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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS1996

Soft-Output Decoding Algorithms in Iterative Decoding of Turbo Codes

In this article, we present two versions of a simplified maximum a posteriori decoding algorithm. The algorithms work in a sliding window form, like the Viterbi algorithm, and can thus be used to decode continuously transmitted sequences obtained by parallel concatenated codes, without requiring code trellis termination. A heuristic explanation is also given of how to embed the maximum a posteriori algorithms into the iterative decoding of parallel concatenated codes (turbo codes). The performances of the two algorithms are compared on the basis of a powerful rate 1/3 parallel concatenated code. Basic circuits to implement the simplified a posteriori decoding algorithm using lookup tables, and two further approximations (linear and threshold), with a very small penalty, to eliminate the need for lookup tables are proposed.

Benedetto, S.↗
NASA NTRS2003

Numerical Simulation of Turbulent MHD Flows Using an Iterative PNS Algorithm

A new parabolized Navier-Stokes (PNS) algorithm has been developed to efficiently compute magnetohydrodynamic (MHD) flows in the low magnetic Reynolds number regime. In this regime, the electrical conductivity is low and the induced magnetic field is negligible compared to the applied magnetic field. The MHD effects are modeled by introducing source terms into the PNS equation which can then be solved in a very efficient manner. To account for upstream (elliptic) effects, the flowfields are computed using multiple streamwise sweeps with an iterated PNS algorithm. Turbulence has been included by modifying the Baldwin-Lomax turbulence model to account for MHD effects. The new algorithm has been used to compute both laminar and turbulent, supersonic, MHD flows over flat plates and supersonic viscous flows in a rectangular MHD accelerator. The present results are in excellent agreement with previous complete Navier-Stokes calculations.

Kato, Hiromasa↗
NASA NTRS1985

Iterative methods for mixed finite element equations

Iterative strategies for the solution of indefinite system of equations arising from the mixed finite element method are investigated in this paper with application to linear and nonlinear problems in solid and structural mechanics. The augmented Hu-Washizu form is derived, which is then utilized to construct a family of iterative algorithms using the displacement method as the preconditioner. Two types of iterative algorithms are implemented. Those are: constant metric iterations which does not involve the update of preconditioner; variable metric iterations, in which the inverse of the preconditioning matrix is updated. A series of numerical experiments is conducted to evaluate the numerical performance with application to linear and nonlinear model problems.

Nakazawa, S.↗
NASA NTRS1985

Mesh-connected processor arrays for the transitive closure problem

The main purpose in this paper is to lay a theoretical foundation for the design of mesh-connected processor arrays for the transitive closure problem. Using a simple path-algebraic formulation of the problem and observing its similarity to certain well-known smoothing problems that occur in digital signal processing, it is shown how to draw upon existing techniques from the signal processing literature to derive regular iterative algorithms for determining the transitive closure of the graph. The regular iterative algorithms that are derived using these considerations, are then analyzed and synthesized on mesh-connected processor arrays. Among the vast number of mesh-connected processor arrays that can be designed using this unified approach, the systolic arrays reported in the literature for this problem are shown to be special cases.

Rao, S. K.↗
NASA NTRS1989

A family of new efficient arrays for matrix multiplication

The authors present a regular iterative algorithm for matrix multiplication and show that several well-known matrix multiplication arrays are directly obtained from it, differing only in the choice of iteration vector. They then present a regular iterative algorithm for matrix multiplication using the method of Winograd (1968) and show in detail how to derive one array from this algorithmic description. Other arrays in the same family can similarly be obtained for different choices of the iteration space. The new arrays compute the product of two matrices faster than available conventional arrays and use a smaller number of processor cells.

Jagadish, H. V.↗
NASA NTRS1992

Complex generalized minimal residual algorithm for iterative solution of quantum-mechanical reactive scattering equations

Complex dense matrices corresponding to the D + H2 and O + HD reactions were solved using a complex generalized minimal residual (GMRes) algorithm described by Saad and Schultz (1986) and Saad (1990). To provide a test case with a different structure, the H + H2 system was also considered. It is shown that the computational effort for solutions with the GMRes algorithm depends on the dimension of the linear system, the total energy of the scattering problem, and the accuracy criterion. In several cases with dimensions in the range 1110-5632, the GMRes algorithm outperformed the LAPACK direct solver, with speedups for the linear equation solution as large as a factor of 23.

