import numpy as np
import matplotlib.pyplot as plt

# x is our message

x = np.random.binomial(size=pow(10, 6), n=1, p= 0.5)

# pe is the error probability of noise

pe = np.linspace(0, 0.5, num=11)

# bsc is the error matrix

bsc = np.zeros(shape=(11,pow(10, 6)))

for i in range(11):
        bsc[i] = np.random.binomial(size=pow(10, 6), n=1, p = pe[i])

y = np.zeros(shape=(11,pow(10, 6)))

# below we compare the error matrix and our message with xor and get the output

for i in range(11):
    for j in range(pow(10, 6)):
        if np.logical_xor(bsc[i,j],x[j]) == True:
            y[i,j]=1
        else:
            y[i,j]=0
    
error = np.zeros(shape=(11,pow(10, 6)))

# in this part we compare message and the output

for i in range(11):
    for j in range(pow(10, 6)):
        if np.logical_xor(y[i,j],x[j]) == True:
            error[i,j]=1
        else:
            error[i,j]=0
    
# calculating error probabilities for different noise error rates    

ps = np.zeros(shape=(11))

for i in range(11):
    ps[i] = np.sum(error[i])/pow(10, 6)
    
# here plotting
    
plt.plot(pe,ps)
plt.ylabel('Ps')
plt.xlabel('Pe')
plt.show()