Determination of Minimal Matrices of Simple Cycles in LDPC Codes

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The performance of Low-Density Parity-Check (LDPC) codes of finite length may be strongly affected by their cycle property such as girth and stopping sets, etc. Here, the girth is the minimum length of cycles in the Tanner graph of a given parity-check matrix. In most cases, it is difficult to analyze explicitly these factors of randomly constructed LDPC codes and predict their performance. One advantage of Quasi-Cyclic LDPC (QC-LDPC) codes based on circulant permutation matrices is that it is easier to analyze their code properties than in the case of random LDPC codes.