Chatfield, David C.↗
NASA NTRS1988

A sparse matrix algorithm on the Boolean vector machine

VLSI technology is being used to implement a prototype Boolean Vector Machine (BVM), which is a large network of very small processors with equally small memories that operate in SIMD mode; these use bit-serial arithmetic, and communicate via cube-connected cycles network. The BVM's bit-serial arithmetic and the small memories of individual processors are noted to compromise the system's effectiveness in large numerical problem applications. Attention is presently given to the implementation of a basic matrix-vector iteration algorithm for space matrices of the BVM, in order to generate over 1 billion useful floating-point operations/sec for this iteration algorithm. The algorithm is expressed in a novel language designated 'BVM'.

Wagner, Robert A.↗
NASA NTRS1973

Iterative methods for plasma sheath calculations: Application to spherical probe

The computer cost of a Poisson-Vlasov iteration procedure for the numerical solution of a steady-state collisionless plasma-sheath problem depends on: (1) the nature of the chosen iterative algorithm, (2) the position of the outer boundary of the grid, and (3) the nature of the boundary condition applied to simulate a condition at infinity (as in three-dimensional probe or satellite-wake problems). Two iterative algorithms, in conjunction with three types of boundary conditions, are analyzed theoretically and applied to the computation of current-voltage characteristics of a spherical electrostatic probe. The first algorithm was commonly used by physicists, and its computer costs depend primarily on the boundary conditions and are only slightly affected by the mesh interval. The second algorithm is not commonly used, and its costs depend primarily on the mesh interval and slightly on the boundary conditions.

Parker, L. W.↗
NASA NTRS1973

Application of the method local potential to the analysis of turbulent shear flows

It has been found that, in general, the local potential cannot be employed to obtain approximate solutions for the various correlations of turbulent properties which appear in the time averaged form of the conservation equations. Although the method of local potential is equivalent to the Galerkin method when the self-consistent condition is applied, the local potential can also be applied as an iterative algorithm in place of using the selfconsistent condition. This procedure offers an alternative to the Galerkin method and may be useful in obtaining approximate solutions for the total turbulent velocity. In addition, for certain simple turbulent shear flows the iterative algorithm may permit approximate, but non-empirical, solutions by modeling only the mean velocity and the Reynolds stress.

Reed, T. D.↗
NASA NTRS1984

Reed Solomon codes for error control in byte organized computer memory systems

A problem in designing semiconductor memories is to provide some measure of error control without requiring excessive coding overhead or decoding time. In LSI and VLSI technology, memories are often organized on a multiple bit (or byte) per chip basis. For example, some 256K-bit DRAM's are organized in 32Kx8 bit-bytes. Byte oriented codes such as Reed Solomon (RS) codes can provide efficient low overhead error control for such memories. However, the standard iterative algorithm for decoding RS codes is too slow for these applications. Some special decoding techniques for extended single-and-double-error-correcting RS codes which are capable of high speed operation are presented. These techniques are designed to find the error locations and the error values directly from the syndrome without having to use the iterative algorithm to find the error locator polynomial.

Lin, S.↗
NASA NTRS1987

Decoding of DBEC-TBED Reed-Solomon codes

A problem in designing semiconductor memories is to provide some measure of error control without requiring excessive coding overhead or decoding time. In LSI and VLSI technology, memories are often organized on a multiple bit (or byte) per chip basis. For example, some 256 K bit DRAM's are organized in 32 K x 8 bit-bytes. Byte-oriented codes such as Reed-Solomon (RS) codes can provide efficient low overhead error control for such memories. However, the standard iterative algorithm for decoding RS codes is too slow for these applications. The paper presents a special decoding technique for double-byte-error-correcting, triple-byte-error-detecting RS codes which is capable of high-speed operation. This technique is designed to find the error locations and the error values directly from the syndrome without having to use the iterative algorithm to find the error locator polynomial.

Deng, Robert H.↗
NASA NTRS1990

Robust control of systems with real parameter uncertainty and unmodelled dynamics

Two significant contributions have been made during this research period in the research 'Robust Control of Systems with Real Parameter Uncertainty and Unmodelled Dynamics' under NASA Research Grant NAG-1-1102. They are: (1) a fast algorithm for computing the optimal H(sub infinity) norm for the four-block, the two block, or the one-block optimal H(sub infinity) optimization problem; and (2) a construction of an optimal H infinity controller without numerical difficulty. In using GD (Glover and Doyle) or DGKF (Doyle, Glover, Khargonekar, and Francis) approach to solve the standard H infinity norm which required bisection search. In this research period, we developed a very fast iterative algorithm for this computation. Our algorithm was developed based on hyperbolic interpolations which is much faster than any existing algorithm. The lower bound of the parameter, gamma, in the H infinity Riccati equation for solution existence is shown to be the square root of the supremum over all frequencies of the maximum eigenvalue of a given transfer matrix which can be computed easily. The lower band of gamma such that the H infinity Riccati equation has positive semidefinite solution can be also obtained by hyperbolic interpolation search. Another significant result in this research period is the elimination of the numerical difficulties arising in the construction of an optimal H infinity controller by directly applying the Glover and Doyle's state-space formulas. With the fast iterative algorithm for the computation of the optimal H infinity norm and the reliable construction of an optimal H infinity controller, we are ready to apply these tools in the design of robust controllers for the systems with unmodelled uncertainties. These tools will be also very useful when we consider systems with structured uncertainties.

