x=np.linspace(0,1,1000)
sigma0=[0.9]
color=['green']
for i in range(len(sigma0)):
    sigma=sigma0[i]
    y=1/(x*sigma*np.sqrt(2*np.pi))*np.exp(-(np.log(x/0.3)+(1/2*sigma*sigma))**2/(2*sigma*sigma))
    plt.plot(x,y,color[i])
plt.title('Lognormal distribution')
plt.xlabel('x')
plt.ylabel('lognormal density distribution')
#plt.xlim((0,0.002))
plt.ylim((0,5))
plt.show()

n1=np.arange(10, 55, 1)
n=10**(-n1/10)


Y0=1*(10**-5)
nd=0.25
ed=0.03
nsys=nd*n
QBER=((1/2*Y0)+(ed*nsys))/(Y0+nsys)
H2=-QBER*np.log2(QBER)-(1-QBER)*np.log2(1-QBER)
Rsp=np.log10((Y0+nsys)*(1-(2*H2)))
print (Rsp)

plt.plot(n1,Rsp)
plt.xlabel('Loss (dB)')
plt.ylabel('log10(Rate)')
plt.show()