Parity Check Matrix Partitioning for Layered Decoding of QC-LDPC Codes

In this paper, we propose two algorithms to partition the parity check matrices (PCMs) for the layered decoding of quasi-cyclic low-density parity-check (QC-LDPC) codes, which targets to reduce the hardware complexity and computation delay. We formulate the optimization problem of PCM partitioning, and systematically propose the principle of partitioning to guarantee a block cyclic shift property for different decoding layers. After that, we develop both greedy and enumerative partitioning algorithms, aiming at minimizing the maximum column weight of each decoding layer. We further derive a tight lower bound for the minimum achievable maximum column weight, which can help to early terminate a searching process once the lower bound is achieved. Simulation results show that the proposed algorithms are generally capable of achieving the lower bound or differ by one.