Modular Aggregation as a Debiasing Method for Non-Stationary Discrete Sources: Convergence and Numerical Validatio

Abstract:We analyze \emph{modular aggregation}---summing $N$ independent outcomes modulo $m$---as a post-processing method for extracting nearly uniform randomness from biased discrete sources. Using discrete Fourier analysis over the cyclic group $\mathbb{Z}_m$, we prove exponential convergence of the output distribution to uniformity, with a rate determined by the largest non-trivial Fourier modulus. The result applies to independent non-stationary (non-IID) sources under a uniform spectral-gap condition on the non-trivial Fourier modes. Numerical simulations under several bias regimes, including cyclic drift and extreme cyclic bias, are used as finite-sample diagnostics and illustrate the theoretical predictions in comparison with Peres extraction and SHA-256 post-processing. The robustness of modular aggregation comes at a retention cost of order $1/N$, yielding an explicit trade-off between statistical quality and throughput.

Data Analysis, Statistics and Probability (physics.data-an); Information Theory (cs.IT); Probability (math.PR); Quantum Physics (quant-ph)

arXiv:2504.18585 [physics.data-an]

(or arXiv:2504.18585v3 [physics.data-an] for this version)

https://doi.org/10.48550/arXiv.2504.18585 Focus to learn more arXiv-issued DOI via DataCite

Gueron, E., Statistics & Probability Letters, 239, 110901 (2026)

https://doi.org/10.1016/j.spl.2026.110901 Focus to learn more DOI(s) linking to related resources

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