LDPC:How to make LDPC parity check matrix H from non-systematic to systematic in C/C+

Hi,
I am working with KINTEX board for LDPC encoding and decoding.Through Vivado HLS, I need to transform a parity-check matrix H (that only consists of ones and zeros) from a non-standard to a standard form through C/C++ programming language. Here below you may find samples of non-standard parity check matrices in which Gauss-Jordan elimination (over GF(2)) can be applied.

Initially, i need C/C++ programming logic please help me if you do have any idea about LDPC. I would need a method that works out with matrices of any dimension.

this is, express it as

Hsys = [I| P]

This is my H matrix

H=[1 1 0 0 1 0;
1 0 0 1 0 1;
1 1 1 0 0 1 ];

Expected Systematic H matrix

Hsys=[1 0 0 1 0 1;
0 1 0 1 1 1;
0 0 1 0 1 1 ];

Code:

---

#include<stdio.h>
int main()
{
    // encoding
    int i,j;
    int message;
    int H_Matrix[3][6]={{1,1,0,0,1,0},{1,0,0,1,0,1},{1,1,1,0,0,1}};
    int temp[3][6]={0};
for(j=0;j<6;j++)
    {
        temp[1][j]=(H_Matrix[1][j]^H_Matrix[0][j]);
        H_Matrix[1][j] = temp[1][j];
        temp[2][j]=(H_Matrix[2][j]^H_Matrix[0][j]);
        H_Matrix[2][j] = temp[2][j];
        temp[0][j]=(H_Matrix[0][j]^H_Matrix[1][j]);
        H_Matrix[0][j] = temp[0][j];
    }
 
for(i=0;i<3;i++)
{
    for(j=0;j<6;j++)
    {
        printf("%d\t ",H_Matrix[i][j]);
    }
    printf("\n");
}
}

---

Logic
n=6 k=3 q=2
Start [0,0] = 1
Pivot [0,0] = 1
r_2 --> r_2 - r_1
r_3 --> r_3 - r_1
1 1 0 0 1 0
0 1 0 1 1 1
0 0 1 0 1 1
--
Start [1,1] = 1
Pivot [1,1] = 1
r_1 --> r_1 - r_2
1 0 0 1 0 1
0 1 0 1 1 1
0 0 1 0 1 1
--
Start [2,2] = 1
Pivot [2,2] = 1
1 0 0 1 0 1
0 1 0 1 1 1
0 0 1 0 1 1

A friend of mine, has written Gauss eliminator which can be easily adopted for int values, here is the code:

Code:

---

void GaussEliminator::solve()
{
m_vecResult.clear();

std::vector<double> v(m_dataMatrix.size() + 1);

unsigned char curr_index = 0, add_index = 0;

//now triagonalize matrix

for (data_matrix::iterator i = m_dataMatrix.begin(), e = m_dataMatrix.end(), k; i != e; ++i, ++curr_index) {

//normalize next row

std::transform(i->begin(), i->end(), i->begin(), std::bind2nd(std::divides<double>(), *(i->begin() + curr_index)));

//remove that item from the next ones

for (k = i + 1; k != e; ++k) {

//base row

v.assign(i->begin(), i->end());

//multiply by the next modified row and then substract

std::transform(v.begin(), v.end(), v.begin(), std::bind2nd(std::multiplies<double>(), *(k->begin() + curr_index)));

std::transform(k->begin(), k->end(), v.begin(), k->begin(), std::minus<double>());

}

}

//now perform reverse process

curr_index = m_dataMatrix.size();

for (data_matrix::reverse_iterator i = m_dataMatrix.rbegin(), e = m_dataMatrix.rend(); i != e; ++i, ++add_index, --curr_index)

m_vecResult.push_front((i->back() - std::inner_product<std::vector<double>::iterator, std::deque<double>::iterator, double>(i->begin() + curr_index, i->end() - 1, m_vecResult.begin(), 0)));

}

---

Hi,

Thanks for your response. Really i can`t understand concept of your code. I am beginner in programming code (C/C++) so i request you to start from the main function.


This is my H matrix

H=[1 1 0 0 1 0;
1 0 0 1 0 1;
1 1 1 0 0 1 ];

Expected Systematic H matrix: Hsys = [Identity matrix | P] //Requirement:Initially, i need C/C++ programming logic please help me if you do have any idea about LDPC. I would need a method that works out with matrices of any dimension.

Hsys=[1 0 0 1 0 1;
0 1 0 1 1 1;
0 0 1 0 1 1 ];

Quote:

---

Originally Posted by AvDav

A friend of mine, has written Gauss eliminator which can be easily adopted for int values, here is the code:

Code:

---

void GaussEliminator::solve()
{
m_vecResult.clear();

std::vector<double> v(m_dataMatrix.size() + 1);

unsigned char curr_index = 0, add_index = 0;

//now triagonalize matrix

for (data_matrix::iterator i = m_dataMatrix.begin(), e = m_dataMatrix.end(), k; i != e; ++i, ++curr_index) {

//normalize next row

std::transform(i->begin(), i->end(), i->begin(), std::bind2nd(std::divides<double>(), *(i->begin() + curr_index)));

//remove that item from the next ones

for (k = i + 1; k != e; ++k) {

//base row

v.assign(i->begin(), i->end());

//multiply by the next modified row and then substract

std::transform(v.begin(), v.end(), v.begin(), std::bind2nd(std::multiplies<double>(), *(k->begin() + curr_index)));

std::transform(k->begin(), k->end(), v.begin(), k->begin(), std::minus<double>());

}

}

//now perform reverse process

curr_index = m_dataMatrix.size();

for (data_matrix::reverse_iterator i = m_dataMatrix.rbegin(), e = m_dataMatrix.rend(); i != e; ++i, ++add_index, --curr_index)

m_vecResult.push_front((i->back() - std::inner_product<std::vector<double>::iterator, std::deque<double>::iterator, double>(i->begin() + curr_index, i->end() - 1, m_vecResult.begin(), 0)));

}

---

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1) Well, I have no idea on what LDPC is.
2) I just thought the code can be useful for this purpose and really it can work out with matrix of arbitrary NxM dimensions.