5,275 research outputs found
Symmetry of information and nonuniform lower bounds
12 pagesIn the first part we provide another proof of the result of [Homer, Mocas 1995] that for all constant c, the class EXP is not included in P/(n^c) . The proof is based on a simple diagonalization, whereas it uses resource-bounded Kolmogorov complexity in [Homer, Mocas 1995]. In the second part, we investigate links between resource-bounded Kolmogorov complexity and nonuniform classes in computational complexity. Assuming a version of polynomial-time symmetry of information, we show that exponential-time problems do not have polynomial-size circuits (in symbols, EXP is not included in P/poly)
Multilevel Coded Modulation for Unequal Error Protection and Multistage Decoding—Part II: Asymmetric Constellations
In this paper, multilevel coded asymmetric modulation with multistage decoding and unequal error protection (UEP) is discussed. These results further emphasize the fact that unconventional signal set partitionings are more promising than traditional (Ungerboeck-type) partitionings, to achieve UEP capabilities with multilevel coding and multistage decoding. Three types of unconventional partitionings are analyzed for asymmetric 8-PSK and 16-QAM constellations over the additive white Gaussian noise channel to introduce design guidelines. Generalizations to other PSK and QAM type constellations follow the same lines. Upper bounds on the bit-error probability based on union bound arguments are first derived. In some cases, these bounds become loose due to the large overlappings of decision regions associated with asymmetric constellations and unconventional partitionings. To overcome this problem, simpler and tighter approximated bounds are derived. Based on these bounds, it is shown that additional refinements can be achieved in the construction of multilevel UEP codes, by introducing asymmetries in PSK and QAM signal constellations
Weighted frames of exponentials and stable recovery of multidimensional functions from nonuniform Fourier samples
In this paper, we consider the problem of recovering a compactly supported
multivariate function from a collection of pointwise samples of its Fourier
transform taken nonuniformly. We do this by using the concept of weighted
Fourier frames. A seminal result of Beurling shows that sample points give rise
to a classical Fourier frame provided they are relatively separated and of
sufficient density. However, this result does not allow for arbitrary
clustering of sample points, as is often the case in practice. Whilst keeping
the density condition sharp and dimension independent, our first result removes
the separation condition and shows that density alone suffices. However, this
result does not lead to estimates for the frame bounds. A known result of
Groechenig provides explicit estimates, but only subject to a density condition
that deteriorates linearly with dimension. In our second result we improve
these bounds by reducing the dimension dependence. In particular, we provide
explicit frame bounds which are dimensionless for functions having compact
support contained in a sphere. Next, we demonstrate how our two main results
give new insight into a reconstruction algorithm---based on the existing
generalized sampling framework---that allows for stable and quasi-optimal
reconstruction in any particular basis from a finite collection of samples.
Finally, we construct sufficiently dense sampling schemes that are often used
in practice---jittered, radial and spiral sampling schemes---and provide
several examples illustrating the effectiveness of our approach when tested on
these schemes
Rotating nonuniform black string solutions
We explore via linearized perturbation theory the Gregory-Laflamme
instability of rotating black strings with equal magnitude angular momenta. Our
results indicate that the Gregory-Laflamme instability persists up to
extremality for all even dimensions between six and fourteen. We construct
rotating nonuniform black strings with two equal magnitude angular momenta in
six dimensions. We see a first indication for the occurrence of a topology
changing transition, associated with such rotating nonuniform black strings.
Charged nonuniform black string configurations in heterotic string theory are
also constructed by employing a solution generation technique.Comment: 36 pages, 10 figures, final versio
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