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Bias-Aware BP Decoding of Quantum Codes via Directional D...
Mohammad Rowshan · 2026-01-12 · via cs.IT updates on arXiv.org

We study directionally informed belief propagation (BP) decoding for quantum CSS codes, where anisotropic Tanner-graph structure and biased noise concentrate degeneracy along preferred directions. We formalize this by placing orientation weights on Tanner-graph edges, aggregating them into per-qubit directional weights, and defining a \emph{directional degeneracy enumerator} that summarizes how degeneracy concentrates along those directions. A single bias parameter~$β$ maps these weights into site-dependent log-likelihood ratios (LLRs), yielding anisotropic priors that plug directly into standard BP$\rightarrow$OSD decoders without changing the code construction. We derive bounds relating directional and Hamming distances, upper bound the number of degenerate error classes per syndrome as a function of distance, rate, and directional bias, and give a MacWilliams-type expression for the directional enumerator. Finite-length simulations under code-capacity noise show significant logical error-rate reductions -- often an order of magnitude at moderate physical error rates -- confirming that modest anisotropy is a simple and effective route to hardware-aware decoding gains.