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An upper bound on the rate of a binary code as a function of minimum code distance (using a Hamming code metric) is arrived at from Delsarte-MacWilliams inequalities. The upper bound so found is asymptotically less than Levenshtein's bound, and a fortiori less than Elias' bound. Appendices review properties of Krawtchouk polynomials and Q-polynomials utilized in the rigorous proofs.
The unequal error protection capabilities of convolutional and trellis codes are studied. In certain environments, a discrepancy in the amount of error protection placed on different information bits is desirable. Examples of environments which have data of varying importance are a number of speech coding algorithms, packet switched networks, multi-user systems, embedded coding systems, and high definition television. Encoders which provide more than one level of error protection to information bits are called unequal error protection (UEP) codes. In this work, the effective free distance vector, d, is defined as an alternative to the free distance as a primary performance parameter for UEP convolutional and trellis encoders. For a given (n, k), convolutional encoder, G, the effective free distance vector is defined as the k-dimensional vector d = (d(sub 0), d(sub 1), ..., d(sub k-1)), where d(sub j), the j(exp th) effective free distance, is the lowest Hamming weight among all code sequences that are generated by input sequences with at least one '1' in the j(exp th) position. It is shown that, although the free distance for a code is unique to the code and independent of the encoder realization, the effective distance vector is dependent on the encoder realization.
This paper presents a generalized Bezout theorem which can be used to determine a tighter lower bound of the number of distinct points of intersection of two or more curves for a large class of plane curves. A new approach to determine a lower bound on the minimum distance (and also the generalized Hamming weights) for algebraic-geometric codes defined from a class of plane curves is introduced, based on the generalized Bezout theorem. Examples of more efficient linear codes are constructed using the generalized Bezout theorem and the new approach. For d = 4, the linear codes constructed by the new construction are better than or equal to the known linear codes. For d greater than 5, these new codes are better than the known codes. The Klein code over GF(2(sup 3)) is also constructed.
The large scale structure of the current sheet in the terrestrial magnetotail is often represented as the superposition of a constant northward-oriented magnetic field component (B(sub z)) and a component along the Earth-Sun direction (B(sub x)) that varies with distance from the center of the sheet (z(sub o) in GSM) as in a Hams neutral sheet. The latter implies that B(sub x) = B(sub Lx) tanh((z - z(sub o))/h) where B(sub Lx) is the magnitude of the B(sub x) component in the northern lobe. Correspondingly, the cross-tail current should be approximated by J(sub y) = (B(sub Lx)/h) sech(sup 2)((z - z(sub o))/h). Using data from the fluxgate magnetometer (FGM) on the Cluster I1 spacecraft tetrad, we have used measured fields and currents to ask if this model represents the large-scale properties of the system. During very quiet crossings of the plasmasheet, we find that the model gives a reasonable estimate of the trend of the average current and field distributions, but during disturbed intervals, the best fit fails to represent the data. If, however, the parameters z(sub o) and h of the model are taken as variable functions of time, the fits can be reasonably good. The temporal variation of the fit parameter h that characterizes the thickness of the current sheet can be interpreted in terms of thinning during the growth phase of a substorm and thickening following the expansion phase. Ground signatures that give insight into the local time of substorm onset can be used to interpret the response of the plasmasheet to substorm related changes of the global system. During a substorm, the field magnitude in the central plasmasheet fluctuates at the period of Pi2 pulsations.
Heaterless hollow cathodes provide an opportunity to reduce complexity and improve reliability in electric propulsion systems. While removal of the heater has little effect on steady-state operation of a hollow cathode, it has a considerable effect on the ignition process. To successfully integrate a heaterless hollow cathode into a spaceflight electric propulsion system, it will be necessary to establish definitive requirements for the propellant feed and electrical subsystems so that ignition of a plasma discharge can be achieved reliably. The aim of this research was to form a better understanding of these requirements by performing an investigation of the propellant flow and voltage conditions required for the ignition of a plasma arc discharge. This aim was achieved by performing discharge initiation experiments using both a specially designed experimental apparatus and a functional heaterless hollow cathode assembly. It was demonstrated that there is a distinct difference in the voltage required to initiate a plasma discharge between two common electric propulsion propellants, xenon and krypton, which suggests that the developmental testing of heaterless hollow cathodes needs to be performed with the appropriate propellant gas species. Heaterless hollow cathode ignition experiments showed that the keeper orifice diameter has a strong effect on the voltage required to ignite a plasma discharge at a given propellant mass flow rate, while the effect of keeper-cathode separation distance was only strong at flow rates below 25 sccm (Xe).
It was shown earlier that for a punctured Reed-Muller (RM) code or a primitive BCH code, which contains a punctured RM code of the same minimum distance as a large subcode, the state complexity of the minimal trellis diagram is much greater than that for an equivalent code obtained by a proper permutation on the bit positions. To find a permutation on the bit positions for a given code that minimizes the state complexity of its minimal trellis diagram is an interesting and challenging problem. This permutation problem is related to the generalized Hamming weight hierarchy of a code, and is shown that for RM codes, the standard binary order of bit positions is optimum at every bit position with respect to the state complexity of a minimal trellis diagram by using a theorem due to Wei. The state complexity of trellis diagram for the extended and permuted (64, 24) BCH code is discussed.
X-ray grating interferometry allows for the simultaneous acquisition of attenuation, differential-phase contrast, and dark-field images, resulting from X-ray attenuation, refraction, and small-angle scattering, respectively. The modulated phase grating (MPG) interferometer is a recently developed grating interferometry system capable of generating a directly resolvable interference pattern using a relatively large period grating envelope function that is sampled at a pitch that is small enough that X-ray spatial coherence can be achieved by using a microfocus X-ray source or G0 grating. We present the theory of the MPG interferometry system for a 2-dimensional staggered grating, derived using Fourier optics, and we compare the theoretical predictions with experiments we have performed with a microfocus X-ray system at Pennington Biomedical Research Center, LSU. The theoretical and experimental fringe visibility is evaluated as a function of grating-to-detector distance. Additionally, quantitative experiments are performed with porous carbon and alumina compounds, and the mean normalized dark-field signal is compared with independent porosimetry measurements. Qualitative analysis of attenuation and dark-field images of a dried anchovy are shown.