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Hamming code - Wikipedia

Hamming code is a simple error correction code, which will be learned in the introduction to computer science in college. I want to try to use it to improve the accuracy of UDP transmission. But I was too lazy to write an encoding and decoding algorithm, so I used the lookup table method.

Coding

Table Generator

After writting and testing,  running attchment file "hamming_code_7_4.ipynb". I got encode and decode table.

Encode table

[0, 15, 19, 28, 37, 42, 54, 57, 70, 73, 85, 90, 99, 108, 112, 127]

Decode table

[0, 0, 0, 2, 0, 4, 8, 1, 0, 9, 5, 1, 3, 1, 1, 1, 0, 2, 2, 2, 3, 10, 6, 2, 3, 7, 11, 2, 3, 3, 3, 1, 0, 4, 5, 12, 4, 4, 6, 4, 5, 7, 5, 5, 13, 4, 5, 1, 14, 7, 6, 2, 6, 4, 6, 6, 7, 7, 5, 7, 3, 7, 6, 15, 0, 9, 8, 12, 8, 10, 8, 8, 9, 9, 11, 9, 13, 9, 8, 1, 14, 10, 11, 2, 10, 10, 8, 10, 11, 9, 11, 11, 3, 10, 11, 15, 14, 12, 12, 12, 13, 4, 8, 12, 13, 9, 5, 12, 13, 13, 13, 15, 14, 14, 14, 12, 14, 10, 6, 15, 14, 7, 11, 15, 13, 15, 15, 15]

Encode before sending

Split one byte to two nibbles

def hamming_encode_table_method(plaintext):
    return_list=list()
    for s in range(len(plaintext)):
        ### for debug check 
        # print(s) 
        # codeword1 = encode_table[int(plaintext[s]/16)]
        # print(codeword1)
        return_list.append(encode_table[int(plaintext[s]/16)])
        # codeword2 = encode_table[int(plaintext[s]%16)]
        # print(codeword2)
        return_list.append(encode_table[int(plaintext[s]%16)])
        # print(return_bytes)
    return bytes(return_list)

Decode

decode and combine two nibbles back to one byte

def hamming_decode_table_method(encryptext):
    return_list=list()
    for s in range(len(encryptext)):
        if s % 2 ==0:
            high_nibble=decode_table[int(encryptext[s])]
            low_nibble=decode_table[int(encryptext[s+1])]
            c_append=high_nibble*16+low_nibble
            # print(high_nibble)
            # print(low_nibble)
            # print(c_append)
            return_list.append(c_append)
        
    return bytes(return_list)

running attachment main.py on W55RP20-EVB-PICO

and

running attachment UDP_hamming.ipynb (or UDP_hamming.py) on PC

Add random 1 bit  error in each bytes in the transmitted data.

import random
def add_1bit_error(input_message):
    for s in range(len(input_message)):
        input_message[s] = (int(input_message[s]) ^ (1<< random.randint(0, 6)))
    return input_message

I tested for 30 minutes and no second bit error occurred. Maybe it’s because the network line in my environment is very short.