Optional-stopping correction for Rateless prefix estimation

Derive an optional-stopping correction for confidence guarantees when Rateless IBLT prefixes are inspected repeatedly during sequential estimation.

Background

The Rateless IBLT adapter provides an asymptotic chi-square confidence interval for a fixed prefix length as the difference cardinality grows. The paper notes that this fixed-prefix result does not directly justify repeated inspection of successive prefixes, because adaptively stopping when an estimate or interval meets a criterion can alter the statistical coverage. A correction is therefore needed to preserve valid inference under optional stopping or sequential monitoring.

References

Repeated inspection would require an optional-stopping correction, which we leave for future work.

— IBLTs Measure Before They Decode: Self-Sizing Set Reconciliation from Pre-Peeling Counts  (2608.26537 - Wu et al., 27 Aug 2026) in Section 3, subsection “Rateless prefix analytic adapter” (following Proposition 3.5)

The variance and confidence intervals of the weighted frequency model, further reduction of the joint capacity, optimal stopping for Rateless sequential estimation, and an impossibility characterization for unsigned channels remain future work.

— IBLTs Measure Before They Decode: Self-Sizing Set Reconciliation from Pre-Peeling Counts  (2608.26537 - Wu et al., 27 Aug 2026) in Section 8, Conclusion