Generation of LDPC Check Matrix Using MadHG Rules with Code Implementation

Implementation of MadHG method for constructing LDPC check matrix H with row weight 6, column weight 3, and row count half of column count (preferably larger row numbers). The algorithm ensures no girth-4 cycles between any two columns in H and produces corresponding generator matrix G satisfying mod(G*H, 2)=0. Function call: [H, G] = MadHG(m, n, x), where x=1 yields identity matrix in left half of G, x=2 in right half.

Function MadHG Generates Parity Check Matrix H for Regular LDPC Codes

The MadHG function generates a regular LDPC code parity check matrix H with row weight 6, column weight 3, and number of rows equal to half the number of columns (larger row counts are preferred). The implementation ensures no girth-4 cycles exist between any two columns in H, while producing a corresponding generator matrix G that satisfies mod(G*H, 2) = 0. The algorithm employs structured construction methods to maintain code regularity and cycle properties. Usage: [H, G] = MadHG(m, n, x), where x = 1 (yields identity matrix in left half of G) or 2 (identity matrix in right half of G).