Entropy-Based and Quadratic Conditional Innovation Metrics for Informed Dynamic Scheduling of Belief-Propagation Decoding for LDPC Codes

We propose two enhanced conditional innovation (CI) metrics for informed dynamic scheduling (IDS) in belief-propagation (BP) decoding of LDPC codes. The CI-based residual BP (CIRBP) algorithm uses the CI metric to guide the selection of the variable node (VN) to be updated and has been shown to outperform several existing IDS-based BP decoders, especially at the early decoding stage. However, the original CI metric uses only the absolute difference between the current and precomputed posterior probabilities and does not separately account for the reliability associated with each probability. By reformulating the CI metric relative to the decision boundary, we separate each posterior probability into its decision side and a linear-distance term reflecting reliability. Replacing the latter with the binary entropy complement yields the proposed entropy-based CI (E-CI) metric. Moreover, the proposed quadratic CI (Q-CI) metric is derived from the leading quadratic term in the local expansion of the entropy complement, avoiding the logarithmic operations required for direct E-CI evaluation. We apply both proposed metrics to the CIRBP decoder and its node-wise variant. Numerical results show that the proposed metrics generally provide lower frame error rates than the original CI metric, with their relative advantages depending on the code and decoding procedure.