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:
- Enter the Data to be transmitted
- Calculate the no of redundant bits required
- Determine the parity bits
- Create error data for testing
- 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 codedef 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 idef 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 arrdef 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 transmitteddata = '1011001'# Calculate the no of Redundant Bits Requiredm = len(data)r = calcRedundantBits(m)# Determine the positions of Redundant Bitsarr = posRedundantBits(data, r)# Determine the parity bitsarr = calcParityBits(arr, r)# Data to be transferredprint("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
