2014/12/31 by Li Xiao, Xiang-Gen Xia, Xiang‐Gen Xia +2
Computer Science · Mathematics · #Advanced Data Storage Technologies #Arithmetic #Bounded function #Chinese remainder theorem #Coding theory and cryptography #Coprime integers #Cryptographic Implementations and Security #Discrete mathematics #FOS: Computer and information sciences #Information Theory (cs.IT) #Mathematical analysis #Mathematics #Moduli #Pairwise comparison #Polynomial #Remainder #Statistics #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.1501.00163
published in arXiv (Cornell University) (Cornell University) · 12 pages, 2 figures
arxiv created 2014/12/31 · openalex publication_date 2014/12/31 · arxiv updated 2015/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
This paper investigates polynomial remainder codes with non-pairwise coprime moduli. We first consider a robust reconstruction problem for polynomials from erroneous residues when the degrees of all residue errors are assumed small, namely robust Chinese Remainder Theorem (CRT) for polynomials. It basically says that a polynomial can be reconstructed from erroneous residues such that the degree of the reconstruction error is upper bounded by τ whenever the degrees of all residue errors are upper bounded by τ, where a sufficient condition for τ and a reconstruction algorithm are obtained. By releasing the constraint that all residue errors have small degrees, another robust reconstruction is then presented when there are multiple unrestricted errors and an arbitrary number of errors with small degrees in the residues. By making full use of redundancy in moduli, we obtain a stronger residue error correction capability in the sense that apart from the number of errors that can be corrected in the previous existing result, some errors with small degrees can be also corrected in the residues. With this newly obtained result, improvements in uncorrected error probability and burst error correction capability in a data transmission are illustrated.