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Hamming(7,4) Error Correction Code (ECC).

Python, 44 lines
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44``` ```# Hamming(7,4) Error Correction Code # https://en.wikipedia.org/wiki/Hamming(7%2C4) # FB - 20160723 import random # the encoding matrix G = ['1101', '1011', '1000', '0111', '0100', '0010', '0001'] # the parity-check matrix H = ['1010101', '0110011', '0001111'] Ht = ['100', '010', '110', '001', '101', '011', '111'] # the decoding matrix R = ['0010000', '0000100', '0000010', '0000001'] p = ''.join([random.choice('01') for k in range(4)]) print 'Input bit string: ' + p x = ''.join([str(bin(int(i, 2) & int(p, 2)).count('1') % 2) for i in G]) print 'Encoded bit string to send: ' + x # add 1 bit error e = random.randint(0, 7) # counted from left starting from 1 print 'Which bit got error during transmission (0: no error): ' + str(e) if e > 0: x = list(x) x[e - 1] = str(1 - int(x[e - 1])) x = ''.join(x) print 'Encoded bit string that got error during tranmission: ' + x z = ''.join([str(bin(int(j, 2) & int(x, 2)).count('1') % 2) for j in H]) if int(z, 2) > 0: e = int(Ht[int(z, 2) - 1], 2) else: e = 0 print 'Which bit found to have error (0: no error): ' + str(e) # correct the error if e > 0: x = list(x) x[e - 1] = str(1 - int(x[e - 1])) x = ''.join(x) p = ''.join([str(bin(int(k, 2) & int(x, 2)).count('1') % 2) for k in R]) print 'Corrected output bit string: ' + p ```
 Created by FB36 on Sat, 23 Jul 2016 (MIT)

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