  We consider automorphism ensemble decoding (AED) of quasi-cyclic (QC)
low-density parity-check (LDPC) codes. Belief propagation (BP) decoding on the
conventional factor graph is equivariant to the quasi-cyclic automorphisms and
therefore prevents gains by AED. However, by applying small modifications to
the parity-check matrix at the receiver side, we can break the symmetry without
changing the code at the transmitter. This way, we can leverage a gain in
error-correcting performance using an ensemble of identical BP decoders,
without increasing the worst-case decoding latency. The proposed method is
demonstrated using LDPC codes from the CCSDS, 802.11n and 5G standards and
produces gains of 0.2 to 0.3 dB over conventional BP decoding. Compared to the
similarly performing saturated BP (SBP), the proposed algorithm reduces the
average decoding latency by more than eight times.
