def conv_Pb_bound(R, dfree, Ck, SNRdB, hard_soft, M=2):
"""
Coded bit error probabilty
Pb = conv_Pb_bound(R,dfree,Ck,SNR,hard_soft,M=2)
Convolution coding bit error probability upper bound
according to Ziemer & Peterson 7-16, p. 507
Mark Wickert November 2014
"""
Pb = np.zeros_like(SNRdB)
SNR = 10.**(SNRdB / 10.)
for n, SNRn in enumerate(SNR):
for k in range(dfree, len(Ck) + dfree):
if hard_soft == 0: # Evaluate hard decision bound
Pb[n] += Ck[k - dfree] * hard_Pk(k, R, SNRn, M)
elif hard_soft == 1: # Evaluate soft decision bound
Pb[n] += Ck[k - dfree] * soft_Pk(k, R, SNRn, M)
else: # Compute Uncoded Pe
if M == 2:
Pb[n] = Q_fctn(np.sqrt(2. * SNRn))
else:
Pb[n] = 4./np.log2(M)*(1 - 1/np.sqrt(M))*\
np.gaussQ(np.sqrt(3*np.log2(M)/(M-1)*SNRn))
return Pb
def conv_Pb_bound(R,dfree,Ck,SNRdB,hard_soft,M=2):
"""
Pb = conv_Pb_bound(R,dfree,Ck,SNR,hard_soft,M=2)
Convolution coding bit error probability upper bound
according to Ziemer & Peterson 7-16, p. 507
Mark Wickert November 2014
"""
Pb = np.zeros_like(SNRdB)
SNR = 10.**(SNRdB/10.)
for n,SNRn in enumerate(SNR):
for k in range(dfree,len(Ck)+dfree):
if hard_soft == 0: # Evaluate hard decision bound
Pb[n] += Ck[k-dfree]*hard_Pk(k,R,SNRn,M)
elif hard_soft == 1: # Evaluate soft decision bound
Pb[n] += Ck[k-dfree]*soft_Pk(k,R,SNRn,M)
else: # Compute Uncoded Pe
if M == 2:
Pb[n] = Q_fctn(np.sqrt(2.*SNRn))
else:
Pb[n] = 4./np.log2(M)*(1 - 1/np.sqrt(M))*\
np.gaussQ(np.sqrt(3*np.log2(M)/(M-1)*SNRn));
return Pb
def conv_Pb_bound(R, dfree, Ck, SNRdB, hard_soft, M=2):
"""
Coded bit error probabilty
Convolution coding bit error probability upper bound
according to Ziemer & Peterson 7-16, p. 507
Mark Wickert November 2014
Parameters
----------
R: Code rate
dfree: Free distance of the code
Ck: Weight coefficient
SNRdB: Signal to noise ratio in dB
hard_soft: 0 hard, 1 soft, 2 uncoded
M: M-ary
Examples
--------
>>> import numpy as np
>>> from sk_dsp_comm import fec_conv as fec
>>> import matplotlib.pyplot as plt
>>> SNRdB = np.arange(2,12,.1)
>>> Pb = fec.conv_Pb_bound(1./2,10,[36, 0, 211, 0, 1404, 0, 11633],SNRdB,2)
>>> Pb_1_2 = fec.conv_Pb_bound(1./2,10,[36, 0, 211, 0, 1404, 0, 11633],SNRdB,1)
>>> Pb_3_4 = fec.conv_Pb_bound(3./4,4,[164, 0, 5200, 0, 151211, 0, 3988108],SNRdB,1)
>>> plt.semilogy(SNRdB,Pb)
>>> plt.semilogy(SNRdB,Pb_1_2)
>>> plt.semilogy(SNRdB,Pb_3_4)
>>> plt.axis([2,12,1e-7,1e0])
>>> plt.xlabel(r'$E_b/N_0$ (dB)')
>>> plt.ylabel(r'Symbol Error Probability')
>>> plt.legend(('Uncoded BPSK','R=1/2, K=7, Soft','R=3/4 (punc), K=7, Soft'),loc='best')
>>> plt.grid();
>>> plt.show()
Notes
-----
The code rate R is given by :math:`R_{s} = \\frac{k}{n}`.
Mark Wickert and Andrew Smit 2018
"""
Pb = np.zeros_like(SNRdB)
SNR = 10.**(SNRdB / 10.)
for n, SNRn in enumerate(SNR):
for k in range(dfree, len(Ck) + dfree):
if hard_soft == 0: # Evaluate hard decision bound
Pb[n] += Ck[k - dfree] * hard_Pk(k, R, SNRn, M)
elif hard_soft == 1: # Evaluate soft decision bound
Pb[n] += Ck[k - dfree] * soft_Pk(k, R, SNRn, M)
else: # Compute Uncoded Pe
if M == 2:
Pb[n] = q_fctn(np.sqrt(2. * SNRn))
else:
Pb[n] = 4./np.log2(M)*(1 - 1/np.sqrt(M))*\
np.gaussQ(np.sqrt(3*np.log2(M)/(M-1)*SNRn))
return Pb
def block_single_error_Pb_bound(j, SNRdB, coded=True, M=2):
"""
Finds the bit error probability bounds according to Ziemer and Tranter
page 656.
parameters:
-----------
j: number of parity bits used in single error correction block code
SNRdB: Eb/N0 values in dB
coded: Select single error correction code (True) or uncoded (False)
M: modulation order
returns:
--------
Pb: bit error probability bound
"""
Pb = np.zeros_like(SNRdB)
Ps = np.zeros_like(SNRdB)
SNR = 10.**(SNRdB / 10.)
n = 2**j - 1
k = n - j
for i, SNRn in enumerate(SNR):
if coded: # compute Hamming code Ps
if M == 2:
Ps[i] = q_fctn(np.sqrt(k * 2. * SNRn / n))
else:
Ps[i] = 4./np.log2(M)*(1 - 1/np.sqrt(M))*\
np.gaussQ(np.sqrt(3*np.log2(M)/(M-1)*SNRn))/k
else: # Compute Uncoded Pb
if M == 2:
Pb[i] = q_fctn(np.sqrt(2. * SNRn))
else:
Pb[i] = 4./np.log2(M)*(1 - 1/np.sqrt(M))*\
np.gaussQ(np.sqrt(3*np.log2(M)/(M-1)*SNRn))
# Convert symbol error probability to bit error probability
if coded:
Pb = ser2ber(M, n, 3, 1, Ps)
return Pb
# .. ._.. .._ #