Division algebra codes achieve MIMO block fading channel capacity within a constant gap

This work addresses the question of achieving capacity with lattice codes in multi-antenna block fading channels when the number of fading blocks tends to infinity. In contrast to the standard approach in the literature which employs random lattice ensembles, the existence results in this paper are derived from number theory. It is shown that a multiblock construction based on division algebras achieves rates within a constant gap from block fading capacity both under maximum likelihood decoding and naive lattice decoding. First the gap to capacity is shown to depend on the discriminant of the chosen division algebra; then class field theory is applied to build families of algebras with small discriminants. The key element in the construction is the choice of a sequence of division algebras whose centers are number fields with small root discriminants.Comment: Submitted to ISIT 201

Overview of the Applied Aerodynamics Division

A major reorganization of the Aeronautics Directorate of the Langley Research Center occurred in early 1989. As a result of this reorganization, the scope of research in the Applied Aeronautics Division is now quite different than that in the past. An overview of the current organization, mission, and facilities of this division is presented. A summary of current research programs and sample highlights of recent research are also presented. This is intended to provide a general view of the scope and capabilities of the division

The disjointness of stabilizer codes and limitations on fault-tolerant logical gates

Stabilizer codes are a simple and successful class of quantum error-correcting codes. Yet this success comes in spite of some harsh limitations on the ability of these codes to fault-tolerantly compute. Here we introduce a new metric for these codes, the disjointness, which, roughly speaking, is the number of mostly non-overlapping representatives of any given non-trivial logical Pauli operator. We use the disjointness to prove that transversal gates on error-detecting stabilizer codes are necessarily in a finite level of the Clifford hierarchy. We also apply our techniques to topological code families to find similar bounds on the level of the hierarchy attainable by constant depth circuits, regardless of their geometric locality. For instance, we can show that symmetric 2D surface codes cannot have non-local constant depth circuits for non-Clifford gates.Comment: 8+3 pages, 2 figures. Comments welcom

Aeronautical engineering: A continuing bibliography with indexes (supplement 256)

This bibliography lists 426 reports, articles, and other documents introduced into the NASA scientific and technical information system in August 1990. Subject coverage includes: design, construction and testing of aircraft and aircraft engines; aircraft components, equipment and systems; ground support systems; and theoretical and applied aspects of aerodynamics and general fluid dynamics

Efficient Gradient-Based Shape Optimization Methodology Using Inviscid/Viscous CFD

The formerly developed preconditioned-biconjugate-gradient (PBCG) solvers for the analysis and the sensitivity equations had resulted in very large error reductions per iteration; quadratic convergence was achieved whenever the solution entered the domain of attraction to the root. Its memory requirement was also lower as compared to a direct inversion solver. However, this memory requirement was high enough to preclude the realistic, high grid-density design of a practical 3D geometry. This limitation served as the impetus to the first-year activity (March 9, 1995 to March 8, 1996). Therefore, the major activity for this period was the development of the low-memory methodology for the discrete-sensitivity-based shape optimization. This was accomplished by solving all the resulting sets of equations using an alternating-direction-implicit (ADI) approach. The results indicated that shape optimization problems which required large numbers of grid points could be resolved with a gradient-based approach. Therefore, to better utilize the computational resources, it was recommended that a number of coarse grid cases, using the PBCG method, should initially be conducted to better define the optimization problem and the design space, and obtain an improved initial shape. Subsequently, a fine grid shape optimization, which necessitates using the ADI method, should be conducted to accurately obtain the final optimized shape. The other activity during this period was the interaction with the members of the Aerodynamic and Aeroacoustic Methods Branch of Langley Research Center during one stage of their investigation to develop an adjoint-variable sensitivity method using the viscous flow equations. This method had algorithmic similarities to the variational sensitivity methods and the control-theory approach. However, unlike the prior studies, it was considered for the three-dimensional, viscous flow equations. The major accomplishment in the second period of this project (March 9, 1996 to March 8, 1997) was the extension of the shape optimization methodology for the Thin-Layer Navier-Stokes equations. Both the Euler-based and the TLNS-based analyses compared with the analyses obtained using the CFL3D code. The sensitivities, again from both levels of the flow equations, also compared very well with the finite-differenced sensitivities. A fairly large set of shape optimization cases were conducted to study a number of issues previously not well understood. The testbed for these cases was the shaping of an arrow wing in Mach 2.4 flow. All the final shapes, obtained either from a coarse-grid-based or a fine-grid-based optimization, using either a Euler-based or a TLNS-based analysis, were all re-analyzed using a fine-grid, TLNS solution for their function evaluations. This allowed for a more fair comparison of their relative merits. From the aerodynamic performance standpoint, the fine-grid TLNS-based optimization produced the best shape, and the fine-grid Euler-based optimization produced the lowest cruise efficiency

