Two-layer Locally Repairable Codes for Distributed Storage Systems

In this paper, we propose locally repairable codes (LRCs) with optimal minimum distance for distributed storage systems (DSS). A two-layer encoding structure is employed to ensure data reconstruction and the designated repair locality. The data is first encoded in the first layer by any existing maximum distance separable (MDS) codes, and then the encoded symbols are divided into non-overlapping groups and encoded by an MDS array code in the second layer. The encoding in the second layer provides enough redundancy for local repair, while the overall code performs recovery of the data based on redundancy from both layers. Our codes can be constructed over a finite field with size growing linearly with the total number of nodes in the DSS, and facilitate efficient degraded reads.Comment: This paper has been withdrawn by the author due to inaccuracy of Claim

Bis(2-methyl­imidazolium) fumarate dihydrate

In the title compound, 2C4H7N2 +·C4H2O4 2−·2H2O, the asymmetric unit consists of one 2-methyl­imidazolium cation, half a fumarate dianion and one water mol­ecule. There is an inversion center at the mid-point of the central C—C bond of the fumarate anion. In the crystal structure, mol­ecules are linked into a three-dimensional network by inter­molecular N—H⋯O, O—H⋯O and weak C—H⋯O hydrogen bonds. In addition, there are weak π–π stacking inter­actions with centroid–centroid distances of 3.640 (1) Å

Cascaded Entanglement Enhancement

We present a cascaded system consisting of three non-degenerate optical parametric amplifiers (NOPAs) for the generation and the enhancement of quantum entanglement of continuous variables. The entanglement of optical fields produced by the first NOPA is successively enhanced by the second and the third NOPAs from -5.3 $dB$ to -8.1 $dB$ below the quantum noise limit. The dependence of the enhanced entanglement on the physical parameters of the NOPAs and the reachable entanglement limitation for a given cascaded NOPA system are calculated. The calculation results are in good agreement with the experimental measurements.Comment: 5 pages, 4 figure