A Modified Shuffling Method to Split the Critical Path Delay in Layered Decoding of QC-LDPC Codes

Layered (or Turbo) decoding of Low-Density Parity-Check (LDPC) codes is considered as a decoding schedule that facilitates partially parallel architectures for performing iterative algorithms based on belief propagation. It has, on one hand, reduced implementation complexity and memory overhead compared to fully parallel architectures and, on the other hand, higher convergence speed compared to both serial and parallel architectures. In this paper, we introduce a general form of shuffling of the parity-check matrix of quasi-cyclic LDPC (QC-LDPC) codes which can split the critical path delay in layered decoding and therefore improve throughput by allowing higher clock rates. We also reveal a valuable property of Latin squares QC-LDPC codes which makes them a good candidate for the proposed shuffling method. As a result of that property, no special caution of choosing offset values in the proposed generalized shuffling method is required.