1,195 research outputs found
Composite Cyclotomic Fourier Transforms with Reduced Complexities
Discrete Fourier transforms~(DFTs) over finite fields have widespread
applications in digital communication and storage systems. Hence, reducing the
computational complexities of DFTs is of great significance. Recently proposed
cyclotomic fast Fourier transforms (CFFTs) are promising due to their low
multiplicative complexities. Unfortunately, there are two issues with CFFTs:
(1) they rely on efficient short cyclic convolution algorithms, which has not
been investigated thoroughly yet, and (2) they have very high additive
complexities when directly implemented. In this paper, we address both issues.
One of the main contributions of this paper is efficient bilinear 11-point
cyclic convolution algorithms, which allow us to construct CFFTs over
GF. The other main contribution of this paper is that we propose
composite cyclotomic Fourier transforms (CCFTs). In comparison to previously
proposed fast Fourier transforms, our CCFTs achieve lower overall complexities
for moderate to long lengths, and the improvement significantly increases as
the length grows. Our 2047-point and 4095-point CCFTs are also first efficient
DFTs of such lengths to the best of our knowledge. Finally, our CCFTs are also
advantageous for hardware implementations due to their regular and modular
structure.Comment: submitted to IEEE trans on Signal Processin
Response of the Coastal Ocean to Tropical Cyclones
The Northwest Pacific and the South China Sea region are the birthplaces of most monsoon disturbances and tropical cyclones and are an important channel for the generation and transmission of water vapor. The Northwest Pacific plays a major role in regulating interdecadal and long-term changes in climate. China experiences the largest number of typhoon landfalls and the most destructive power affected by typhoons in the world. The hidden dangers of typhoon disasters are accelerating with the acceleration of urbanization, the rapid development of economic construction and global warming. The coastal cities are the most dynamic and affluent areas of China’s economic development. They are the strong magnetic field that attracts international capital in China, and are also the most densely populated areas and important port groups in China. Although these regions are highly developed, they are vulnerable to disasters. When typhoons hit, the economic losses and casualties caused by gale, heavy rain and storm surges were particularly serious. This chapter reviews the response of coastal ocean to tropical cyclones, included sea surface temperature, sea surface salinity, storm surge simulation and extreme rainfall under the influence of tropical cyclones
A CO observation of the galactic methanol masers
Context: We investigated the molecular gas associated with 6.7 GHz methanol
masers throughout the Galaxy using a J=1-0 transition of the CO isotopologues.
Methods:Using the 13.7-meter telescope at the Purple Mountain Observatory
(PMO), we have obtained ^{12}CO and ^{13}CO (1-0) lines for 160 methanol masers
sources from the first to the third Galactic quadrants. We made efforts to
resolve the distance ambiguity by careful comparison with the radio continuum
and HI 21 cm observations.
Results: First, the maser sources show increased ^{13}CO line widths toward
the Galactic center, suggesting that the molecular gas are more turbulent
toward the Galactic center. This trend can be noticeably traced by the ^{13}CO
line width. Second, the ^{12}CO excitation temperature shows a noticeable
correlation with the H_2 column density. A possible explanation consistent with
the collapse model is that the higher surface-density gas is more efficient to
the stellar heating and/or has a higher formation rate of high-mass stars.
Third, comparing the IRDCs, the maser sources on average have significantly
lower H_2 column densities, moderately higher temperatures, and similar line
widths. Fourth, in the mapped regions, 51 ^{13}CO cores have been revealed.
Only 17 coincide with the radio continuum emission (F_{cm}>6 mJy), while a
larger fraction (30 cores) coincide with the infrared emissions. The IR-bright
and radio-bright sources exhibit significantly higher CO excitation
temperatures than the IR-faint and radio-faint sources, respectively.
Conclusions: The 6.7 GHz masers show a moderately low ionization rate but
have a common-existing stellar heating that generates the IR emissions. The
relevant properties can be characterized by the ^{12}CO and ^{13}CO (1-0)
emissions in several aspects as described above.Comment: 38 pages, 13 figures, 4 tables, accepted to Astronomy and
Astrophysic
Reduced-Complexity Decoder of Long Reed-Solomon Codes Based on Composite Cyclotomic Fourier Transforms
Long Reed-Solomon (RS) codes are desirable for digital communication and
storage systems due to their improved error performance, but the high
computational complexity of their decoders is a key obstacle to their adoption
in practice. As discrete Fourier transforms (DFTs) can evaluate a polynomial at
multiple points, efficient DFT algorithms are promising in reducing the
computational complexities of syndrome based decoders for long RS codes. In
this paper, we first propose partial composite cyclotomic Fourier transforms
(CCFTs) and then devise syndrome based decoders for long RS codes over large
finite fields based on partial CCFTs. The new decoders based on partial CCFTs
achieve a significant saving of computational complexities for long RS codes.
Since partial CCFTs have modular and regular structures, the new decoders are
suitable for hardware implementations. To further verify and demonstrate the
advantages of partial CCFTs, we implement in hardware the syndrome computation
block for a shortened RS code over GF. In comparison
to previous results based on Horner's rule, our hardware implementation not
only has a smaller gate count, but also achieves much higher throughputs.Comment: 7 pages, 1 figur
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