A Construction of Linearly Encodable QC-LDPC Codes by Grouping Cyclic Shift and Block Elimination

In this paper, the girth and rank property based on grouping cyclic shift of a parity-check matrix is proved firstly. Then a quasi-cyclic square matrix with full rank is constructed by grouping cyclic shift and block elimination. By proper matrix extension, we construct a parity-check matrix based on the square matrix whose column weight is close or equal to three, which is suitable for efficient encoding procedure in [3][4][11] with a near linear complexity. Simulation results show a better performance compared to array based LDPC codes and LDPC codes in 802.11n standard.