Related papers: Generic design of Chinese remaindering schemes
We propose a generic design for Chinese remainder algorithms. A Chinese remainder computation consists in reconstructing an integer value from its residues modulo non coprime integers. We also propose an efficient linear data structure, a…
This paper introduces two forms of modular inverses and proves their reciprocity formulas respectively. These formulas are then applied to formulate new and generalized algorithm for computing these modular inverses. The same algorithm is…
Residue arithmetic is an elegant and convenient way of computing with integers that exceed the natural word size of a computer. The algorithms are highly parallel and hence naturally adapted to quantum computation. The process differs from…
A well-known generalisation of positional numeration systems is the case where the base is the residue class of $x$ modulo a given polynomial $f(x)$ with coefficients in (for example) the integers, and where we try to construct finite…
A generalized Chinese remainder theorem (CRT) for multiple integers from residue sets has been studied recently, where the correspondence between the remainders and the integers in each residue set modulo several moduli is not known. A…
This paper explores the ability of the Chinese Remainder Theorem formalism to model Montgomery-type algorithms. A derivation of CRT based on Qin's Identity gives Montgomery reduction algorithm immediately. This establishes a unified…
Generalized Chinese Remainder Theorem (CRT) is a well-known approach to solve ambiguity resolution related problems. In this paper, we study the robust CRT reconstruction for multiple numbers from a view of statistics. To the best of our…
In this paper we propose several strategies for the exact computation of the determinant of a rational matrix. First, we use the Chinese Remaindering Theorem and the rational reconstruction to recover the rational determinant from its…
Using an adaptation of Qin Jiushao's method from the 13th century, it is possible to prove that a system of linear modular equations a(i,1) x(i) + ... + a(i,n) x(n) = b(i) mod m(i), i=1, ..., n has integer solutions if m(i)>1 are pairwise…
The Chinese remainder theorem (CRT) provides an efficient way to reconstruct an integer from its remainders modulo several integer moduli, and has been widely applied in signal processing and information theory. Its multidimensional…
Chinese Remainder Theorem (CRT) has been widely studied with its applications in frequency estimation, phase unwrapping, coding theory and distributed data storage. Since traditional CRT is greatly sensitive to the errors in residues due to…
The Chinese Remainder Theorem for the integers says that every system of congruence equations is solvable as long as the system satisfies an obvious necessary condition. This statement can be generalized in a natural way to arbitrary…
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 $m_i = \Gamma_i m$ ($1 \le i \le L$), where…
Based on unique decoding of the polynomial residue code with non-pairwise coprime moduli, a polynomial with degree less than that of the least common multiple (lcm) of all the moduli can be accurately reconstructed when the number of…
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…
A standard method for finding a rational number from its values modulo a collection of primes is to determine its value modulo the product of the primes via Chinese remaindering, and then use Farey sequences for rational reconstruction.…
Chinese Remainder Theorem (CRT) is a powerful approach to solve ambiguity resolution related problems such as undersampling frequency estimation and phase unwrapping which are widely applied in localization. Recently, the deterministic…
It is well-known that the traditional Chinese remainder theorem (CRT) is not robust in the sense that a small error in a remainder may cause a large error in the reconstruction solution. A robust CRT was recently proposed for a special case…
In this paper, we introduce a new family of codes relevent for rank and sum-rank metrics. These codes are based on an effective Chinese remainders theorem for linearized polynomials over finite fields. We propose a decoding algorithm for…
The problem of robustly reconstructing an integer vector from its erroneous remainders appears in many applications in the field of multidimensional (MD) signal processing. To address this problem, a robust MD Chinese remainder theorem…