Abstract—Low-Density Parity-Check (LDPC) codes are widely used in many applications including high-speed communications such as 802.11n and 802.16e and data memory/storage systems such as NAND flash memory. For practical use, most of them take Quasi-Cyclic (QC) structure and good QC LDPC codes with various parameters are still necessary to be constructed. In this paper, we proposed a construction method of QC LDPC codes whose parity-check matrix consists of a single row of circulant matrices by using a class of balanced incomplete block design, called perfect difference family (PDF). We alter the structure of PDFs with irregular block sizes and then use them to construct the proposed QC LDPC codes to support various lengths, code rates, and degree distributions. We construct two QC LDPC codes based on PDFs and compare them with the random-like LDPC codes constructed from the progressive edge-growth (PEG) algorithm via the additive white Gaussian noise channel simulation. The results show that the proposed QC LDPC codes have a very similar error-correcting performance to the PEG LDPC codes while supporting the QC structure for easy hardware implementation.
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