DMT Optimality of LR-Aided Linear Decoders for a General Class of Channels, Lattice Designs, and System Models

The work identifies the first general, explicit, and non-random MIMO encoder-decoder structures that guarantee optimality with respect to the diversity-multiplexing tradeoff (DMT), without employing a computationally expensive maximum-likelihood (ML) receiver. Specifically, the work establishes the DMT optimality of a class of regularized lattice decoders, and more importantly the DMT optimality of their lattice-reduction (LR)-aided linear counterparts. The results hold for all channel statistics, for all channel dimensions, and most interestingly, irrespective of the particular lattice-code applied. As a special case, it is established that the LLL-based LR-aided linear implementation of the MMSE-GDFE lattice decoder facilitates DMT optimal decoding of any lattice code at a worst-case complexity that grows at most linearly in the data rate. This represents a fundamental reduction in the decoding complexity when compared to ML decoding whose complexity is generally exponential in rate. The results' generality lends them applicable to a plethora of pertinent communication scenarios such as quasi-static MIMO, MIMO-OFDM, ISI, cooperative-relaying, and MIMO-ARQ channels, in all of which the DMT optimality of the LR-aided linear decoder is guaranteed. The adopted approach yields insight, and motivates further study, into joint transceiver designs with an improved SNR gap to ML decoding.Comment: 16 pages, 1 figure (3 subfigures), submitted to the IEEE Transactions on Information Theor

An aeroacoustic study of industrial gas turbine intake and exhaust systems.

The purpose of this study was to seek a means of numerically simulating and analyzing the aerodynamic and acoustic behaviour of industrial gas turbine intake or exhaust systems. The method was developed in an effort to advance the current state of the art employed for the prediction of intake and exhaust noise. Current methods rely upon the summation of experimentally gathered insertion loss data for individual system components. This approach requires that physical testing of chosen components be undertaken which can be both costly and time consuming. The proposed numerical method is based upon a two stage finite volume solution of the two dimensional non linear Euler equations whereby an aerodynamic solution for the mean flow is first obtained followed by a solution for the acoustic field. The method has been found to be both accurate and easy to implement, furthermore being numerically based it eliminates the need for the costly and time consuming procurement and testing of physical prototypes. In this respect it is considered to advance the present state of the art. The two step Euler solver developed herein employs a multiblock finite volume formulation wherein the hyperbolic Euler equations are solved using a cell centred finite volume technique employing a second order central differencing method for spatial discretisation on a multiblock grid and with temporal integration being undertaken using an explicit time marching two stage second order Runge Kutta scheme. In the first step the mean flow is solved using the finite volume method to obtain a transient or pseudo steady state solution. This provides both the general aerodynamic characteristics of the system and a baseline steady state solution for the acoustic analysis. In the second step a perturbation representing an acoustic disturbance is introduced to the mean flow and the non linear Euler equations are again solved using the finite volume scheme. Spurious non physical numerical reflections at the domain boundaries are prevented by the application of the characteristic based non reflecting boundary conditions. The resulting unsteady pressure field is then post processed to generate the unsteady pressure disturbance due to the applied acoustic perturbation. The interaction of the acoustic disturbance can then be evaluated by examination of the pressure amplitudes and frequency spectra at any location within the domain. The scheme was applied to the study of the aerodynamic and acoustic characteristics of an industrial gas turbine emergency shutdown compressor bleed system. It was found to accurately predict the acoustic attenuation characteristics of the system, furthermore it was shown that it could also be usefully applied as a design tool and as an example of this a change of attenuation performance of the bleed system is demonstrated by a simple relocation of the baffle silencer within the system ducting. It is concluded that the method developed herein demonstrates that a numerical solution to predict the acoustic attenuation characteristics of an industrial gas turbine silencing system is possible and as such offers an improved means for undertaking the acoustic design of products for noise control in industrial gas turbine applications. In this respect it is considered to advance the present state of the art

NAS (Numerical Aerodynamic Simulation Program) technical summaries, March 1989 - February 1990

Given here are selected scientific results from the Numerical Aerodynamic Simulation (NAS) Program's third year of operation. During this year, the scientific community was given access to a Cray-2 and a Cray Y-MP supercomputer. Topics covered include flow field analysis of fighter wing configurations, large-scale ocean modeling, the Space Shuttle flow field, advanced computational fluid dynamics (CFD) codes for rotary-wing airloads and performance prediction, turbulence modeling of separated flows, airloads and acoustics of rotorcraft, vortex-induced nonlinearities on submarines, and standing oblique detonation waves

Aeronautical engineering: A continuing bibliography with indexes (supplement 303)

This bibliography lists 211 reports, articles, and other documents introduced into the NASA scientific and technical information database. Subject coverage includes: design, construction, and testing of aircraft and aircraft engines; aircraft components, equipment, and systems; ground support systems; and theoretical and applied aspects of aerodynamics and general fluid dynamics