The Dynamics of Group Codes: Dual Abelian Group Codes and Systems

Fundamental results concerning the dynamics of abelian group codes (behaviors) and their duals are developed. Duals of sequence spaces over locally compact abelian groups may be defined via Pontryagin duality; dual group codes are orthogonal subgroups of dual sequence spaces. The dual of a complete code or system is finite, and the dual of a Laurent code or system is (anti-)Laurent. If C and C^\perp are dual codes, then the state spaces of C act as the character groups of the state spaces of C^\perp. The controllability properties of C are the observability properties of C^\perp. In particular, C is (strongly) controllable if and only if C^\perp is (strongly) observable, and the controller memory of C is the observer memory of C^\perp. The controller granules of C act as the character groups of the observer granules of C^\perp. Examples of minimal observer-form encoder and syndrome-former constructions are given. Finally, every observer granule of C is an "end-around" controller granule of C.Comment: 30 pages, 11 figures. To appear in IEEE Trans. Inform. Theory, 200

Effects of cockpit lateral stick characteristics on handling qualities and pilot dynamics

This report presents the results of analysis of cockpit lateral control feel-system studies. Variations in feel-system natural frequency, damping, and command sensing reference (force and position) were investigated, in combination with variations in the aircraft response characteristics. The primary data for the report were obtained from a flight investigation conducted with a variable-stability airplane, with additional information taken from other flight experiments and ground-based simulations for both airplanes and helicopters . The study consisted of analysis of handling qualities ratings and extraction of open-loop, pilot-vehicle describing functions from sum-of-sines tracking data, including, for a limited subset of these data, the development of pilot models. The study confirms the findings of other investigators that the effects on pilot opinion of cockpit feel-system dynamics are not equivalent to a comparable level of added time delay, and until a more comprehensive set of criteria are developed, it is recommended that feel-system dynamics be considered a delay-inducing element in the aircraft response. The best correlation with time-delay requirements was found when the feel-system dynamics were included in the delay measurements, regardless of the command reference. This is a radical departure from past approaches

Plasmonic gold nanodiscs using piezoelectric substrate birefringence for liquid sensing

This article presents the simulation, fabrication, and experimental characterization of a surface plasmonic resonance (SPR) sensor integrated with an acoustic sensing compatible substrate. The SPR sensor is designed to work in the visible region with gold nanodisc arrays fabricated on LiNbO3, which is both piezoelectric and birefringent. A linear relationship between resonance wavelength and varying liquid refractive indices were observed in experiments, and a sensitivity of 165 nm/refractive index unit was obtained. Polarization effects of the birefringent property of the Y-cut LiNbO3 substrate have been investigated, which can also be applied to X-cut LiNbO3. Our study demonstrates the feasibility of an SPR sensor device utilizing a birefringent substrate, which has acoustic wave compatibility and can pave the way toward much more robust and flexible biosensing device

Characterization of Alkali Metal Dispensers and Non-Evaporable Getter Pumps in Ultra-High Vacuum Systems for Cold Atomic Sensors

A glass ultrahigh vacuum chamber with rubidium alkali metal dispensers and non-evaporable getter pumps has been developed and used to create a cold atomic sample in a chamber that operates with only passive vacuum pumps. The ion-mass spectrum of evaporated gases from the alkali metal dispenser has been recorded as a function of dispenser current. The efficacy of the non-evaporable getter pumps in promoting and maintaining vacuum has been characterized by observation of the Rb vapor optical absorption on the D2 transition at 780 nm and vacuum chamber pressure rate of rise tests. We have demonstrated a sample of laser-cooled Rb atoms in this chamber when isolated and operating without active vacuum pumps

On the Minimum Distance of Generalized Spatially Coupled LDPC Codes

Families of generalized spatially-coupled low-density parity-check (GSC-LDPC) code ensembles can be formed by terminating protograph-based generalized LDPC convolutional (GLDPCC) codes. It has previously been shown that ensembles of GSC-LDPC codes constructed from a protograph have better iterative decoding thresholds than their block code counterparts, and that, for large termination lengths, their thresholds coincide with the maximum a-posteriori (MAP) decoding threshold of the underlying generalized LDPC block code ensemble. Here we show that, in addition to their excellent iterative decoding thresholds, ensembles of GSC-LDPC codes are asymptotically good and have large minimum distance growth rates.Comment: Submitted to the IEEE International Symposium on Information Theory 201

Spatially Coupled LDPC Codes Constructed from Protographs

In this paper, we construct protograph-based spatially coupled low-density parity-check (SC-LDPC) codes by coupling together a series of L disjoint, or uncoupled, LDPC code Tanner graphs into a single coupled chain. By varying L, we obtain a flexible family of code ensembles with varying rates and frame lengths that can share the same encoding and decoding architecture for arbitrary L. We demonstrate that the resulting codes combine the best features of optimized irregular and regular codes in one design: capacity approaching iterative belief propagation (BP) decoding thresholds and linear growth of minimum distance with block length. In particular, we show that, for sufficiently large L, the BP thresholds on both the binary erasure channel (BEC) and the binary-input additive white Gaussian noise channel (AWGNC) saturate to a particular value significantly better than the BP decoding threshold and numerically indistinguishable from the optimal maximum a-posteriori (MAP) decoding threshold of the uncoupled LDPC code. When all variable nodes in the coupled chain have degree greater than two, asymptotically the error probability converges at least doubly exponentially with decoding iterations and we obtain sequences of asymptotically good LDPC codes with fast convergence rates and BP thresholds close to the Shannon limit. Further, the gap to capacity decreases as the density of the graph increases, opening up a new way to construct capacity achieving codes on memoryless binary-input symmetric-output (MBS) channels with low-complexity BP decoding.Comment: Submitted to the IEEE Transactions on Information Theor