Chang, Bor-Chin↗
NASA NTRS1995

Design tool for multiprocessor scheduling and evaluation of iterative dataflow algorithms

A graph-theoretic design process and software tool is defined for selecting a multiprocessing scheduling solution for a class of computational problems. The problems of interest are those that can be described with a dataflow graph and are intended to be executed repetitively on a set of identical processors. Typical applications include signal processing and control law problems. Graph-search algorithms and analysis techniques are introduced and shown to effectively determine performance bounds, scheduling constraints, and resource requirements. The software tool applies the design process to a given problem and includes performance optimization through the inclusion of additional precedence constraints among the schedulable tasks.

Jones, Robert L., III↗
NASA NTRS1993

A multi-level solution algorithm for steady-state Markov chains

A new iterative algorithm, the multi-level algorithm, for the numerical solution of steady state Markov chains is presented. The method utilizes a set of recursively coarsened representations of the original system to achieve accelerated convergence. It is motivated by multigrid methods, which are widely used for fast solution of partial differential equations. Initial results of numerical experiments are reported, showing significant reductions in computation time, often an order of magnitude or more, relative to the Gauss-Seidel and optimal SOR algorithms for a variety of test problems. The multi-level method is compared and contrasted with the iterative aggregation-disaggregation algorithm of Takahashi.

Horton, Graham↗
NASA NTRS2009

Highly Scalable Matching Pursuit Signal Decomposition Algorithm

Matching Pursuit Decomposition (MPD) is a powerful iterative algorithm for signal decomposition and feature extraction. MPD decomposes any signal into linear combinations of its dictionary elements or atoms . A best fit atom from an arbitrarily defined dictionary is determined through cross-correlation. The selected atom is subtracted from the signal and this procedure is repeated on the residual in the subsequent iterations until a stopping criterion is met. The reconstructed signal reveals the waveform structure of the original signal. However, a sufficiently large dictionary is required for an accurate reconstruction; this in return increases the computational burden of the algorithm, thus limiting its applicability and level of adoption. The purpose of this research is to improve the scalability and performance of the classical MPD algorithm. Correlation thresholds were defined to prune insignificant atoms from the dictionary. The Coarse-Fine Grids and Multiple Atom Extraction techniques were proposed to decrease the computational burden of the algorithm. The Coarse-Fine Grids method enabled the approximation and refinement of the parameters for the best fit atom. The ability to extract multiple atoms within a single iteration enhanced the effectiveness and efficiency of each iteration. These improvements were implemented to produce an improved Matching Pursuit Decomposition algorithm entitled MPD++. Disparate signal decomposition applications may require a particular emphasis of accuracy or computational efficiency. The prominence of the key signal features required for the proper signal classification dictates the level of accuracy necessary in the decomposition. The MPD++ algorithm may be easily adapted to accommodate the imposed requirements. Certain feature extraction applications may require rapid signal decomposition. The full potential of MPD++ may be utilized to produce incredible performance gains while extracting only slightly less energy than the standard algorithm. When the utmost accuracy must be achieved, the modified algorithm extracts atoms more conservatively but still exhibits computational gains over classical MPD. The MPD++ algorithm was demonstrated using an over-complete dictionary on real life data. Computational times were reduced by factors of 1.9 and 44 for the emphases of accuracy and performance, respectively. The modified algorithm extracted similar amounts of energy compared to classical MPD. The degree of the improvement in computational time depends on the complexity of the data, the initialization parameters, and the breadth of the dictionary. The results of the research confirm that the three modifications successfully improved the scalability and computational efficiency of the MPD algorithm. Correlation Thresholding decreased the time complexity by reducing the dictionary size. Multiple Atom Extraction also reduced the time complexity by decreasing the number of iterations required for a stopping criterion to be reached. The Course-Fine Grids technique enabled complicated atoms with numerous variable parameters to be effectively represented in the dictionary. Due to the nature of the three proposed modifications, they are capable of being stacked and have cumulative effects on the reduction of the time complexity.

Christensen, Daniel↗