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In this paper, we propose a modified iterative decoding algorithm to decode a special class of quasi-cyclic low- density parity-check (QC-LDPC) codes such as QC-LDPC codes used in the IEEE 802.16e standards. The proposed decoding is implemented by serially decoding block codes with identical parity-check matrix H1 derived from the parity-check matrix H of the QC-LDPC codes. The dimensions of H1 are much smaller than those of H. Extrinsic values can be passed among these block codes since the code bits of these block codes are overlapped. Hence, the proposed decoding can reduce the number of iterations required by up to forty percent without error performance loss as compared to the conventional message- passing decoding algorithm. A partially-parallel very large-scale integration (VLSI) architecture is proposed to implement such a decoding algorithm. The proposed VLSI decoder can fully take advantage of the proposed decoding to increase its throughput. In addition, the proposed decoder only needs to store check-to- variable messages and hence is memory efficient.