Construction of high-rate QC-LDPC codes with multi-weight circulants

In this paper, we propose a construction method of quasi-cyclic low-density parity-check (QC-LDPC) codes with multi-weight circulants (MQC-LDPC codes) which is suitable for high-rate LDPC codes with moderate length. MQC-LDPC codes can achieve better degree distributions, Hamming weight distributions, and stopping set weight distributions than conventional QC-LDPC codes with single-weight circulants (SQC-LDPC codes). Within the same framework, we generalize and simplify the error minimization progressive edge growth (EMPEG) algorithm for supporting the structure with multi-weight circulants. Simulation results show that the constructed MQC-LDPC codes offer better performance at both high and low signal to noise ratio (SNR) regions in additive white Gaussian noise (AWGN) channels than the conventional SQC-LDPC codes defined in 802.11ad and 802.16e.