Reliability Limits and Decoding for Partial Nanopore Protein Rereads With Persistent State

Abstract

Repeated observations of one physical object need not constitute independent channel uses. We model partial nanopore protein rereads as a finite-alphabet channel with canonical content, persistent readout, and pass-local coverage and synchronization. For exact compound-pass data, matched inference approaches the equivalence-class canonical posterior, and sitewise excess Bayes risk admits an action-aware achievable exponent. In an aligned specialization, observation-local redraw can cause linear-in-$K$ growth in true-label negative log-likelihood (NLL). We derive order-$b$ projection-stability bounds and an exact passwise-fusion diagnostic. On a PASTOR-informed semi-synthetic hard-symbol channel, label-blind deterministic-mixture importance sampling (LB-IS) agrees with exact enumeration at $L=7$. At $L=24, K=10$, LB-IS meets every prespecified aggregate absolute marginal-posterior and score-agreement criterion against a fixed high-allocation reference in three selected conditions. Joint agreement holds for the representative and high-NLL conditions, while the near-zero condition remains inconclusive. Exact $L \leq 6$ benchmarks identify order 4 as the smallest tested common cap. At target scale, the reference supports selected unprojected functionals, while neither order 4 nor 5 attains joint agreement, defining a tested finite-memory boundary. Across 16 cells, the order-4 shared branch lowers NLL by 0.033-0.224 nats per residue relative to pass-local.