On the Encoding Complexity of Quasi-Cyclic LDPC Codes

In this paper, we propose a parity check matrix (PCM) construction technique that reduces the encoding complexity of quasi-cyclic (QC)-LDPC codes. The proposed construction method is based on a constraint selection of shifting factors, shown here to reduce the density of an inverted matrix used in several encoding algorithms. Furthermore, it demonstrates that the complexity of encoding schemes involving inverted matrices, can be defined by the density of the small inverted binary base matrix and not by the extended QC-PCM. Comparisons of the proposed codes with codes employed in international standards and with randomly shifted QC-LDPC codes of comparable characteristics, show the low complexity of the corresponding hardware implementations and a BER performance equivalent to that of previously reported codes without increasing the decoding complexity. Furthermore, adoption of the proposed method can decrease the complexity of several encoding procedures; in particular, an area reduction of 40%–55% is reported for QC-LDPC encoders, while a reduction of 86% is reported for Multi-Level-QC-LDPC encoders.