Efficient Search of Compact QC-LDPC and SC-LDPC Convolutional Codes With Large Girth

We propose a low-complexity method to find quasi-cyclic low-density parity-check block codes with girth 10 or 12 and length shorter than those designed through classical approaches. The method is extended to time-invariant spatially coupled low-density parity-check convolutional codes, permitting to achieve small syndrome former constraint lengths. Several numerical examples are given to show its effectiveness.