QSOLKCB/QEC: QSOLKCB/QEC v2.2.0 — Belief Propagation Stability Hardening for QLDPC CSS Codes

Read full text
Authors: Trent Slade, Claude
Cited by: 0

Abstract

Release Description — v2.2.0 Version 2.2.0 introduces a numerical stability correction to the belief-propagation (sum-product) decoder implemented in the JointSPDecoder class of the QSOLKCB/QEC framework. This release resolves the handling of degree-1 parity-check nodes in the Tanner graph, ensuring consistency with proper extrinsic belief-propagation semantics. In prior versions, degree-1 checks implicitly fell through to the general tanh-product update rule: L_{c->v} = 2 * atanh( Π_{v' ≠ v} tanh( L_{v'->c} / 2 ) ) For a single-neighbor check node, the product is taken over an empty set. By definition, the empty product equals 1. This leads to: atanh(1) → ∞ Under finite-precision arithmetic, this produces extremely large log-likelihood values, injecting artificial confidence into the decoding process and effectively double-counting intrinsic channel information. Under finite-precision arithmetic, this injected artificial log-likelihood amplification into the decoding process, effectively double-counting intrinsic channel evidence and potentially destabilizing sparse or irregular LDPC structures. The updated implementation explicitly sets the outgoing check-to-variable message to 0.0 for degree-1 parity checks, enforcing zero extrinsic contribution and restoring mathematically correct BP behavior. This modification: Eliminates artificial confidence injection, Improves numerical robustness for sparse Tanner graphs, Preserves convergence behavior under low-noise regimes, Maintains deterministic decoder operation. No changes were made to the construction layer, additive lift invariants (v2.1.0), CSS orthogonality guarantees, finite-field lifting framework, or rank computation logic. All existing regression tests pass unchanged. This release constitutes a decoder stability hardening increment with no architectural modifications to the QLDPC CSS construction framework.

Publication details

Journal / source
Zenodo (CERN European Organization for Nuclear Research)
Publication date
18 February 2026