Generation of LDPC Check Matrix Using MadHG Rules with Code Implementation

This paper presents the implementation of MadHG generation rules for constructing LDPC check matrix H. The generated matrix exhibits specific properties: row weight of 6, column weight of 3, with the number of rows being half the number of columns (where larger row counts are preferable). The algorithm incorporates cycle detection to ensure no girth-4 cycles exist between any two columns in H. The corresponding generator matrix G is derived from H, maintaining the fundamental property where mod(G*H, 2) equals zero, ensuring proper orthogonal relationship between the matrices for LDPC encoding. The implementation uses the function call [H, G] = MadHG(m, n, x), where parameter x controls the structure of G: when x=1, the left half of G forms an identity matrix; when x=2, the identity matrix occupies the right half. This flexible implementation allows generation of longer LDPC codes with optimized characteristics. The generated LDPC codes are particularly valuable in communication systems and data transmission applications, offering improved error correction capabilities through their carefully designed matrix structures. The algorithm employs combinatorial mathematics and matrix manipulation techniques to achieve the desired code properties while maintaining computational efficiency.