Hamming code Implementation in C/C++

Pre-requisite: Hamming Code

Given a message bit in the form of an array msgBit[], the task is to find the Hamming Code of the given message bit.

Examples:

Input: S = “0101”
Output:
Generated codeword:
r1 r2 m1 r4 m2 m3 m4
0  1   0    0  1     0    1
Explanation:
Initially r1, r2, r4 is set to ‘0’.
r1 = Bitwise XOR of all bits position that has ‘1’ in its 0th-bit position.
r2 = Bitwise XOR of all bits that has ‘1’ in its 1st-bit position.
r3 = Bitwise XOR of all bits that has ‘1’ in its 2nd-bit position.

Input: S  = “0111”
Output: 
Generated codeword: 
r1 r2 m1 r4 m2 m3 m4 
0  0   0    1  1     1    1 



 

Approach: The idea is to first find the number of redundant bits which can be found by initializing r with 1 and then incrementing it by 1 each time while 2r is smaller than (m + r + 1) where m is the number of bits in the input message. Follow the below steps to solve the problem:

  • Initialize r by 1 and increment it by 1 until 2r is smaller than m+r+1.
  • Initialize a vector hammingCode of size r + m which will be the length of the output message.
  • Initialize all the positions of redundant bits with -1 by traversing from i = 0 to r – 1 and setting hammingCode [2i 1] = -1. Then place the input message bits in all the positions where hammingCode[j] is not -1 in order where 0 <= j < (r + m).
  • Initialize a variable one_count with 0 to store the number of ones and then traverse from i = 0 to (r + m – 1).
  • If the current bit i.e., hammingCode[i] is not -1 then find the message bit containing set bit at log2(i+1)th position by traversing from j = i+2 to r+m by incrementing one_count by 1 if (j & (1<<x)) is not 0 and hammingCode[j – 1] is 1.
  • If for index i, one_count is even, set hammingCode[i] = 0 otherwise set hammingCode[i] = 1.
  • After traversing, print the hammingCode[] vector as the output message.

Below is the implementation of the above approach:

C

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// C program for the above approach
  
#include <math.h>
#include <stdio.h>
  
// Store input bits
int input[32];
  
// Store hamming code
int code[32];
  
int ham_calc(int, int);
void solve(int input[], int);
  
// Function to calculate bit for
// ith position
int ham_calc(int position, int c_l)
{
    int count = 0, i, j;
    i = position - 1;
  
    // Traverse to store Hamming Code
    while (i < c_l) {
  
        for (j = i; j < i + position; j++) {
  
            // If current boit is 1
            if (code[j] == 1)
                count++;
        }
  
        // Update i
        i = i + 2 * position;
    }
  
    if (count % 2 == 0)
        return 0;
    else
        return 1;
}
  
// Function to calculate hamming code
void solve(int input[], int n)
{
    int i, p_n = 0, c_l, j, k;
    i = 0;
  
    // Find msg bits having set bit
    // at x'th position of number
    while (n > (int)pow(2, i) - (i + 1)) {
        p_n++;
        i++;
    }
  
    c_l = p_n + n;
  
    j = k = 0;
  
    // Traverse the msgBits
    for (i = 0; i < c_l; i++) {
  
        // Update the code
        if (i == ((int)pow(2, k) - 1)) {
            code[i] = 0;
            k++;
        }
  
        // Update the code[i] to the
        // input character at index j
        else {
            code[i] = input[j];
            j++;
        }
    }
  
    // Traverse and update the
    // hamming code
    for (i = 0; i < p_n; i++) {
  
        // Find current position
        int position = (int)pow(2, i);
  
        // Find value at current position
        int value = ham_calc(position, c_l);
  
        // Update the code
        code[position - 1] = value;
    }
  
    // Print the Hamming Code
    printf("\nThe generated Code Word is: ");
    for (i = 0; i < c_l; i++) {
        printf("%d", code[i]);
    }
}
  
// Driver Code
void main()
{
    // Given input message Bit
    input[0] = 0;
    input[1] = 1;
    input[2] = 1;
    input[3] = 1;
  
    int N = 4;
  
    // Function Call
    solve(input, N);
}

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C++

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// C++ program for the above approach
  
#include <bits/stdc++.h>
using namespace std;
  
// Function to generate hamming code
vector<int> generateHammingCode(
    vector<int> msgBits, int m, int r)
{
    // Stores the Hamming Code
    vector<int> hammingCode(r + m);
  
    // Find positions of redundant bits
    for (int i = 0; i < r; ++i) {
  
        // Placing -1 at redundant bits
        // place to identify it later
        hammingCode[pow(2, i) - 1] = -1;
    }
  
    int j = 0;
  
    // Iterate to update the code
    for (int i = 0; i < (r + m); i++) {
  
        // Placing msgBits where -1 is
        // absent i.e., except redundant
        // bits all postions are msgBits
        if (hammingCode[i] != -1) {
            hammingCode[i] = msgBits[j];
            j++;
        }
    }
  
    for (int i = 0; i < (r + m); i++) {
  
        // If current bit is not redundant
        // bit then continue
        if (hammingCode[i] != -1)
            continue;
  
        int x = log2(i + 1);
        int one_count = 0;
  
        // Find msg bits containing
        // set bit at x'th position
        for (int j = i + 2;
             j <= (r + m); ++j) {
  
            if (j & (1 << x)) {
                if (hammingCode[j - 1] == 1) {
                    one_count++;
                }
            }
        }
  
        // Generating hamming code for
        // even parity
        if (one_count % 2 == 0) {
            hammingCode[i] = 0;
        }
        else {
            hammingCode[i] = 1;
        }
    }
  
    // Return the generated code
    return hammingCode;
}
  
// Function to find the hamming code
// of the given message bit msgBit[]
void findHammingCode(vector<int>& msgBit)
{
  
    // Message bit size
    int m = msgBit.size();
  
    // r is the number of redundant bits
    int r = 1;
  
    // Find no. of redundant bits
    while (pow(2, r) < (m + r + 1)) {
        r++;
    }
  
    // Generating Code
    vector<int> ans
        = generateHammingCode(msgBit, m, r);
  
    // Print the code
    cout << "Message bits are: ";
    for (int i = 0; i < msgBit.size(); i++)
        cout << msgBit[i] << " ";
  
    cout << "\nHamming code is: ";
    for (int i = 0; i < ans.size(); i++)
        cout << ans[i] << " ";
}
  
// Driver Code
int main()
{
    // Given message bits
    vector<int> msgBit = { 0, 1, 0, 1 };
  
    // Function Call
    findHammingCode(msgBit);
  
    return 0;
}

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Output:

The generated Code Word is: 0001111

Time Complexity: O((M + R)2) where M is the number of bits in the input message and R is the number of redundant bits 
Auxiliary Space: O(M + R)

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