Structure-aware decoding using PRISM meta-checks

Develop and assess decoders for PRISM codes that explicitly exploit the inherited meta-check constraints, including hierarchical decoders that first identify and repair inconsistent syndrome bits and unified decoders that jointly infer data and syndrome errors while enforcing stabilizer and meta-check constraints.

Background

PRISM codes inherit meta-check structures from the chain-complex construction of their underlying Steinberg codes. These constraints provide additional relations among syndrome bits, but the numerical experiments in the paper use BP-LSD directly and do not exploit the meta-check information.

The paper identifies several unresolved possibilities: a hierarchical procedure that repairs inconsistent syndromes before BP-LSD decoding, or a unified procedure that jointly estimates data and measurement errors under both stabilizer and meta-check constraints. Because the meta-check distance is smaller than the code distance, single-shot decoding may fail asymptotically; nevertheless, the authors leave open whether structure-aware decoding can improve finite-size performance under circuit-level noise relative to direct BP-LSD decoding.