Construction of quasi-cyclic low-density parity-check codes for simplifying shuffle networks in layered decoder

Offset Shuffle Networks (OSNs) interleave a-posterior probability messages in the Block Row-Layered Decoder (BRLD) of Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes. However, OSNs usually consume a significant amount of computational resources and limit the clock frequency, particularly when the size of the Circulant Permutation Matrix (CPM) is large. To simplify the architecture of the OSN, we propose a Simplified Offset Shuffle Network Block Progressive Edge-Growth (SOSN-BPEG) algorithm to construct a class of QC-LDPC codes. The SOSN-BPEG algorithm constrains the shift values of CPMs and the difference of the shift values in the same column by progressively appending check nodes. Simulation results indicate that the error performance of the SOSN-BPEG codes is the same as that of the codes in WiMAX and DVB-S2. The SOSN-BPEG codes can reduce the complexity of the OSNs by up to 54.3%, and can improve the maximum frequency by up to 21.7% for various code lengths and rates.