Noisy Channel

Information Theory and Coding Methods
Assignment 1

I realized that plotting the length of the word against the transmission success rate, in all probability graphs using different frequency zeros, seem to be related to the same function, which I believe is exponential.

This is one of the graphics given.

In the next two graphics we can appreciate all the information given by the programs and script.

The next graphic is for word length versus frequency of zeros, and the color is given by the average percentage of correct transmitions, so yellow indicate high percentage of correct transmitions and black is practically a bad level.

And here we have the same but with the difference that the average is releated with the radius of the bubbles.

Código

For this assignment I write code in different languages, but I only run channel.sh in the terminal, and then channel.R inside the R console.

channel.py

	import sys, random
	def bit_generator(zero_freq):
	if random.uniform(0, 1) < zero_freq:
	return '0'
	else:
	return '1'
	def word_generator(word_length, zero_freq):
	word = ''
	for i in range(word_length):
	word = word + bit_generator(zero_freq)
	return word
	def transmitter(word, word_length, zeros_occur, ones_occur):
	sended = ''
	for i in range(word_length):
	if word[i] == '0':
	if random.random() < zeros_occur:
	sended += '0'
	else:
	sended += '1'
	else:
	if random.random() < ones_occur:
	sended += '1'
	else:
	sended += '0'
	return sended
	def simulation(word_length, repetitions, zero_freq, zeros_occur, ones_occur):
	word = word_generator(word_length, zero_freq)
	counter = 0.0
	for i in range(repetitions):
	sended = transmitter(word, word_length, zeros_occur, ones_occur)
	if word == sended:
	counter += 1
	porcentage = counter/repetitions
	print '%.2f' % porcentage
	def main():
	if len(sys.argv) > 5:
	word_length = int(sys.argv[1])
	repetitions = int(sys.argv[2])
	zero_freq = float(sys.argv[3])
	zeros_occur = float(sys.argv[4])
	ones_occur = float(sys.argv[5])
	simulation(word_length, repetitions, zero_freq, zeros_occur, ones_occur)
	else:
	print 'Missing parameters'
	if __name__ == '__main__':
	main()

view raw channel.py hosted with ❤ by GitHub

channel.sh

	limit=512
	potency=0
	length=1
	words=20
	repetitions=30
	zeros_occur=0.8
	ones_occur=0.9
	touch channel.dat
	rm channel.dat
	touch channel.dat
	while [[ length -le limit ]]
	do
	echo Running with length $length
	for zero_freq in 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
	do
	echo And frequency of zeros $zero_freq
	touch temp.dat
	rm temp.dat
	touch temp.dat
	iteration=1
	while [[ iteration -le words ]]
	do
	response=`python channel.py $length$repetitions $zero_freq$zeros_occur $ones_occur`
	echo $response >> temp.dat
	iteration=$(($iteration+1))
	done
	response=`awk -f channel.awk -v len=$length -v zero_freq=$zero_freq temp.dat`
	echo $potency$zero_freq $response >> channel.dat
	rm temp.dat
	done
	echo '' >> channel.dat
	length=$(($length*2))
	potency=$(($potency+1))
	done
	`gnuplot channel.plot`

view raw channel.sh hosted with ❤ by GitHub

channel.awk

	{
	sum += $1
	counter++
	}
	END {
	print sum/counter
	}

view raw channel.awk hosted with ❤ by GitHub

channel.plot

	set term postscript eps color 20
	set pm3d map
	set xlabel 'Word length'
	set ylabel 'Frecuency of zeros'
	set title 'Average porcentage of correct transmitions'
	set output 'channel.eps'
	splot 'channel.dat' using 1:2:($3*100)

view raw channel.plot hosted with ❤ by GitHub

channel.R

	postscript("channel_bubbles.eps")
	data <- read.table("channel.dat", sep = " ")
	circles_radius <- sqrt(data$V3/pi)
	symbols(data$V1, data$V2, circles = circles_radius,
	inches = 0.35, fg = "white", bg = "#336699",
	xlab = "Word length", ylab = "Frecuency of zeros",
	main = "Average porcentage of correct transmitions")
	dev.off()

view raw channel.R hosted with ❤ by GitHub

References:
Noisy channel by Elisa Schaeffer