.dat
	conta=1
	while [[ conta -le palabras ]]
	#crea 30 palabras con el mismo largo
	do
	res=`python tarea_1.py $tam $fr $q0 $q1 $rep`
	echo $conta $tam $fr $res >> tmp.dat
	conta=$((1+$conta))
	done
	resu=`./experimento.awk -v tam=$tam -v fr=$fr tmp.dat`
	echo $pot $fr $resu $q0 $q1 >> datos.dat
	rm tmp.dat
	done
	done
	done
	pot=$((1+$pot))#sirve para graficar
	tam=$((2*$tam))
	done

view raw gistfile1.sh hosted with ❤ by GitHub

In awk script I get the average and standard deviation
AWK script

	#!/bin/bash
	pot=0
	tam=1
	fr=0.5
	rep=30
	lim=100
	init=1
	count=0
	res=1
	palabras=30
	touch datos.dat
	touch tmp.dat
	rm datos.dat
	rm tmp.dat
	#se comienzan a crear las palabras con diferentes tamanos
	while [[ tam -le lim ]]
	do
	for fr in 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
	#diferentes frecuencias
	do
	for q0 in 0.1 0.3 0.5 0.7
	#probabilidades de obtener 0
	do
	for q1 in 0.1 0.3 0.5 0.7
	#probabilidades de obtener 1
	do
	touch temp.dat
	rm temp.dat
	touch temp.dat
	conta=1
	while [[ conta -le palabras ]]
	#crea 30 palabras con el mismo largo
	do
	res=`python tarea_1.py $tam $fr $q0 $q1 $rep`
	echo $conta $tam $fr $res >> tmp.dat
	conta=$((1+$conta))
	done
	resu=`./experimento.awk -v tam=$tam -v fr=$fr tmp.dat`
	echo $pot $fr $resu $q0 $q1 >> datos.dat
	rm tmp.dat
	done
	done
	done
	pot=$((1+$pot))#sirve para graficar
	tam=$((2*$tam))
	done

view raw gistfile1.sh hosted with ❤ by GitHub

With gnuplot I produce a graph to know what happened in the experiment.

	set grid layerdefault
	set term png
	set pm3d map
	set xlabel "Frecuencia de ceros" offset 1,-1,1
	set ylabel "Probabilidades de exito" offset 1,-1,1
	set zlabel "Probabilidad de 0" offset 6,4,1
	set cblabel "Probabilidad de 0"
	set title "Largo 4 "
	set output "largo_4_6.png"
	set palette color positive
	set size square
	set key off
	splot "cuatro_palabra.dat" using 2:3:5

view raw gistfile1.matlab hosted with ❤ by GitHub

And some plots that can help us to underestand the results.

q0 = 0.1
q1 = 0.1

 After I implemented more functions to analyze probabilities of 0 and 1 (q0, q1), and also compute the standard deviation.

While the length of the chain grows the probability of success is weakened and if the frequency of 0 is high but the probability of success to 0 It is not as high like the probability of 1 then while the frequencies of 0 going up so these will lose the success rate because In longer words are more failures.