  Algebraic codes such as BCH code are receiving renewed interest as their
short block lengths and low/no error floors make them attractive for
ultra-reliable low-latency communications (URLLC) in 5G wireless networks. This
paper aims at enhancing the traditional adaptive belief propagation (ABP)
decoding, which is a soft-in-soft-out (SISO) decoding for high-density
parity-check (HDPC) algebraic codes, such as Reed-Solomon (RS) codes,
Bose-Chaudhuri-Hocquenghem (BCH) codes, and product codes. The key idea of
traditional ABP is to sparsify certain columns of the parity-check matrix
corresponding to the least reliable bits with small log-likelihood-ratio (LLR)
values. This sparsification strategy may not be optimal when some bits have
large LLR magnitudes but wrong signs. Motivated by this observation, we propose
a Perturbed ABP (P-ABP) to incorporate a small number of unstable bits with
large LLRs into the sparsification operation of the parity-check matrix. In
addition, we propose to apply partial layered scheduling or hybrid dynamic
scheduling to further enhance the performance of P-ABP. Simulation results show
that our proposed decoding algorithms lead to improved error correction
performances and faster convergence rates than the prior-art ABP variants.
