  The medium-density parity-check (MDPC) code-based McEliece cryptosystem
remains a finalist of the post-quantum cryptography standard. The Min-sum
decoding algorithm achieves better performance-complexity tradeoff than other
algorithms for MDPC codes. However, the prior Min-sum MDPC decoder requires
large memories, whose complexity dominates the overall complexity. Besides, its
actual achievable parallelism is limited. This paper has four contributions:
For the first time, the row-layered scheduling scheme is exploited to
substantially reduce the memory requirement of MDPC decoders; A low-complexity
scheme is developed to mitigate the performance loss caused by finite precision
representation of the messages and high column weights of MDPC codes in
row-layered decoding; Constraints are added to the parity check matrix
construction to enable effective parallel processing with negligible impacts on
the decoder performance and resilience towards attacks; A novel parity check
matrix division scheme for highly efficient parallel processing is proposed and
the corresponding parallel row-layered decoder architecture is designed. The
number of clock cycles for each decoding iteration is reduced by a factor of L
using the proposed L-parallel decoder with very small memory overhead. For an
example 2-parallel decoder, the proposed design leads to 26% less memory
requirement and 70% latency reduction compared to the prior decoder.
