609 research outputs found
Optimal and Efficient Decoding of Concatenated Quantum Block Codes
We consider the problem of optimally decoding a quantum error correction code
-- that is to find the optimal recovery procedure given the outcomes of partial
"check" measurements on the system. In general, this problem is NP-hard.
However, we demonstrate that for concatenated block codes, the optimal decoding
can be efficiently computed using a message passing algorithm. We compare the
performance of the message passing algorithm to that of the widespread
blockwise hard decoding technique. Our Monte Carlo results using the 5 qubit
and Steane's code on a depolarizing channel demonstrate significant advantages
of the message passing algorithms in two respects. 1) Optimal decoding
increases by as much as 94% the error threshold below which the error
correction procedure can be used to reliably send information over a noisy
channel. 2) For noise levels below these thresholds, the probability of error
after optimal decoding is suppressed at a significantly higher rate, leading to
a substantial reduction of the error correction overhead.Comment: Published versio
Good Quantum Convolutional Error Correction Codes And Their Decoding Algorithm Exist
Quantum convolutional code was introduced recently as an alternative way to
protect vital quantum information. To complete the analysis of quantum
convolutional code, I report a way to decode certain quantum convolutional
codes based on the classical Viterbi decoding algorithm. This decoding
algorithm is optimal for a memoryless channel. I also report three simple
criteria to test if decoding errors in a quantum convolutional code will
terminate after a finite number of decoding steps whenever the Hilbert space
dimension of each quantum register is a prime power. Finally, I show that
certain quantum convolutional codes are in fact stabilizer codes. And hence,
these quantum stabilizer convolutional codes have fault-tolerant
implementations.Comment: Minor changes, to appear in PR
Processing and Transmission of Information
Contains research objectives and reports on three research projects.National Science Foundation (Grant GP-2495)National Institutes of Health (Grant MH-04737-04)National Aeronautics and Space Administration (Grant NsG-334)National Aeronautics and Space Administration (Grant NsG-496
Superregular matrices and applications to convolutional codes
The main results of this paper are twofold: the first one is a matrix theoretical result. We say that a matrix is superregular if all of its minors that are not trivially zero are nonzero. Given a a×b, a ≥ b, superregular matrix over a field, we show that if all of its rows are nonzero then any linear combination of its columns, with nonzero coefficients, has at least a−b + 1 nonzero entries. Secondly, we make use of this result to construct convolutional codes that attain the maximum possible distance for some fixed parameters of the code, namely, the rate and the Forney indices. These results answer some open questions on distances and constructions of convolutional codes posted in the literature
Complexity of Discrete Energy Minimization Problems
Discrete energy minimization is widely-used in computer vision and machine
learning for problems such as MAP inference in graphical models. The problem,
in general, is notoriously intractable, and finding the global optimal solution
is known to be NP-hard. However, is it possible to approximate this problem
with a reasonable ratio bound on the solution quality in polynomial time? We
show in this paper that the answer is no. Specifically, we show that general
energy minimization, even in the 2-label pairwise case, and planar energy
minimization with three or more labels are exp-APX-complete. This finding rules
out the existence of any approximation algorithm with a sub-exponential
approximation ratio in the input size for these two problems, including
constant factor approximations. Moreover, we collect and review the
computational complexity of several subclass problems and arrange them on a
complexity scale consisting of three major complexity classes -- PO, APX, and
exp-APX, corresponding to problems that are solvable, approximable, and
inapproximable in polynomial time. Problems in the first two complexity classes
can serve as alternative tractable formulations to the inapproximable ones.
This paper can help vision researchers to select an appropriate model for an
application or guide them in designing new algorithms.Comment: ECCV'16 accepte
Dentine Oxygn Isotopes (δ18O) as a Proxy for Odontocete Distributions and Movements.
Spatial variation in marine oxygen isotope ratios ( δ18O) resulting from differential evaporation rates and precipitation inputs is potentially useful for characterizing marine mammal distributions and tracking movements across δ18O gradients. Dentine hydroxyapatite contains carbonate and phosphate that precipitate in oxygen isotopic equilibrium with body water, which in odontocetes closely tracks the isotopic composition of ambient water. To test whether dentine oxygen isotope composition reliably records that of ambient water and can therefore serve as a proxy for odontocete distribution and movement patterns, we measured δ18O values of dentine structural carbonate (δ18OSC) and phosphate (δ18OP) of seven odontocete species (n = 55 individuals) from regional marine water bodies spanning a surface water δ18O range of several per mil. Mean dentine δ18OSC (range +21.2 to +25.5‰ VSMOW) and δ18OP (+16.7 to +20.3‰) values were strongly correlated with marine surface water δ18O values, with lower dentine δ18OSC and δ18OP values in high-latitude regions (Arctic and Eastern North Pacific) and higher values in the Gulf of California, Gulf of Mexico, and Mediterranean Sea. Correlations between dentine δ18OSC and δ18OP values with marine surface water δ18O values indicate that sequential δ18O measurements along dentine, which grows incrementally and archives intra- and interannual isotopic composition over the lifetime of the animal, would be useful for characterizing residency within and movements among water bodies with strong δ18O gradients, particularly between polar and lower latitudes, or between oceans and marginal basins
Identification of manganese superoxide dismutase from Sphingobacterium sp. T2 as a novel bacterial enzyme for lignin oxidation
The valorisation of aromatic heteropolymer lignin is an important unsolved problem in the development of a biomass-based biorefinery, for which novel high-activity biocatalysts are needed. Sequencing of the genomic DNA of lignin-degrading bacterial strain Sphingobacterium sp. T2 revealed no matches to known lignin-degrading genes. Proteomic matches for two manganese superoxide dismutase proteins were found in partially purified extracellular fractions. Recombinant MnSOD1 and MnSOD2 were both found to show high activity for oxidation of Organosolv and Kraft lignin, and lignin model compounds, generating multiple oxidation products. Structure determination revealed that the products result from aryl-Cα and Cα-Cβ bond oxidative cleavage and O-demethylation. The crystal structure of MnSOD1 was determined to 1.35 Å resolution, revealing a typical MnSOD homodimer harbouring a 5-coordinate trigonal bipyramidal Mn(II) centre ligated by three His, one Asp and a water/hydroxide in each active site. We propose that the lignin oxidation reactivity of these enzymes is due to the production of hydroxyl radical, a highly reactive oxidant. This is the first demonstration that MnSOD is a microbial lignin-oxidising enzyme
Radiation Characteristics of a 0.11 Micrometer Modified Commercial CMOS Process
We present radiation data, Total Ionizing Dose and Single Event Effects, on the LSI Logic 0.11 micron commercial process and two modified versions of this process. Modified versions include a buried layer to guarantee Single Event Latchup immunity
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