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Improving the minimum distance of QC-LDPC codes by removing cycles

We focus on regular and irregular quasi-cyclic low-density parity-check codes and analyze their codewords. We show that any codeword can be decomposed into component codewords with smaller weight belonging to some component codes. Component codewords can be associated to cycles in the Tanner graph of the code. We transfer these theoretical results into the code design, finding that the removal of some specific classes of cycles yields benefits in terms of minimum distance and error rate performance.