Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Towards Robustness in Residue Number Systems   The problem of robustly reconstructing a large number from its erroneous
remainders with respect to several moduli, namely the robust remaindering
problem, may occur in many applications including phase unwrapping, frequency
detection from several undersampled waveforms, wireless sensor networks, etc.
Assuming that the dynamic range of the large number is the maximal possible
one, i.e., the least common multiple (lcm) of all the moduli, a method called
robust Chinese remainder theorem (CRT) for solving the robust remaindering
problem has been recently proposed. In this paper, by relaxing the assumption
that the dynamic range is fixed to be the lcm of all the moduli, a trade-off
between the dynamic range and the robustness bound for two-modular systems is
studied. It basically says that a decrease in the dynamic range may lead to an
increase of the robustness bound. We first obtain a general condition on the
remainder errors and derive the exact dynamic range with a closed-form formula
for the robustness to hold. We then propose simple closed-form reconstruction
algorithms. Furthermore, the newly obtained two-modular results are applied to
the robust reconstruction for multi-modular systems and generalized to real
numbers. Finally, some simulations are carried out to verify our proposed
theoretical results.

8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys