{"ID":2836126,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.22757","arxiv_id":"2511.22757","title":"Moduli Selection in Robust Chinese Remainder Theorem: Closed-Form Solutions and Layered Design","abstract":"We study the fundamental problem of \\emph{moduli selection} in the Robust Chinese Remainder Theorem (RCRT), where each residue may be perturbed by a bounded error. Consider $L$ moduli of the form $m_i = Γ_i m$ ($1 \\le i \\le L$), where $Γ_i$ are pairwise coprime integers and $m \\in \\mathbb{R}^+$ is a common scaling factor. For small $L$ ($L = 2, 3, 4$), we obtain exact solutions that maximize the robustness margin under dynamic-range and modulus-bound constraints. We also introduce a Fibonacci-inspired \\emph{layered} construction (for $L = 2$) that produces exactly $K$ robust decoding layers, enabling predictable trade-offs between error tolerance and dynamic range. We further analyze how robustness and range evolve across layers and provide a closed-form expression to estimate the success probability under common data and noise models. The results are promising for various applications, such as sub-Nyquist sampling, phase unwrapping, range estimation, modulo analog-to-digital converters (ADCs), and robust residue-number-system (RNS)-based accelerators for deep learning. Our framework thus establishes a general theory of moduli design for RCRT, complementing prior algorithmic work and underscoring the broad relevance of robust moduli design across diverse information-processing domains.","short_abstract":"We study the fundamental problem of \\emph{moduli selection} in the Robust Chinese Remainder Theorem (RCRT), where each residue may be perturbed by a bounded error. Consider $L$ moduli of the form $m_i = Γ_i m$ ($1 \\le i \\le L$), where $Γ_i$ are pairwise coprime integers and $m \\in \\mathbb{R}^+$ is a common scaling fact...","url_abs":"https://arxiv.org/abs/2511.22757","url_pdf":"https://arxiv.org/pdf/2511.22757v1","authors":"[\"Wenyi Yan\",\"Lu Gan\",\"Hongqing Liu\",\"Shaoqing Hu\"]","published":"2025-11-27T21:06:57Z","proceeding":"eess.SP","tasks":"[\"eess.SP\"]","methods":"[]","has_code":false}