On Linear Product Codes and Their Duals Scientific Report No. 4
Tensor products of linear codes, and product codes with dual cyclic component codes
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Tensor products of linear codes, and product codes with dual cyclic component codes
Concept of energy compression ratio and its application to run length coding
A method for obtaining the complete path enumerator T(D, L, I) of a convolutional code is described. A system of algebraic equations is solved, using a new algorithm for computing determinants, to obtain T(D, L, I) for the (7,1/2) NASA standard code. Generating functions, derived from T(D, L, I) are used to upper bound Viterbi decoder error rates. This technique is currently feasible for constraint length K less than 10 codes. A practical, fast algorithm is presented for computing the leading nonzero coefficients of the generating functions used to bound the performance of constraint length K less than 20 codes. Code profiles with about 50 nonzero coefficients are obtained with this algorithm for the experimental K = 15, rate 1/4, code in the Galileo mission and for the proposed K = 15, rate 1/6, 2-dB code.
This paper investigates the performance of a coded quaternary Gaussian minimum shift keying (GMSK) signal with the Low Density Parity Check (LDPC) code.
The nonlinear physics of cross-beam energy transfer (CBET) for multi-speckled laser beams is examined using large-scale particle-in-cell simulations for a range of laser and plasma conditions relevant to indirect-drive inertial confinement fusion (ICF) experiments. The time-dependent growth and saturation of CBET involve complex, nonlinear ion and electron dynamics, including ion trapping-induced enhancement and detuning, ion acoustic wave (IAW) nonlinearity, oblique forward stimulated Raman scattering (FSRS), and backward stimulated Brillouin scattering (BSBS) in a CBET-amplified seed beam. Ion-trapping-induced detuning of CBET is captured in the kinetic linear response by a new δf-Gaussian-mixture algorithm, enabling an accurate characterization of trapping-induced non-Maxwellian distributions. Ion trapping induces nonlinear processes, such as changes to the IAW dispersion and nonlinearities (e.g., bowing and self-focusing), which, together with pump depletion, FSRS, and BSBS, determine the time-dependent nature and level of CBET gain as the system approaches a steady state. Using VPIC simulations at intensities at and above the onset threshold for ion trapping and the insight from the time-dependent saturation analyses, we construct a nonlinear CBET model from local laser and plasma conditions that predicts the CBET gain and the energy deposition into the plasma. This model is intended to provide a more accurate, physics-based description of CBET saturation over a wide range of conditions encountered in ICF hohlraums compared with linear CBET gain models with ad hoc saturation clamps often used in laser ray-based methods in multi-physics codes.
Construction of three types of pseudonoise /PN/ SEQUENCES /two-level autocorrelation sequences/ which give rise to simplex codes
COHORT 2 Monte Carlo general purpose shielding computer code
Blizard decoding algorithm for binary linear error correcting codes
Using stiffness matrix and lumped-mass representation specified number of natural frequencies are obtained using inverse iteration method. Mode shapes for each frequency are also obtained. These frequencies and mode shapes can be found in reasonable periods of computer time utilizing this code.
A recursive procedure is derived for decoding of rate R=1/n binary convolutional codes which minimizes the probability of the individual decoding decisions for each information bit subject to the constraint that the decoding delay be limited to Delta branches. This new decoding algorithm is similar to, but somewhat more complex than, the Viterbi decoding algorithm. A real-time, i.e. fixed decoding delay, version of the Viterbi algorithm is also developed and used for comparison to the new algorithm on simulated channels. It is shown that the new algorithm offers advantages over Viterbi decoding in soft-decision applications such as in the inner coding system for concatenated coding.
A recursive procedure is derived for decoding of rate R = 1/n binary convolutional codes which minimizes the probability of the individual decoding decisions for each information bit, subject to the constraint that the decoding delay be limited to Delta branches. This new decoding algorithm is similar to, but somewhat more complex than, the Viterbi decoding algorithm. A real-time, i.e., fixed decoding delay, version of the Viterbi algorithm is also developed and used for comparison to the new algorithm on simulated channels. It is shown that the new algorithm offers advantages over Viterbi decoding in soft-decision applications, such as in the inner coding system for concatenated coding.
System can transmit range-indicating pseudonoise (PN) codes and simultaneously transmit auxiliary information as binary data at a rate at least on order of pseudonoise chipping rate. PN code is modulated by data stream with relatively low bit rate. Data stream with high bit rate can be transmitted in same frequency band as PN ranging code.
A general technique, called decoding with multipliers, is presented that can be used to decode any linear code. The technique is applied to the (48,24) quadratic residue code and yields the first known practical decoding algorithm for this powerful code.
It is shown that Reed-Solomon (RS) codes can be decoded by using a fast Fourier transform algorithm over finite fields GF(F sub n) where F sub n is a Fermat prime, and continued fractions. This new transform decoding method is simpler than the standard method for RS codes. The computing time of this new decoding algorithm in software can be faster than the standard decoding method for RS codes.
The performance of certain block codes on a Gaussian channel is evaluated. The BCH codes are markedly superior to convolutional codes currently used for deep space missions. The algorithm is used to derive results, which provides a basis for a simple, almost optimum procedure for decoding these codes.
Experimental measurements of the velocity components in the blade to blade (axial tangential) plane were obtained with an axial flow turbine stator passage and were compared with calculations from three turbomachinery computer programs. The theoretical results were calculated from a quasi three dimensional inviscid code, a three dimensional inviscid code, and a three dimensional viscous code. Parameter estimation techniques and a particle dynamics calculation were used to assess the accuracy of the laser measurements, which allow a rational basis for comparison of the experimenal and theoretical results. The general agreement of the experimental data with the results from the two inviscid computer codes indicates the usefulness of these calculation procedures for turbomachinery blading. The comparison with the viscous code, while generally reasonable, was not as good as for the inviscid codes.
The theory of Reed-Solomon code shortening in general was developed and the degradation due to shortening in the context of concatenated coding was qualified. It is shown that in the NASA/ESA concatenated system, significant degradations occur only when N 180. A Reed-Solomon code was concatenated with an inner (7, 1/2) convolutional code. Under some circumstances, it would be desirable to use a shorter outer code word length. For example, the format of the data coming from science instruments on board a spacecraft may lend itself naturally to a word length of 200 symbols rather than 223. To accommodate such code word lengths, the Reed-Solomon code can be shortened to an (N, N-32) code where N can be any integer between 33 and 255. Shortening the code, however, changes its performance. On one hand, the amount of redundancy per information symbol increases. Because of this increased redundancy, the amount of energy per information symbol is decreased by code shortening. The overall effect is to degrade the performance of the code.
The Weight Analysis of Turbine Engines (WATE) computer code was developed by Boeing under contract to NASA Lewis. It was designed to function as an adjunct to the Navy/NASA Engine Program (NNEP). NNEP calculates the design and off-design thrust and sfc performance of User defined engine cycles. The thermodynamic parameters throughout the engine as generated by NNEP are then combined with input parameters defining the component characteristics in WATE to calculate the bare engine weight of this User defined engine. Preprocessor programs for NNEP were previously developed to simplify the task of creating input datasets. This report describes a similar preprocessor for the WATE code.