Function MadHG Generates Parity Check Matrix H for Regular LDPC Codes
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Resource Overview
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).
Detailed Documentation
The MadHG function constructs a regular LDPC code's parity check matrix H with specified parameters: row weight of 6, column weight of 3, and row count equal to half the column count (higher row counts improve performance). The algorithm incorporates cycle detection mechanisms to eliminate girth-4 cycles between any column pairs in H. The corresponding generator matrix G is derived through systematic encoding techniques, ensuring mod(G*H, 2) = 0 for valid codeword generation. The function implements two encoding configurations through parameter x: when x=1, the left half of G forms an identity matrix; when x=2, the right half becomes an identity matrix. This structured approach facilitates efficient encoding while maintaining the code's error-correction properties.
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