115 lines
2.4 KiB
Python
115 lines
2.4 KiB
Python
import random
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import matplotlib.pyplot as plt
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# Linear Feedback Shift Register
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class LFSR:
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def __init__(self, poly):
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# LSB -> MSB
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self.g = []
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self.reg = []
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'''
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poly = str(n, n-1, ..., 0) => g = [0, ..., n-1]
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0, 1, ..., -1
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[-1:0:-1] = von(inkl.):bis(exkl.):Schritt => [Ende:Anfang[
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'''
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for ziffer in poly[-1:0:-1]:
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self.reg.append(0)
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self.g.append(int(ziffer))
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def get_reg_as_string(self):
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reg_string = ""
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for i in self.reg:
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reg_string += str(i) # LSB -> MSB
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return reg_string
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def shift(self, s_i):
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reg_old = self.reg.copy() # alter Zustand, um überschreibungen zu vermeiden
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feedback = reg_old[-1] ^ int(s_i)
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for i, value in enumerate(self.g):
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if i == 0:
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self.reg[i] = feedback
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else:
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if value == 1:
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self.reg[i] = reg_old[i - 1] ^ feedback
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else:
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self.reg[i] = reg_old[i - 1]
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def CRC_Parity(s, g):
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schiebe_reg = LFSR(g)
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# LSB -> MSB => MSB -> LSB
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for s_i in s[::-1]:
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schiebe_reg.shift(s_i)
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return schiebe_reg.get_reg_as_string()
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def channel_bsc(p, n):
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f = ""
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for i in range(n):
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p_i = random.random()
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# p_i <= p ? F += "1" : F += "0"
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f += "1" if p_i <= p else "0"
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return f
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def p_k_Fehler(p):
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# P_k = (nCk) * p^k * (1-p)^(n-k)
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n = 1000
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p_k = []
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k_values = list(range(1, n + 1))
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for k in k_values:
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nCk = 1
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for i in range(1, k + 1, 1):
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nCk = nCk * ((n + 1 - i) / i)
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# p_k = (nCk) * p^k * (1-p)^(n-k)
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p_k.append(nCk * pow(p, k) * pow((1 - p), (n - k)))
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plt.figure(figsize=(12, 8))
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plt.plot(k_values, p_k) # plot(x,y)
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# Achsenbeschriftung
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plt.xlabel('k (Anzahl Fehler)', fontsize=12)
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plt.ylabel('p_k', fontsize=12)
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plt.title(f'Fehlerwahrscheinlichkeiten BSC Kanal (p={p}, n={n})', fontsize=14)
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# Grid
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plt.grid(True, alpha=0.3)
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# Zeige Plot
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plt.tight_layout() # Besseres Layout
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plt.show()
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def main():
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p = 0.1
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# LSB -> MSB
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s = "110011101100101"
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# MSB -> LSB
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g = "100101"
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prf = CRC_Parity(s, g)
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print(prf)
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print(channel_bsc(p, 15))
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p_k_Fehler(p)
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if __name__ == '__main__':
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main()
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