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Hamming Code implementation in Python

  • Difficulty Level : Medium
  • Last Updated : 17 May, 2022

Hamming code is a set of error-correction codes that can be used to detect and correct the errors that can occur when the data is moved or stored from the sender to the receiver. It is a technique developed by R.W. Hamming for error correction.

Note: It is suggested to be well versed with Hamming Code as it serves as an pre-requisite. 

Steps:

  1. Enter the Data to be transmitted
  2. Calculate the no of redundant bits required
  3. Determine the parity bits
  4. Create error data for testing
  5. Check for errors

Examples: 

Input: 
1011001

Output:
Data transferred is 10101001110
Error Data is 11101001110
The position of error is 10
Input:
10101111010

Output:
Data transferred is 101011111010000
Error Data is 101011111010100
The position of error is 3

 Example

Python3




# Python program to demonstrate
# hamming code
 
 
def calcRedundantBits(m):
 
    # Use the formula 2 ^ r >= m + r + 1
    # to calculate the no of redundant bits.
    # Iterate over 0 .. m and return the value
    # that satisfies the equation
 
    for i in range(m):
        if(2**i >= m + i + 1):
            return i
 
def posRedundantBits(data, r):
 
    # Redundancy bits are placed at the positions
    # which correspond to the power of 2.
    j = 0
    k = 1
    m = len(data)
    res = ''
 
    # If position is power of 2 then insert '0'
    # Else append the data
    for i in range(1, m + r+1):
        if(i == 2**j):
            res = res + '0'
            j += 1
        else:
            res = res + data[-1 * k]
            k += 1
 
    # The result is reversed since positions are
    # counted backwards. (m + r+1 ... 1)
    return res[::-1]
 
 
def calcParityBits(arr, r):
    n = len(arr)
 
    # For finding rth parity bit, iterate over
    # 0 to r - 1
    for i in range(r):
        val = 0
        for j in range(1, n + 1):
 
            # If position has 1 in ith significant
            # position then Bitwise OR the array value
            # to find parity bit value.
            if(j & (2**i) == (2**i)):
                val = val ^ int(arr[-1 * j])
                # -1 * j is given since array is reversed
 
        # String Concatenation
        # (0 to n - 2^r) + parity bit + (n - 2^r + 1 to n)
        arr = arr[:n-(2**i)] + str(val) + arr[n-(2**i)+1:]
    return arr
 
 
def detectError(arr, nr):
    n = len(arr)
    res = 0
 
    # Calculate parity bits again
    for i in range(nr):
        val = 0
        for j in range(1, n + 1):
            if(j & (2**i) == (2**i)):
                val = val ^ int(arr[-1 * j])
 
        # Create a binary no by appending
        # parity bits together.
 
        res = res + val*(10**i)
 
    # Convert binary to decimal
    return int(str(res), 2)
 
 
# Enter the data to be transmitted
data = '1011001'
 
# Calculate the no of Redundant Bits Required
m = len(data)
r = calcRedundantBits(m)
 
# Determine the positions of Redundant Bits
arr = posRedundantBits(data, r)
 
# Determine the parity bits
arr = calcParityBits(arr, r)
 
# Data to be transferred
print("Data transferred is " + arr) 
 
# Stimulate error in transmission by changing
# a bit value.
# 10101001110 -> 11101001110, error in 10th position.
 
arr = '11101001110'
print("Error Data is " + arr)
correction = detectError(arr, r)
if(correction==0):
    print("There is no error in the received message.")
else:
    print("The position of error is ",len(arr)-correction+1,"from the left")
Output
Data transferred is 10101001110
Error Data is 11101001110
The position of error is  2 from the left

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