1,522 research outputs found
Information Transmission using the Nonlinear Fourier Transform, Part I: Mathematical Tools
The nonlinear Fourier transform (NFT), a powerful tool in soliton theory and
exactly solvable models, is a method for solving integrable partial
differential equations governing wave propagation in certain nonlinear media.
The NFT decorrelates signal degrees-of-freedom in such models, in much the same
way that the Fourier transform does for linear systems. In this three-part
series of papers, this observation is exploited for data transmission over
integrable channels such as optical fibers, where pulse propagation is governed
by the nonlinear Schr\"odinger equation. In this transmission scheme, which can
be viewed as a nonlinear analogue of orthogonal frequency-division multiplexing
commonly used in linear channels, information is encoded in the nonlinear
frequencies and their spectral amplitudes. Unlike most other fiber-optic
transmission schemes, this technique deals with both dispersion and
nonlinearity directly and unconditionally without the need for dispersion or
nonlinearity compensation methods. This first paper explains the mathematical
tools that underlie the method.Comment: This version contains minor updates of IEEE Transactions on
Information Theory, vol. 60, no. 7, pp. 4312--4328, July 201
Information Transmission using the Nonlinear Fourier Transform, Part III: Spectrum Modulation
Motivated by the looming "capacity crunch" in fiber-optic networks,
information transmission over such systems is revisited. Among numerous
distortions, inter-channel interference in multiuser wavelength-division
multiplexing (WDM) is identified as the seemingly intractable factor limiting
the achievable rate at high launch power. However, this distortion and similar
ones arising from nonlinearity are primarily due to the use of methods suited
for linear systems, namely WDM and linear pulse-train transmission, for the
nonlinear optical channel. Exploiting the integrability of the nonlinear
Schr\"odinger (NLS) equation, a nonlinear frequency-division multiplexing
(NFDM) scheme is presented, which directly modulates non-interacting signal
degrees-of-freedom under NLS propagation. The main distinction between this and
previous methods is that NFDM is able to cope with the nonlinearity, and thus,
as the the signal power or transmission distance is increased, the new method
does not suffer from the deterministic cross-talk between signal components
which has degraded the performance of previous approaches. In this paper,
emphasis is placed on modulation of the discrete component of the nonlinear
Fourier transform of the signal and some simple examples of achievable spectral
efficiencies are provided.Comment: Updated version of IEEE Transactions on Information Theory, vol. 60,
no. 7, pp. 4346--4369, July, 201
Information Transmission using the Nonlinear Fourier Transform, Part II: Numerical Methods
In this paper, numerical methods are suggested to compute the discrete and
the continuous spectrum of a signal with respect to the Zakharov-Shabat system,
a Lax operator underlying numerous integrable communication channels including
the nonlinear Schr\"odinger channel, modeling pulse propagation in optical
fibers. These methods are subsequently tested and their ability to estimate the
spectrum are compared against each other. These methods are used to compute the
spectrum of various signals commonly used in the optical fiber communications.
It is found that the layer-peeling and the spectral methods are suitable
schemes to estimate the nonlinear spectra with good accuracy. To illustrate the
structure of the spectrum, the locus of the eigenvalues is determined under
amplitude and phase modulation in a number of examples. It is observed that in
some cases, as signal parameters vary, eigenvalues collide and change their
course of motion. The real axis is typically the place from which new
eigenvalues originate or are absorbed into after traveling a trajectory in the
complex plane.Comment: Minor updates to IEEE Transactions on Information Theory, vol. 60,
no. 7, pp. 4329--4345, July 201
Observable Gravity Waves from Supersymmetric Hybrid Inflation II
It is shown that a tensor-to-scalar ratio close to r = 0.03, which can be
observed by Planck, is realized in supersymmetric hybrid inflation models with
TeV-scale soft supersymmetry breaking terms. This extends our previous
analysis, which also found r <~ 0.03 but employed intermediate scale soft
terms. Other cosmological observables such as the scalar spectral index are in
good agreement with the WMAP data.Comment: 4 pages, 4 figure
Upper Bound on the Capacity of a Cascade of Nonlinear and Noisy Channels
An upper bound on the capacity of a cascade of nonlinear and noisy channels
is presented. The cascade mimics the split-step Fourier method for computing
waveform propagation governed by the stochastic generalized nonlinear
Schroedinger equation. It is shown that the spectral efficiency of the cascade
is at most log(1+SNR), where SNR is the receiver signal-to-noise ratio. The
results may be applied to optical fiber channels. However, the definition of
bandwidth is subtle and leaves open interpretations of the bound. Some of these
interpretations are discussed.Comment: The main change is to define the noise as bandlimited already in (8)
rather than before (15). This serves to clarify subsequent step
Red Spectral Tilt and Observable Gravity Waves in Shifted Hybrid Inflation
We consider supersymmetric shifted hybrid inflation models with a red tilted
scalar spectral index n_s in agreement with the WMAP 7-yr central value. If
non-minimal supergravity corrections are included, these models can also
support a tensor-to-scalar ratio as large as r = 0.02, which may be observable
by the Planck Satellite. In contrast to the standard supersymmetric hybrid
inflation scenario, topological defects produced via gauge symmetry breaking
are inflated away in the shifted version of the theory.Comment: 22 pages, 4 figures, and 1 tabl
Design and evaluation of a new pharmaceutical pictogram sequence to convey medicine usage
Pictorials may be used to augment textual instructions in the depiction of safety and warning information on medicines. The objective of this study was to design, develop and evaluate a simple and culturally appropriate pictogram sequence for using nystatin suspension, and to assess its understandability in low-literate Xhosa participants. A new pharmaceutical pictogram sequence was designed through focus group discussions and evaluated in a 2-phase process. The results of Phase 1 (30 participants) identified various problems associated with the new pictogram sequence. It was modified accordingly and re-evaluated in Phase 2 with 20 participants. All participants belonged to the Xhosa group, had between 0 and 7 years of formal schooling and had English as their second language. Acceptance of the new pictogram sequence was based on international standards (ANSI and ISO criterion) for evaluating the comprehensibility of pictograms. In Phase 1, the new pictogram sequence was correctly interpreted by 66.7% of the participants and this complied with the ISO criterion of 67% correct. In Phase 2, 95% of the participants were able to correctly interpret the new pictogram sequence. This result complied with the ANSI criterion of 85% correct, therefore, this new pictogram sequence was considered to be acceptable. This study has illustrated the success of using a consultative approach in the design of new pictograms
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