  A new protograph-based framework for message passing (MP) decoding of low
density parity-check (LDPC) codes with Hamming weight amplifiers (HWAs), which
are used e.g. in the NIST post-quantum crypto candidate LEDAcrypt, is proposed.
The scheme exploits the correlations in the error patterns introduced by the
HWA using a turbo-like decoding approach where messages between the decoders
for the outer code given by the HWA and the inner LDPC code are exchanged.
Decoding thresholds for the proposed scheme are computed using density
evolution (DE) analysis for belief propagation (BP) and ternary message passing
(TMP) decoding and compared to existing decoding approaches. The proposed
scheme improves upon the basic approach of decoding LDPC code from the
amplified error and has a similar performance as decoding the corresponding
moderate-density parity-check (MDPC) code but with a significantly lower
computational complexity.
