Finite-size error rate

Determine the finite-size error rate of the failure-conditioned measurement and coverage approximations for the ideal Plain IBLT peeling model.

Background

The paper establishes asymptotic laws for the count-energy measurement conditional on ideal peeling failure, including a Gaussian-selection law in the critical window and a two-mechanism mixture along much of the load axis. The authors explicitly leave the finite-size error rate of these approximations unresolved, so quantitative finite-size accuracy remains an open problem.

References

The following questions are left for future work: the error rate at finite size; in the moving subcritical region with $|r_M|/\sqrt{\log M}\to\infty$, the relative probability and the fine conditional law of the macroscopic layer itself, a region beyond the scope of Proposition~\ref{prop:mda}, where the failure-conditioned law is dominated by the repeated-edge layer; the complete classification of the sparse end $d=O(\sqrt M)$; $k$ growing with the size; and non-ideal checksums and other mapping families.

— Decoding Failure Biases IBLT Count Measurements: A Gaussian-Selection Law at the Peeling Threshold  (2610.21418 - Wu, 15 Oct 2026) in Section Discussion and conclusion

The following questions are left for future work: the error rate at finite size; in the moving subcritical region with $|r_M|/\sqrt{\log M}\to\infty$, the relative probability and the fine conditional law of the macroscopic layer itself, a region beyond the scope of Proposition~\ref{prop:mda}, where the failure-conditioned law is dominated by the repeated-edge layer; the complete classification of the sparse end $d=O(\sqrt M)$; $k$ growing with the size; and non-ideal checksums and other mapping families.

— Decoding Failure Biases IBLT Count Measurements: A Gaussian-Selection Law at the Peeling Threshold  (2610.21418 - Wu, 15 Oct 2026) in Section Discussion and conclusion; Proposition \ref{prop:axis}

The following questions are left for future work: the error rate at finite size; in the moving subcritical region with $|r_M|/\sqrt{\log M}\to\infty$, the relative probability and the fine conditional law of the macroscopic layer itself, a region beyond the scope of Proposition~\ref{prop:mda}, where the failure-conditioned law is dominated by the repeated-edge layer; the complete classification of the sparse end $d=O(\sqrt M)$; $k$ growing with the size; and non-ideal checksums and other mapping families.

— Decoding Failure Biases IBLT Count Measurements: A Gaussian-Selection Law at the Peeling Threshold  (2610.21418 - Wu, 15 Oct 2026) in Section Discussion and conclusion

The following questions are left for future work: the error rate at finite size; in the moving subcritical region with $|r_M|/\sqrt{\log M}\to\infty$, the relative probability and the fine conditional law of the macroscopic layer itself, a region beyond the scope of Proposition~\ref{prop:mda}, where the failure-conditioned law is dominated by the repeated-edge layer; the complete classification of the sparse end $d=O(\sqrt M)$; $k$ growing with the size; and non-ideal checksums and other mapping families.

— Decoding Failure Biases IBLT Count Measurements: A Gaussian-Selection Law at the Peeling Threshold  (2610.21418 - Wu, 15 Oct 2026) in Section Discussion and conclusion; Section \ref{sec:model}

This conclusion is a numerical verification; whether the shift order transfers to the Plain model still requires a separate proof.

— Decoding Failure Biases IBLT Count Measurements: A Gaussian-Selection Law at the Peeling Threshold  (2610.21418 - Wu, 15 Oct 2026) in Section \ref{sec:threshold}