Other mapping families

Extend the failure-conditioned measurement and coverage analysis from the ideal Plain mapping to other mapping families.

Background

The paper's proofs and asymptotic laws are developed for the Plain mapping, in which each element independently chooses a uniformly random kk-subset of the MM cells. The authors explicitly identify other mapping families as future work, leaving open how the peeling threshold, overlap statistics, selection correlation, and conditional measurement law change under alternative mappings.

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